Academic Commons Search Results
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Academic Commons Search Resultsen-usArtificial Graphene in Nano-patterned GaAs Quantum Wells and Graphene Growth by Molecular Beam Epitaxy
http://academiccommons.columbia.edu/catalog/ac:202371
Wang, Shenghttp://dx.doi.org/10.7916/D8DF6RGWWed, 21 Sep 2016 12:09:53 +0000In this dissertation I present advances in the studies of artificial lattices with honeycomb topology, called artificial graphene (AG), in nano-patterned GaAs quantum wells (QWs). AG lattices with very small lattice constants as low as 40 nm are achieved for the first time in GaAs. The high quality AG lattices are created by optimized electron-beam (E-beam) lithography followed by inductively coupled plasma reactive-ion etching (ICP-RIE) process. E-beam lithography is used to define a honeycomb lattice etch mask on the surface of the GaAs QW sample and the optimized anisotropic ICP-RIE process is developed to transfer the pattern into the sample and create the AG lattices. Such high-resolution AG lattices with small lattice constants are essential to form AG miniband structures and create well-developed Dirac cones.
Characterization of electron states in the nanofabricated artificial lattices is by optical experiments. Optical emission (photoluminescence) yields a determination of the Fermi energy of the electrons. A significant reduction of the Fermi energy is due to the nano-patterning process. Resonant inelastic light scattering (RILS) spectra reveal novel transitions related to the electron band structures of the AG lattices. These transitions exhibit a remarkable agreement with the predicted joint density of states (JDOS) based on the band structure calculation for the honeycomb topology.
I calculate the electron band structures of AG lattices in nano-patterned GaAs QWs using a periodic muffin-tin potential model. The evaluations predict linear energy-momentum dispersion and Dirac cones, where the massless Dirac fermions (MDFs) appear, occur in the band structures. Requirements of the parameters of the AG potential to achieve isolated and well-developed Dirac cones are discussed. Density of states (DOS) and JDOS from AG band structures are calculated, which provide a basis to interpret quantitatively observed transitions of electrons involving AG bands.
RILS of intersubband transitions reveal intriguing satellite peaks that are not present in the as-grown QWs. These additional peaks are interpreted as combined intersubband transitions with simultaneous change of QW subband and AG band index. The calculated JDOS for the electron transitions within the AG lattice model provide a remarkably accurate description of the combined intersubband excitations.
Novel low-lying excitation peaks in RILS spectra, interpreted as direct transitions between AG bands without change in QW subband, provide a more direct insight on the AG band structures. We discovered that RILS transitions around the Dirac cones are resonantly enhanced by varying the incident photon energies. The spectral lineshape of these transitions provides insights into the formation of Dirac cones that are characteristic of the honeycomb symmetry of the AG lattices. The results confirm the formation of AG miniband structures and well-developed Dirac cones. The realization of AG lattices in a nanofabricated high mobility semiconductor offers the advantage of tunability through methods suitable for device scalability and integration.
The last part of this thesis describes the growth of nanocrystalline single layer and bilayer graphene on sapphire substrates by molecular beam epitaxy (MBE) with a solid carbon source. Raman spectroscopy reveals that fabrication of single layer, bilayer or multilayer graphene crucially depends on MBE growth conditions. Etch pits revealed by atomic force microscopy indicate a removal mechanism of carbon by reduction of sapphire. Tuning the interplay between carbon deposition and its removal, by varying the incident carbon flux and substrate temperature, should enable the growth of high quality graphene layers on large area sapphire substrates.Physics, Condensed matter physics, Opticssw2677Applied Physics and Applied MathematicsDissertationsImproved magnetic feedback system on the fast rotating kink mode
http://academiccommons.columbia.edu/catalog/ac:202134
Peng, Qianhttp://dx.doi.org/10.7916/D8VD6ZPRThu, 08 Sep 2016 12:06:22 +0000This thesis presents an improved feedback system on HBT-EP and suppression of the fast rotating kink mode using this system. HBT-EP is an experimental tokamak at Columbia University designed to study the magnetohydrodynamic (MHD) instabilities in confined fusion. The most damaging instabilities are global long wavelength kink modes, which break the toroidal symmetry of the magnetic structure and lead to plasma disruption and termination. When a tokamak is surrounded by a close fitting conducting wall, then the single helicity linear dispersion relation of the kink instability has two ominating branches: one is the "slow mode", rotating at the time scale of wall time, known as resistive wall mode (RWM), the other is the fast mode, that becomes unstable near the ideal wall stability limit. Both instabilities are required to be controlled by the feedback system in HBT-EP. In this thesis, improvements have been made upon the previous GPU-based system to enhance the feedback performance and obtain clear evidence of the feedback suppression effect. Specifically, a new algorithm is implemented that maintains an accurate phase shift between the applied perturbation and the unstable mode. This prevents the excitation of the slow kink mode observed in previous studies and results in high gain suppression for fast mode control at all frequency for the first time. When the system is turned off, suppression is lost and the fast mode is observed to grow back. The feedback performance is tested with several wall configurations including the presence of ferritic material. This provides the first comparison of feedback control between the ferritic and stainless wall. The effect of plasma rotation on feedback control is tested by applying a static voltage on a bias probe. As the mode rotation being slowed by the radial current flow, a higher gain on the kink mode is required to achieve feedback suppression. The change in plasma rotation also modifies the plasma response to the external perturbation. The optimal phase shift for suppression changes with the modified response and these observations are consistent with the predictions of the single helicity model.Plasma physics, Engineeringqp2105Applied Physics and Applied MathematicsDissertationsEnlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations
http://academiccommons.columbia.edu/catalog/ac:201869
Dandapani, Aditihttp://dx.doi.org/10.7916/D8XW4JZ2Tue, 02 Aug 2016 12:25:23 +0000In this thesis, we study the strict local martingale property of solutions of various types of stochastic differential equations and the effect of an initial expansion of the filtration on this property. For the models we consider, we either use existing criteria or, in the case where the stochastic differential equation has jumps, develop new criteria that can can detect the presence of the strict local martingale property. We develop deterministic sufficient conditions on the drift and diffusion coefficient of the stochastic process such that an enlargement by initial expansion of the filtration can produce a strict local martingale from a true martingale. We also develop a way of characterizing the martingale property in stochastic volatility models where the local martingale has a general diffusion coefficient.Mathematics, Applied mathematicsad2259Applied Physics and Applied Mathematics, StatisticsDissertationsHybridization of Van Der Waals Materials and Close-Packed Nanoparticle Monolayers
http://academiccommons.columbia.edu/catalog/ac:200622
Zhang, Datonghttp://dx.doi.org/10.7916/D8Q52PR5Tue, 05 Jul 2016 18:28:39 +0000Van der Waals materials and inorganic nanoparticles are two categories of nanomaterials that have been widely investigated in the past two decades. Both of them have been considered to be promising as candidates for the next generation electrical, optical, and mechanical applications. However, both of them have a few limitations that greatly affect the performance of devices, e.g. zero bandgap for graphene; poor contact quality, low mobility and quantum efficiency for MoS2; and poor interparticle conductivity for nanoparticles. This thesis tries to explore a new way of combining these two categories of material into hybrids, so that the intrinsic limitations of materials from each category will be overcome by the other materials that are introduced into the hybrid.
This thesis consists of five parts. The first part (Chapter 1) introduces the background and motivation of the thesis. The second part (Chapters 2, 3, 4, and 5) describes the detailed processes and methods, starting from preparing each element to the assembly of these element into a hybrid structure device. This part also includes understanding the mechanisms of 2D and 3D self-assembly of nanoparticles. The third part (Chapter 6 and 7) describes two examples of hybrid structures, including the investigation of electron or molecule transfer inside the hybrid. The fourth part (Chapter 8) introduces other findings and technical innovations, including alternative ways of thin film nanoparticle self-assembly/deposition, and fabrication methods for the band structure analysis of transition metal dichalcogenides by angle resolved photo-electron spectroscopy. The fifth part (Chapter 9) describes several possible future work directions that could be investigated to improve the understanding of the nanoparticle assembly and translating the conceptual device into real applications.Nanotechnology, Neurosciencesdz2218Applied Physics, Applied Physics and Applied MathematicsDissertationsCrystallite Size Dependency of the Pressure and Temperature Response in Nanoparticles of Ceria and Other Oxides
http://academiccommons.columbia.edu/catalog/ac:200433
Rodenbough, Philip Porterhttp://dx.doi.org/10.7916/D8QN66WHMon, 27 Jun 2016 12:38:50 +0000The short title of this dissertation is Size Matters. And it really does. Before diving into the original findings of this dissertation, this abstract starts by contextualizing their significance. To that end, recall that some of the earliest concepts learned by sophomore organic chemistry students include explaining physical properties based on carbon chain length, for example, and polymer length has enormous influence on macroscopic material properties. In the 1980s it was found that the electronic properties of small inorganic semiconductor crystallites can be rigorously tied to the physical size of the crystallites, and this understanding has led directly to the successful integration of so-called quantum dots into readily available technologies today, including flat screen televisions, as well as emerging technologies, such as quantum dot solar cells. Oxides, for their part, are important components of many technologies, from paints and cosmetics to microelectronics and catalytic converters. The crystallite size dependency of fundamental mechanical properties of oxides is the topic of this dissertation.
First, this dissertation reports that consistent preparation methods were used to produce batches of specific crystallite sizes for a diverse family of five cubic oxides: CeO2 (ceria), MgO (magnesia), Cu2O (cuprite), Fe3O4 (magnetite), and Co3O4. The size-based lattice changes for small crystallites was carefully measured with X-ray diffraction. Expanded lattice parameters were found in small crystallites of all five oxides (notably for the first time in Fe3O4). This behavior is rationalized with an atomic model reliant on differing coordination levels of atoms at the surface, and fundamental calculations of physical properties including surface stress and expansion energy are derived from the measured lattice expansion for these oxides.
Then, the size dependency of the pressure response in ceria nanoparticles was measured using diamond anvil cells and synchrotron radiation. In a study unmatched in its comprehensiveness, it was found that the bulk modulus of ceria peaked at an intermediate crystallite size of 33 nm. This is rationalized with a core-shell model with a size dependent shell compressibility whose influence naturally grows as crystallite size shrinks. Complimentary thermal expansion measurements were carried out to probe the structural response of crystallites to heat. Overall, the thermal expansion of ceria decreased with crystallite size. Through careful heating cycles, it was possible to separate out quantitatively the two primary factors contributing to negative surface stress in ceria: ambient surface adsorbents and surface non-stoichiometry. These may be the first instances of such a calculation that provides this insight into the surface stress of oxide nanoparticles.
Next, pressure and temperature studies parallel to those in ceria were carried out on magnesia as well. Magnesia is an important oxide to compare to ceria because it does not share ceria's tendency to form oxygen vacancy defects with cation charge variances. Nonetheless, magneisa was shown to possess a peak (albeit a less dramatic peak) in bulk modulus at an intermediate crystallite size, about 14 nm. Magnesia, like ceria, also had decreased thermal expansion at smaller crystallite sizes.
Finally, experiments on molecular oxygen exchange properties of a series of oxides were carried out using a thermocycling reactor system designed and built in-house, with the aim of developing materials to convert carbon dioxide to carbon monoxide. Experiments were carried out under 1200C, much lower than the 1500C typically required for ceria oxygen exchange. It is thought that crystallite morphology could play an important role in dictating the effectiveness of this catalytic process. The increased understanding of fundamental physical properties of oxide nanoparticles, as explored here, may lead to their more rational integration into such emerging technologies.Chemistry, Materials scienceppr2113Chemistry, Applied Physics and Applied MathematicsDissertationsMHD Effects of a Ferritic Wall on Tokamak Plasmas
http://academiccommons.columbia.edu/catalog/ac:199733
Hughes, Paul Ernesthttp://dx.doi.org/10.7916/D87D2V64Fri, 03 Jun 2016 12:32:44 +0000It has been recognized for some time that the very high fluence of fast (14.1MeV) neutrons produced by deuterium-tritium fusion will represent a major materials challenge for the development of next-generation fusion energy projects such as a fusion component test facility and demonstration fusion power reactor. The best-understood and most promising solutions presently available are a family of low-activation steels originally developed for use in fission reactors, but the ferromagnetic properties of these steels represent a danger to plasma confinement through enhancement of magnetohydrodynamic instabilities and increased susceptibility to error fields.
At present, experimental research into the effects of ferromagnetic materials on MHD stability in toroidal geometry has been confined to demonstrating that it is still possible to operate an advanced tokamak in the presence of ferromagnetic components. In order to better quantify the effects of ferromagnetic materials on tokamak plasma stability, a new ferritic wall has been installated in the High Beta Tokamak—Extended Pulse (HBT-EP) device. The development, assembly, installation, and testing of this wall as a modular upgrade is described, and the effect of the wall on machine performance is characterized. Comparative studies of plasma dynamics with the ferritic wall close-fitting against similar plasmas with the ferritic wall retracted demonstrate substantial effects on plasma stability. Resonant magnetic perturbations (RMPs) are applied, demonstrating a 50% increase in n = 1 plasma response amplitude when the ferritic wall is near the plasma. Susceptibility of plasmas to disruption events increases by a factor of 2 or more with the ferritic wall inserted, as disruptions are observed earlier with greater frequency. Growth rates of external kink instabilities are observed to be twice as large in the presence of a close-fitting ferritic wall. Initial studies are made of the influence of mode rotation frequency on the ferritic effect, as well as observations of the effect of the ferritic wall on disruption halo currents.Plasma physicspeh2109Applied Physics, Applied Physics and Applied MathematicsDissertationsMelting in Superheated Silicon Films Under Pulsed-Laser Irradiation
http://academiccommons.columbia.edu/catalog/ac:197822
Wang, Jin Jimmyhttp://dx.doi.org/10.7916/D8NV9J7QThu, 21 Apr 2016 12:34:54 +0000This thesis examines melting in superheated silicon ﬁlms in contact with SiO₂ under pulsed laser irradiation. An excimer-laser pulse was employed to induce heating of the ﬁlm by irradiating the ﬁlm through the transparent fused-quartz substrate such that most of the beam energy was deposited near the bottom Si-SiO₂ interface. Melting dynamics were probed via in situ transient reﬂectance measurements. The temperature proﬁle was estimated computationally by incorporating temperature- and phase-dependent physical parameters and the time-dependent intensity proﬁle of the incident excimer-laser beam obtained from the experiments.
The results indicate that a signiﬁcant degree of superheating occurred in the subsurface region of the ﬁlm. Surface-initiated melting was observed in spite of the internal heating scheme, which resulted in the ﬁlm being substantially hotter at and near the bottom Si-SiO₂ interface. By considering that the surface melts at the equilibrium melting point, the solid-phase-only heat-ﬂow analysis estimates that the bottom Si-SiO₂ interface can be superheated by at least 220K during excimer-laser irradiation.
It was found that at higher laser ﬂuences (i.e., at higher temperatures), melting can be triggered internally. At heating rates of 10¹⁰ K/s, melting was observed to initiate at or near the (100)-oriented Si-SiO₂ interface at temperatures estimated to be over 300K above the equilibrium melting point. Based on theoretical considerations, it was deduced that melting in the superheated solid initiated via a nucleation and growth process. Nucleation rates were estimated from the experimental data using Johnson-Mehl-Avrami-Kolmogorov (JMAK) analysis. Interpretation of the results using classical nucleation theory suggests that nucleation of the liquid phase occurred via the heterogeneous mechanism along the Si-SiO₂ interface.Materials science, Physical chemistryjjw2154Materials Science and Engineering, Applied Physics and Applied MathematicsDissertationsBifurcation perspective on topologically protected and non-protected states in continuous systems
http://academiccommons.columbia.edu/catalog/ac:197647
Lee-Thorp, James Patrickhttp://dx.doi.org/10.7916/D8J38SJRThu, 14 Apr 2016 12:21:18 +0000We study Schrödinger operators perturbed by non-compact (spatially extended) defects. We consider two models: a one-dimensional (1D) dimer structure with a global phase shift, and a two-dimensional (2D) honeycomb structure with a line-defect or "edge''. In both the 1D and 2D settings, the non-compact defects are modeled by adiabatic, domain wall modulations of the respective dimer and honeycomb structures. Our main results relate to the rigorous construction of states via bifurcations from continuous spectra. These bifurcations are controlled by asymptotic effective (homogenized) equations that underlie the protected or non-protected character of the states.
In 1D, the states we construct are localized solutions. In 2D, they are "edge states'' - time-harmonic solutions which are propagating (plane-wave-like) parallel to a line-defect or "edge'' and are localized transverse to it. The states are described as protected if they persist in the presence of spatially localized (even strong) deformations of the global phase defect (in 1D) or edge (in 2D). The protected states bifurcate from "Dirac points'' (linear/conical spectral band-crossings) in the continuous spectra and are seeded by an effective Dirac equation. The (more conventional) non-protected states bifurcate from spectral band edges are seeded by an effective Schrödinger equation.
Our 2D model captures many aspects of the phenomenon of topologically protected edge states observed in honeycomb structures such as graphene and "artificial graphene''. The protected states we construct in our 1D dimer model can be realized as highly robust TM- electromagnetic modes for a class of photonic waveguides with a phase-defect. We present a detailed computational study of an experimentally realizable photonic waveguide array structure.Applied mathematics, Mathematics, Physicsjpl2154Applied Physics and Applied MathematicsDissertationsInvestigation of Melting and Solidification of Thin Polycrystalline Silicon Films via Mixed-Phase Solidification
http://academiccommons.columbia.edu/catalog/ac:196419
Wang, Yinghttp://dx.doi.org/10.7916/D8W95935Wed, 16 Mar 2016 18:35:09 +0000Melting and solidification constitute the fundamental pathways through which a thin-film material is processed in many beam-induced crystallization methods. In this thesis, we investigate and leverage a specific beam-induced, melt-mediated crystallization approach, referred to as Mixed-Phase Solidification (MPS), to examine and scrutinize how a polycrystalline Si film undergoes the process of melting and solidification. On the one hand, we develop a more general understanding as to how such transformations can transpire in polycrystalline films. On the other hand, by investigating how the microstructure evolution is affected by the thermodynamic properties of the system, we experimentally reveal, by examining the solidified microstructure, fundamental information about such properties (i.e., the anisotropy in interfacial free energy).
Specifically, the thesis consists of two primary parts: (1) conducting a thorough and extensive investigation of the MPS process itself, which includes a detailed characterization and analysis of the microstructure evolution of the film as it undergoes MPS cycles, along with additional development and refinement of a previously proposed thermodynamic model to describe the MPS melting-and-solidification process; and (2) performing MPS-based experiments that were systematically designed to reveal more information on the anisotropic nature of Si-SiO₂ interfacial energy (i.e., σ_{Si-SiO₂}).
MPS is a recently developed radiative-beam-based crystallization technique capable of generating Si films with a combination of several sought-after microstructural characteristics. It was conceived, developed, and characterized within our laser crystallization laboratory at Columbia University. A preliminary thermodynamic model was also previously proposed to describe the overall melting and solidification behavior of a polycrystalline Si film during an MPS cycle, wherein the grain-orientation-dependent solid-liquid interface velocity is identified as being the key parameter responsible for inducing the observed microstructure evolution.
The present thesis builds on the abovementioned body of work on MPS. To this end, we note that the limited scope of previous investigations motivates us to perform more thorough characterization and analysis of the experimental results. Also, we endeavor to provide more involved explanations and expressions to account for the observed microstructure evolution in terms of the proposed thermodynamic model. To accomplish these tasks forms the motivation for the first portion of this thesis. In this section we further develop the thermodynamic model by refining the expression for the solid-liquid interface velocities. In addition, we develop an expression for the grain-boundary-location-displacement distance in an MPS cycle. This is a key fundamental quantity that effectively captures the essence of the microstructure evolution resulting from MPS processing. Experimentally, we conduct a thorough investigation of the MPS process by focusing on examining the details of the microstructure evolution of {100}-surface-oriented grains. Firstly, we examine and analyze the gradual evolution in the microstructure of polycrystalline Si films being exposed to multiple MPS cycles. A Johnson-Mehl-Avrami-Kolmogorov-type (JMAK-type) analysis is proposed and developed to describe the microstructure transformation. Secondly, we investigate the behavior of grains with surface orientations close to the <100> pole. Orientation-dependent (in terms of their extent of deviation from the <100> pole) microstructure evolution is revealed. This observation indicates that the microstructure of the film continues to evolve to form an even tighter distribution of grains around the <100> pole as the MPS process proceeds.
During MPS melting-and-solidification cycles, a unique near-equilibrium environment is created and stabilized by radiative beam heating. Therefore, the microstructure of the resulting films is expected to be explicitly and dominantly affected by various thermodynamic properties of the system. Specifically, we identify the orientation-dependent value of the Si-SiO₂ interfacial energy as a key factor. This being the case, the MPS method actually provides us with an ideal platform to experimentally study the Si-SiO₂ interfacial energy. In the second part of this thesis, we perform MPS-based experiments to systematically investigate the orientation-dependent Si-SiO₂ interfacial energy. Two complementary approaches are designed and conducted, both of which are built on examining the texture evolution of different surface orientations resulting from MPS melting-and-solidification cycles. The first approach, “Large-Area Statistical Analysis”, statistically examines the overall microstructure evolution of non-{100}-surface-oriented grains. By interpreting the changes in the surface-orientation distribution of the grains in terms of the thermodynamic model, we identify the orientation-dependent hierarchical order of Si-SiO₂ interfacial energies. The second approach, “Same-Area Local Analysis”, keeps track of the same set of grains that undergo several MPS cycles. An equivalent set of information on the Si-SiO₂ interfacial energy is extracted. Both methods reveal, in a consistent manner, an essentially identical Si-SiO₂ interfacial energy hierarchical order for a selected group of orientations. Also, the “Same-Area Local Analysis” provides some additional information that cannot otherwise be obtained (such as information about the evolution of two adjacent grains of specific orientations). Using such information and based on the grain-boundary-location-displacement distance derived using the thermodynamic model, we further deduce and evaluate the magnitude of Δσ_{Si-SiO₂} for certain orientation pairs.Materials scienceyw2434Materials Science and Engineering, Applied Physics and Applied MathematicsDissertationsOptimization methods for power grid reliability
http://academiccommons.columbia.edu/catalog/ac:194133
Harnett, Sean R.http://dx.doi.org/10.7916/D8MS3SM8Thu, 04 Feb 2016 18:18:39 +0000This dissertation focuses on two specific problems related to the reliability of the modern power grid. The first part investigates the economic dispatch problem with uncertain power sources. The classic economic dispatch problem seeks generator power output levels that meet demand most efficiently; we add risk-awareness to this by explicitly modeling the uncertainty of intermittent power sources using chance-constrained optimization and incorporating the chance constraints into the standard optimal power flow framework. The result is a dispatch of power which is substantially more robust to random fluctuations with only a small increase in economic cost. Furthermore, it uses an algorithm which is only moderately slower than the conventional practice.
The second part investigates “the power grid attack problem”: aiming to maximize disruption to the grid, how should an attacker distribute a budget of “damage” across the power lines? We formulate it as a continuous problem, which bypasses the combinatorial explosion of a discrete formulation and allows for interesting attacks containing lines that are only partially damaged rather than completely removed. The result of our solution to the attack problem can provide helpful information to grid planners seeking to improve the resilience of the power grid to outages and disturbances. Both parts of this dissertation include extensive experimental results on a number of cases, including many realistic large-scale instances.Applied mathematics, Operations researchsrh2144Applied Physics and Applied MathematicsDissertationsStudy of kink modes and error fields through rotation control with a biased electrode
http://academiccommons.columbia.edu/catalog/ac:192548
Stoafer, Christopher Charleshttp://dx.doi.org/10.7916/D8X92B0DFri, 18 Dec 2015 15:19:33 +0000Experimental studies of MHD modes, including dynamics and stability, using a biased electrode for rotation control on the High Beta Tokamak –- Extended Pulse (HBT-EP) are presented. When the probe is inserted into the edge of the plasma and a voltage applied, the rotation of long-wavelength kink instabilities is strongly modified. A large poloidal plasma flow results at the edge, measured with a bi-directional Mach probe with changes in edge kink mode rotation at different biases. This poloidal plasma rotation cannot fully account for the large mode rotation frequency on HBT-EP. By including the electron fluid motion, the mode rotation predictions agree with measurements, indicating that the modes travel with the electron fluid. A GPU-based digital feedback system is used to adjust the probe voltage in real time for controlling both the plasma flow and mode rotation. This active mode rotation control is desirable because it allows for MHD stabilization, as well as studies under conditions of varying mode rotation rates. Mode dynamics were studied using various diagnostics to understand how plasma conditions fluctuate during mode activity and to understand the interaction of the bias probe with the plasma during this activity. Phase-dependent mode behavior was observed, especially at slow mode rotation, which might be attributed to an intrinsic error field or a nonlinear interaction between the bias probe and the mode. Applied resonant magnetic perturbations were used to study the dynamic response of a stable plasma with different mode rotations. At slower rotation, the plasma had a greater response to the perturbations and the plasma reached a saturated response with large perturbations, similar to previous results. At large positive biases, the probe current induces a torque that opposes the natural direction of mode rotation. By applying a sufficiently large torque, a transition is induced into a fast rotation state (both mode and plasma rotation). High poloidal shear flows at the edge were measured in this state, similar to conditions in H-mode plasmas on other devices. The bias required to induce the transition is shown to depend on an applied error field. A technique was established using this transition to determine the natural error field on HBT-EP.Plasma physics, Physicsccs2142Applied Physics and Applied MathematicsDissertationsNovel torques on magnetization measured through ferromagnetic resonance
http://academiccommons.columbia.edu/catalog/ac:189664
Li, Yihttp://dx.doi.org/10.7916/D8FN15NKWed, 30 Sep 2015 18:07:01 +0000New torques acting on magnetization in metallic ferromagnets, accompanied by new terms to the Landau-Lifshitz-Gilbert (LLG) equation which governs GHz magnetization dynamics, are important for both the fundamental understanding of magnetism and applications in magnetoelectronic devices. In this thesis, we have carried out experimental investigations of several proposed novel torques acting on magnetization dynamics using broadband ferromagnetic resonance (FMR) between 2-26 GHz. The FMR technique is well-suited for materials studies, as it investigates unpatterned (sheet-level) films with relatively high throughput, enabling comparison of the response of several room-temperature, device-relevant ferromagnetic alloys (e.g. Ni₇₉Fe₂₁, or ‘Py’, Co, and CoFeB.)
The common aspect of the torques which we have investigated by FMR is their origin in nonequilibrium spin populations, related to spin transfer torque. In Chapter 3 we have identified intrinsic “inertial” torques on magnetization, significant only at very high frequencies (up to 300 GHz), where the electron population cannot quite keep pace with the precession of magnetization. In Chapters 4 and 5 we have studied torques from “pumped” pure spin current due to the texture of precessing magnetization (intralayer spin pumping) and the precession of noncollinear magnetizations in trilayer structures (spin pumping). These three studies extend understanding of magnetism and magnetization dynamics at room temperature, and in limits of high speed and small dimension relevant for emerging applications.Materials science, Condensed matter physicsyl2600Materials Science and Engineering, Applied Physics and Applied MathematicsDissertationsLocal structure and lattice dynamics study of low dimensional materials using atomic pair distribution function and high energy resolution inelastic x-ray scattering
http://academiccommons.columbia.edu/catalog/ac:189523
Shi, Chenyanghttp://dx.doi.org/10.7916/D8C53K5KTue, 15 Sep 2015 18:15:44 +0000Structure and dynamics lie at the heart of the materials science. A detailed knowledge of both subjects would be foundational in understanding the materials' properties and predicting their potential applications. However, the task becomes increasingly difficult as the particle size is reduced to the nanometer scale. For nanostructured materials their laboratory x-ray scattering patterns are overlapped and broadened, making structure determination impossible. Atomic pair distribution function technique based on either synchrotron x-ray or neutron scattering data is known as the tool of choice for probing local structures. However, to solve the \structure problem" in low-dimensional materials with PDF is still challenging. For example for 2D materials of interest in this thesis the crystallographic modeling approach often yields unphysical thermal factors along stacking direction where new chemical intuitions about their actual structures and new modeling methodology/program are needed. Beyond this, lattice dynamical investigations on nanosized particles are extremely dicult. Laboratory tools such as Raman and infra-red only probe phonons at Brillouin zone center. Although in literature there are a great number of theoretical studies of their vibrational properties based on either empirical force elds or density functional theory, various approximations made in theories make the theoretical predictions less reliable. Also, there lacks the direct experiment result to validate the theory against.
In this thesis, we studied the structure and dynamics of a wide variety of technologically relevant low-dimensional materials through synchrotron based x-ray PDF and high energy resolution inelastic x-ray scattering (HERIX) techniques. By collecting PDF data and employing advanced modeling program such as DiPy-CMI, we successfully determined the atomic structures of (i) emerging Ti3C2, Nb4C3 MXenes (transition metal carbides and/or nitrides) that are promising for energy storage applications, and of (ii) zirconium phenylphosphonate ion exchange materials that are proposed to separate lanthanide ions from actinide ions in nuclear waste. Both material systems have two-dimensional layered nanocrystalline structure where we observed that the stacking of layers are not in good registry, also known as "turbostratic" disorder. Consequently the signals from a single layer of atoms dominate the experimental PDF{thus building up a single slab model and simulating PDF using Debye function analysis was sucient to capture the main structural features in the measured PDF data. The information on correlation length of layers along the stacking direction, however, is contained in low-Q diraction peaks in either laboratory x-ray or synchrotron x-ray scattering patterns.
On the lattice dynamics side, we first investigated the trend of atomic bonding strength in size dependent platinum nanoparticles based on temperature dependent PDF data and measured Debye temperatures. An anomalous bond softening was observed at a particle size less than 2 nm. Since Debye model gives a simple quadratic phonon density of states (PDOS) curve, which is a simplified version of real lattice dynamics, we are motivated to measure full PDOS curves on three CdSe nanoclusters by using non-resonant inelastic x-ray scattering technique. We observed an overall blue-shift of PDOS curves with decreased sizes. Our current exemplary studies will open the door to a large number of future structural and lattice dynamical studies on a much broader range of low-dimensional material systems.Materials science, Condensed matter physics, Physical chemistrycs3000Materials Science and Engineering, Applied Physics and Applied MathematicsDissertationsIdealized cloud-system resolving modeling for tropical convection studies
http://academiccommons.columbia.edu/catalog/ac:189400
Anber, Usama Mostafahttp://dx.doi.org/10.7916/D8H13185Wed, 19 Aug 2015 18:07:52 +0000A three-dimensional limited-domain Cloud-Resolving Model (CRM) is used in idealized settings to study the interaction between tropical convection and the large scale dynamics. The model domain is doubly periodic and the large-scale circulation is parameterized using the Weak Temperature Gradient (WTG) Approximation and Damped Gravity Wave (DGW) methods. The model simulations fall into two main categories: simulations with a prescribed radiative cooling profile, and others in which radiative cooling profile interacts with clouds and water vapor.
For experiments with a prescribed radiative cooling profile, radiative heating is taken constant in the vertical in the troposphere. First, the effect of turbulent surface fluxes and radiative cooling on tropical deep convection is studied. In the precipitating equilibria, an increment in surface fluxes produces a greater increase in precipitation than an equal increment in column-integrated radiative heating. The gross moist stability remains close to constant over a wide range of forcings.
With dry initial conditions, the system exhibits hysteresis, and maintains a dry state with for a wide range of net energy inputs to the atmospheric column under WTG. However, for the same forcings the system admits a rainy state when initialized with moist conditions, and thus multiple equilibria exist under WTG. When the net forcing is increased enough that simulations, which begin dry, eventually develop precipitation. DGW, on the other hand, does not have the tendency to develop multiple equilibria under the same conditions.
The effect of vertical wind shear on tropical deep convection is also studied. The strength and depth of the shear layer are varied as control parameters. Surface fluxes are prescribed. For weak wind shear, time-averaged rainfall decreases with shear and convection remains disorganized. For larger wind shear, rainfall increases with shear, as convection becomes organized into linear mesoscale systems. This non-monotonic dependence of rainfall on shear is observed when the imposed surface fluxes are moderate. For larger surface fluxes, convection in the unsheared basic state is already strongly organized, but increasing wind shear still leads to increasing rainfall. In addition to surface rainfall, the impacts of shear on the parameterized large-scale vertical velocity, convective mass fluxes, cloud fraction, and momentum transport are also discussed.
For experiments with interactive radiative cooling profile, the effect of cloud- radiation interaction on cumulus ensemble is examined in sheared and unsheared environments with both fixed and interactive sea surface temperature (SST). For fixed SST, interactive radiation, when compared to simulations in which radiative profile has the same magnitude and vertical shape but does not interact with clouds or water vapor, is found to suppress mean precipitation by inducing strong descent in the lower troposphere, increasing the gross moist stability.
For interactive SST, using a slab ocean mixed layer, there exists a shear strength above which the system becomes unstable and develops oscillatory behavior. Oscillations have periods of wet precipitating states followed by periods of dry non-precipitating states. The frequencies of oscillations are intraseasonal to subseasonal, depending on the mixed layer depth.
Finally, the model is coupled to a land surface model with fully interactive radiation and surface fluxes to study the diurnal and seasonal radiation and water cycles in the Amazon basin. The model successfully captures the afternoon precipitation and cloud cover peak and the greater latent heat flux in the dry season for the first time; two major biases in GCMs with implications for correct estimates of evaporation and gross primary production in the Amazon. One of the key findings is that the fog layer near the surface in the west season is crucial for determining the surface energy budget and precipitation. This suggests that features on the diurnal time scale can significantly impact climate on the seasonal time scale.Atmospheric sciencesuma2103Earth and Environmental Sciences, Applied Physics and Applied MathematicsDissertationsBifurcation of On-site and Off-site Solitary Waves of Discrete Nonlinear Schrödinger Type Equations
http://academiccommons.columbia.edu/catalog/ac:189391
Jenkinson, Michael Jameshttp://dx.doi.org/10.7916/D8J102F0Wed, 19 Aug 2015 12:13:41 +0000A feature of immeasurable interest in nonlinear systems is that of spatially localized traveling pulses, or solitary waves - states which persist indefinitely in time, focus energy, and facilitate its transfer. Furthermore, in many lattice systems, discreteness effects are important and play a key role in these dynamics.
In this thesis, we construct the multiple families of solitary standing (time-periodic) waves of the discrete, focusing cubically nonlinear Schrödinger equation (DNLS). These states are related to the so-called Peierls-Nabarro energy barrier, which refers to the energy difference between these distinct states and is thought to be responsible for the absence of indefinitely traveling, non-deforming solitary (spatially localized) waves of arbitrary velocity in many (non-dissipative) discrete systems. Instead, one observes that traveling waves of many discrete equations radiate energy and deform until they eventually cease to propagate and settle to a stationary time-periodic standing wave centered at a vertex.
We address two specific cases of DNLS: (1) nearest-neighbor coupling on a cubic lattice in dimensions d = 1,2,3, and (2) long-range site coupling in dimension d = 1. These states are obtained via a bifurcation analysis about the continuum nonlinear Schrödinger equation (NLS) limit, with respect to a natural small parameter. Depending on the spatial dimension, these may be vertex-, bond-, cell-, or face-centered. In the first case of nearest-neighbor coupling, we construct an explicit asymptotic expansion. In the second case of one-dimensional long-range coupling when the decay of the site coupling with respect to distance is sufficiently slow, the continuum limiting NLS equation has Laplacian of fractional power. Finally, we show that the energy difference among distinct states of the same frequency is exponentially small with respect to the small parameter beyond all polynomial orders. This provides a rigorous bound for the Peierls-Nabarro barrier.Applied mathematics, Mathematics, Physicsmjj2122Applied Physics and Applied MathematicsDissertationsStudy of complex structure using mixed data and complex modeling
http://academiccommons.columbia.edu/catalog/ac:189385
Yang, Xiaohaohttp://dx.doi.org/10.7916/D8N015SPThu, 13 Aug 2015 18:04:34 +0000The new complex materials have wide applications in next generation technologies in industrial fields such as electronics, energy production, environment engineering, etc. Understanding their structure is the key in keeping developing new materials and improving their performance. As they are more and more complex in different length scale, new methods that utilize information from different sources and be able to provide complex structural information are on the horizon of this new era.
In this thesis, we developed new methods that process the mixed data and provide the extra information that people are interested in. First one is extending the computed tomography technique with other analysis method including texture analysis and Pair Distribution Function (PDF) method. The new methods enable us to study the coupling of desired structural properties, such as texture and local local structure of nano-particles, at meso-scale. For example, by applying the texture-CT analysis on the LiCoO₂ coin cell, we found the texture of LiCoO₂ particles was quite inhomogeneous. By combining PDF and CT method, we successfully studied the catalyst reaction and the participle size distribution in industrial catalyst. Second one is a new method of obtaining reliable anomalous differential Pair Distribution Function (adPDF) by using diffraction data sets in wide energy range and an ad-hoc algorithm that perform the data correction automatically. The new method was demonstrated using both simulated data and real experimental data.Materials sciencexy2151Materials Science and Engineering, Applied Physics and Applied MathematicsDissertationsAnisotropic inverse problems with internal measurements
http://academiccommons.columbia.edu/catalog/ac:187031
Guo, Chenxihttp://dx.doi.org/10.7916/D88914XRMon, 11 May 2015 15:32:01 +0000This thesis concerns the hybrid inverse problem of reconstructing a tensor-valued conductivity from knowledge of internal measurements. This problem finds applications in the medical imaging modalities Current Density Imaging and Magnetic Resonance Electrical Impedance Tomography.
In the first part of the thesis, we investigate the reconstruction of the anisotropic conductivity in a second-order elliptic partial differential equation, from knowledge of internal current densities. We show that the unknown coefficient can be uniquely and stably reconstructed via explicit inversion formulas with a loss of one derivative compared to errors in the measurement. This improves the resolution of quantitative reconstructions in Calderón's problem(i.e. reconstruction problems from knowledge of boundary measurements). We then extend the problem to the full anisotropic Maxwell system and show that the complex-valued anisotropic admittivity can be uniquely reconstructed from knowledge of several internal magnetic fields. We also proved a unique continuation property and Runge approximation property for an anisotropic Maxwell system.
In the second part, we performed some numerical experiments to demonstrate the computational feasibility of the reconstruction algorithms and assess their robustness to noisy measurements.Applied mathematicscg2597Applied Physics and Applied MathematicsDissertationsSurface Chemistry Studies of Transition Metal Oxides: Titanium Oxide and Iron Oxide
http://academiccommons.columbia.edu/catalog/ac:186539
Li, Zhishenghttp://dx.doi.org/10.7916/D8R2109ZTue, 21 Apr 2015 18:16:14 +0000Surface chemistry studies of two transition-metal oxides: titanium oxide and iron oxide are presented, which are focused on thermal induced chemistry using proximal probe imaging and spectroscopy. In the first, using single crystal of rutile TiO2 (110), arrays of nano-scale locally varying surface strain field were generated by introducing highly pressurized nanoscale argon clusters 4-11 layers below the surface. The characteristics of the argon clusters are explored through STM tip-assisted surface excavation, combining with a continuum mechanical model. This work experimentally demonstrates that surface elastic strain influences the adsorption energy of adsorbates significantly and, thus, can be used for applications of surface nanopatterning. As a comparison with work on nanoscale, two forms of titanium oxide in reduced dimensionalities are experimentally synthesized and investigated for their surface reactivity: 3D nano TiO2 crystals and monolayer TiO films, both of which are supported on single crystal Au(111) surface. This work demonstrates that both nano crystals and ultrathin films of titanium oxide exhibit distinctive surface structural and catalytic properties compared to the bulk surface terminations. In particular, TiO2 nano crystals are more catalytically active and provide a new dissociation channel for adsorbed 2-propanol, a probe molecule chosen for this study. In the process of undertaking this research, it was found that monolayer TiO film can be used to employ moire varied chemistry. In particular, a long range pinwheel-shaped surface moiré pattern due to gradual shift of atom registry on Au (111), was found to further influence the adsorption geometry of adsorbates and to cause thereby smoothly varying sites for reactions.
In the case, of the second transition metal oxide surface, Fe3O4 (111), a comparison was made with rutile TiO2 (110) surface, Fe3O4 (111) is a polar surface with apparent surface charge, and thus undergoes various surface reconstructions. Therefore, its surface structure is of great complexity. Our work shows that the reaction of methanol on this iron-oxide surface is highly sensitive to atomic-level surface reconstructions.Chemistryzl2247Applied Physics and Applied Mathematics, Applied PhysicsDissertationsBifurcation of localized eigenstates of perturbed periodic Schrödinger operators
http://academiccommons.columbia.edu/catalog/ac:182973
Vukicevic, Ivahttp://dx.doi.org/10.7916/D88C9V2ZThu, 05 Feb 2015 18:20:43 +0000A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays as time advances. This dispersion is associated with the continuous spectrum of the underlying differential operator and the absence of discrete eigenvalues. The introduction of spatially localized perturbations in a periodic medium leads to ``defect modes'', states in which the wave is spatially localized and periodic in time. These modes are associated with eigenvalues which bifurcate from the continuous spectrum induced by the perturbation.
This thesis investigates specific families of perturbations of one-dimensional periodic Schrödinger operators and studies the resulting bifurcating eigenvalues from the unperturbed continuous spectrum. For Q(x) a real-valued periodic function, the Schrödinger operator H_Q = -∂_x^2 + Q(x) has a continuous spectrum equal to the union of closed intervals, called spectral bands, separated by open spectral gaps. We find that upon the introduction of a bounded, ``small'', and sufficiently decaying perturbation W(x), the spectrum of H_{Q+W} has discrete eigenvalues (with corresponding eigenstates which are exponentially decaying in |x|) which lie in the open spectral gaps of H_Q.
Our analysis covers two large classes of perturbations W(x): 1. W(x) = λ V(x), 0<λ ≪ 1, and V(x) sufficiently rapidly decaying as x → ± ∞; 2. W(x) = q(x, x/ε), 0<ε ≪ 1, where x ⟼ q(x,y) is spatially localized, q(x,y+1) = q(x,y) for x ∈ ℝ, and y ⟼ q(x,y) has mean zero.
In Case 1. W(x) corresponds to a small and localized absolute change in the medium's material properties. In Case 2. W(x) corresponds to a high-contrast microstructure. Q(x) + W(x) may be pointwise very large, but on average it is a small perturbation of Q(x).Applied mathematics, Mathematicsiv2143Applied Physics and Applied MathematicsDissertationsThe Effect of Electrode Coupling on Single Molecule Device Characteristics: An X-Ray Spectroscopy and Scanning Probe Microscopy Study
http://academiccommons.columbia.edu/catalog/ac:178216
Batra, Arunabhhttp://dx.doi.org/10.7916/D8MC8XMPTue, 07 Oct 2014 18:11:29 +0000This thesis studies electronic properties of molecular devices in the limiting cases of strong and weak electrode-molecule coupling. In these two limits, we use the complementary techniques of X-Ray spectroscopy and Scanning Tunneling Microscopy (STM) to understand the mechanisms for electrode-molecule bond formation, the energy level realignment due to metal-molecule bonds, the effect of coupling strength on single-molecule conductance in low-bias measurements, and the effect of coupling on transport under high-bias. We also introduce molecular designs with inherent asymmetries, and develop an analytical method to determine the effect of these features on high-bias conductance. This understanding of the role of electrode-molecule coupling in high-bias regimes enables us to develop a series of functional electronic devices whose properties can be predictably tuned through chemical design.
First, we explore the weak electrode-molecule coupling regime by studing the interaction of two types of paracyclophane derivates that are coupled `through-space' to underlying gold substrates. The two paracyclophane derivatives differ in the strength of their intramolecular through-space coupling. X-Ray photoemission spectroscopy (XPS) and Near-Edge X-ray Absorbance Fine Structure (NEXAFS) spectroscopy allows us to determine the orientation of both molecules; Resonant Photoemission Spectroscopy (RPES) then allows us to measure charge transfer time from molecule to metal for both molecules. This study provides a quantititative measure of charge transfer time as a function of through-space coupling strength. Next we use this understanding in STM based single-molecule current-voltage measurements of a series of molecules that couple through-space to one electrode, and through-bond to the other. We find that in the high-bias regime, these molecules respond differently depending on the direction of the applied field. This asymmetric response to electric field direction results in diode-like behavior. We vary the length of these asymmetrically coupled molecules, and find that we can increase the rectifying characteristics of these molecules by increasing length.
Next, we explore the strong-coupling regime with an X-Ray spectroscopy study of the formation of covalent gold-carbon bonds using benzyltrimethyltin molecules on gold surfaces in ultra high vacuum conditions. Through X-ray Photoemission Spectroscopy (XPS) and X-ray absorption measurements, we find that the molecule fragments at the Sn-Benzyl bond when exposed to gold and the resulting benzyl species only forms covalent Au-C bonds on less coordinated Au surfaces like Au(110). We also find spectroscopic evidence for a gap state localized on the Au-C bond that results from the covalent nature of the bond. Finally, we use Density Functional Theory based Nudged Elastic Band methods to find reaction pathways and energy barriers for this reaction.
We use our knowledge of the electronic structure of these bonds to create single-molecule junctions containing Au-C bonds in STM-based break junction experiments. In analogy with our approach for the weakly coupled `through-space' systems, we study the high-bias current-voltage characteristics of molecules with one strong Au-C bond, and one weaker donor-acceptor bond. These experiments reveal that the `gap state' created due to the covalent nature of the Au-C bond remains essentially pinned to the Fermi level of its corresponding electrode, and that most of the electric potential drop in the junction occurs on the donor-acceptor bond; as a result, these molecules behave like rectifiers. We use this principle to create a series of three molecular rectifiers, and show that the unique properties of the Au-C bond allow us to easily tune the rectification ratio by modifying a single electronic parameter.
We then explore the process of molecular self-assembly to create organic electronic structures on metal surfaces. Specifically, we study the formation of graphene nanoribbons using a brominated precursor deposited on Au(111) surface in ultra high vacuum. We find that the halogen atoms cleave from the precursors at surprisingly low temperatures of <100C, and find that the resulting radicals bind to Au, forming Au-C and Au-Br bonds. We show that the Br desorbs at relatively low temperatures of <250C, and that polymerization of the precursor molecules to form nanoribbons proceeds only after the debrominization of the surface. Finally, with Angle-Resolved Photoemission and Density Functional Theory calculations, we quantify the interaction strength of the resulting nanoribbons with the underlying gold substrate.
Taken together, the results presented in this thesis offer a mechanistic understanding of the formation of electrode-molecule bonds, and also an insight into the high-bias behavior of molecular junctions as a function of electrode-molecule coupling. In addition, our work in developing tunable, functional electronic devices serves as a framework for future technological advances towards molecule-based computation.Nanoscience, Condensed matter physics, Molecular physicsab3279Applied Physics and Applied MathematicsDissertationsDirected Biomolecular Assembly of Functional Nanodevices
http://academiccommons.columbia.edu/catalog/ac:202218
Penzo, Erikahttp://dx.doi.org/10.7916/D83N21Z7Tue, 30 Sep 2014 14:43:33 +0000One of the objectives of nanotechnology is to develop ways to build functional nanoscale devices from nanostructures. Whether these nanodevices will constitute the basis for new technologies rests on the ability to precisely manipulate the nanostructures in such a way that large numbers of functional devices can be built in parallel, with each nanodevice precisely located and addressed.
In this work nanostructures dispersed in solution are organized onto surfaces by means of molecular-scale directed assembly. This technique combines top down high resolution lithographic patterning to bottom up self-assembly: specific molecular interactions take place at locations precisely defined by lithography, resulting in the parallel assembly of an arbitrarily large number of devices into complex and precisely ordered arrangements. While different molecules are used in this study, DNA plays a key role throughout the work due to the specificity of its interactions, its programmability and outstanding chemical flexibility.
Two approaches are developed to direct the assembly of nanostructures on a surface. The first involves the patterning and selective functionalization of metallic nanodots that are used as anchors for the attachment of DNA molecules, proteins, DNA nanostructures and single-wall carbon nanotube (SWCNT) segments wrapped by DNA. Different strategies are explored to maximize the yield of the desired assembly. This platform also allows the monitoring of DNA-protein interactions with single molecule resolution, which has many potential biomedical applications. In the second approach, lithographic patterning is used to define regions of high surface energy that promote the binding of DNA origami and SWCNT segments. The high patterning resolution again allows for single nanostructure manipulation. This method facilitates the assembly of SWCNT field effect transistors from DNA-wrapped SWCNT segments.
The formation of multi-component nano-objects in solution, by directing the linkage of properly functionalized nanostructures, is also studied. The products of these reactions are suitable for surface placement with the developed directed assembly techniques, thereby resulting in a hierarchical directed assembly process. Among others, the synthesis of SWCNT-dsDNA heterostructures is described. These hybrid objects can be used to electrically probe dsDNA using the SWCNTs as electrodes, by assembling solid state devices by means of the directed assembly methods, and also by conductive AFM. The results of some electrical measurements of double stranded DNA are discussed.
The techniques developed in this thesis are directly applicable to fundamental studies of electron transport in molecules and other nanostructures, but they also have utility in other fields, such as chemistry and biology, where single molecule resolution is required. In addition, the approaches developed in this work may facilitate the advancement of new electronics technologies, including, but not limited to, future circuits based on single-wall carbon nanotubes with specific electronic properties.Nanotechnology, Nanoscience, Materials Scienceep2443Applied Physics and Applied MathematicsDissertationsAdvancements for three-dimensional remote sensing of the atmosphere
http://academiccommons.columbia.edu/catalog/ac:178170
Martin, William George Kuleszhttp://dx.doi.org/10.7916/D8WM1BZCTue, 23 Sep 2014 18:13:02 +0000Climate modeling efforts depend on remote sensing observations of clouds and aerosols in the atmosphere. This dissertation presents a foundation for using three-dimensional (3D) remote sensing techniques to retrieve cloud and aerosol properties in complex cloud fields. The initial research was aimed at establishing a set of single-scattering properties that could be used in subsequent 3D remote sensing applications. A theoretical stability analysis was used to evaluate what information about the particulate scattering material could be determined from in situ radiance and polarization measurements, and particle size and refractive index were retrieved from synthetic measurements with noise levels comparable to those of existing laboratory instruments. Subsequent research focused on the techniques necessary to retrieve 3D atmosphere and surface properties from images taken by an airborne or space-borne instrument. With the goal of using 3D retrieval methods to extend monitoring capabilities to regions with broken cloud fields, we formulated an efficient procedure for using codes that solve the 3D vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties to fit multi-angle/multi-pixel polarimetric measurements of the atmosphere. Taken together, these two bodies of work contribute to ongoing research which focuses on developing new methods for retrieving aerosols in complex 3D cloud fields, and may extend monitoring capabilities to these currently unresolved scenes.Applied mathematics, Atmospheric scienceswgm2111Applied Physics and Applied MathematicsDissertationsProjected Changes in the Annual Cycle of Surface Temperature and Precipitation Due to Greenhouse Gas Increases
http://academiccommons.columbia.edu/catalog/ac:177091
Dwyer, Johnhttp://dx.doi.org/10.7916/D8CN7248Mon, 28 Jul 2014 15:19:23 +0000When forced with increasing greenhouse gases, global climate models project changes to the seasonality of several key climate variables. These include delays in the phase of surface temperature, precipitation, and vertical motion indicating maxima and minima occurring later in the year. The changes also include an increase in the amplitude (or annual range) of low-latitude surface temperature and tropical precipitation and a decrease in the amplitude of high-latitude surface temperature and vertical motion. The aim of this thesis is to detail these changes, understand the links between them and ultimately relate them to simple physical mechanisms.
At high latitudes, all of the global climate models of the CMIP3 intercomparison suite project a phase delay and amplitude decrease in surface temperature. Evidence is provided that the changes are mainly driven by sea ice loss: as sea ice melts during the 21st century, the previously unexposed open ocean increases the effective heat capacity of the surface layer, slowing and damping the temperature response at the surface. In the tropics and subtropics, changes in phase and amplitude are smaller and less spatially uniform than near the poles, but they are still prevalent in the models. These regions experience a small phase delay, but an amplitude increase of the surface temperature cycle, a combination that is inconsistent with changes to the effective heat capacity of the system. Evidence suggests that changes in the tropics and subtropics are linked to changes in surface heat fluxes.
The next chapter investigates the nature of the projected phase delay and amplitude increase of precipitation using AGCM experiments forced by SST perturbations representing idealizations of the changes in annual mean, amplitude, and phase as simulated by CMIP5 models. A uniform SST warming is sufficient to force both an amplification and a delay of the annual cycle of precipitation. The amplification is due to an increase in the annual mean vertical water vapor gradient, while the delay is linked to a phase delay in the annual cycle of the circulation. A budget analysis of this simulation reveals a large degree of similarity with the CMIP5 results. In the second experiment, only the seasonal characteristics of SST are changed. For an amplified annual cycle of SST there is an amplified annual cycle of precipitation, while for a delayed SST there is a delayed annual cycle of precipitation. Assuming that SST changes can entirely explain the seasonal precipitation changes, the AGCM simulations suggest that the annual mean warming explains most of the amplitude increase and much of the phase delay in the CMIP5 models. However, imperfect agreement between the changes in the SST-forced AGCM simulations and the CMIP5 coupled simulations suggests that coupled effects may play a significant role.
Finally, the connections between changes in the seasonality of precipitation, temperature and circulation are studied in the tropics using models of varying complexity. These models include coupled model simulations with idealized forcing, a simple, semi-empirical model to describe the effect of land-ocean interactions, an aquaplanet model, and a dry, dynamical model. Each gives insights into the projected CMIP changes. Taken together they suggest that changes in the amplitude of vertical motions are consistent with a weakening of the annual mean circulation and can explain part of the changes in the amplitude of precipitation over both ocean and land, when combined with the thermodynamic effect described previously. By increasing the amplitude of the annual cycle of surface winds, the changes in circulation may also increase the amplitude of the surface temperature via the surface energy balance. The delay in the phase of circulation directly leads to a delay in the phase of precipitation, especially over ocean.Climate change, Atmospheric sciencesjgd2102Applied Physics and Applied Mathematics, Lamont-Doherty Earth ObservatoryDissertationsHigh-Speed Videography on HBT-EP
http://academiccommons.columbia.edu/catalog/ac:175984
Angelini, Sarahhttp://dx.doi.org/10.7916/D87942VVMon, 07 Jul 2014 11:42:34 +0000In this thesis, I present measurements from a high-speed video camera diagnostic on the High Beta Tokamak - Extended Pulse (HBT-EP). This work represents the first use of video data to analyze and understand the behavior of long wavelength kink perturbations in a wall-stabilized tokamak. A Phantom v7.3 camera was installed to capture the plasma's global behavior using visible light emissions and it operates at frame rates from 63 to 125 kfps. A USB2000 spectrometer was used to identify the dominant wavelength of light emitted in HBT-EP. At 656 nm, it is consistent with the D-alpha light expected from interactions between neutral deuterium and plasma electrons. The fast camera in combination with an Acktar vacuum black background produced images which were inverted using Abel techniques to determine the average radial emissivity profiles. These profiles were found to be hollow with a radial scale length of approximately 4 cm at the plasma edge. As a result, the behavior measured and analyzed using visible light videography is limited to the edge region. Using difference subtraction, biorthogonal decomposition and Fourier analysis, the structures of the observed edge fluctuations are computed. By comparing forward modelling results to measurements, the plasma is found to have an m/n = 3/1 helical shape that rotates in the electron drift direction with a lab-frame frequency between 5 and 10 kHz.
The fast camera was also used to measure the plasma's response to applied helical magnetic perturbations which resonate with the equilibrium magnetic field at the plasma's edge. The static plasma response to non-rotating resonant magnetic perturbations (RMPs) is measured by comparing changes in the recorded image following a fast reversal, or phase flip, of the applied RMP. The programmed toroidal angle of the RMP is directly inferred from the resulting images of the plasma response. The plasma response and the intensityof the RMP are compared under different conditions. I found the resulting amplitude correlations to be consistent with previous measurements of the static response using an array of magnetic sensors.
My work has shown that high-speed videography can be an extremely useful diagnostic for measuring edge perturbations in a tokamak. Future measurements, such as those using multiple cameras with different views, are expected to improve our understanding of plasma behavior and to detect edge fluctuations with higher temporal and spatial resolution.
Supplementary Videos:
Video 1 - This is an example of the video data from Shot 77324, an unforced plasma shot
taken with the shells inserted.
Video 2 - The strongest naturally-rotating mode has been extracted from a subset of the
raw data shown in Video 1 using a biorthogonal decomposition. Long striations can be
seen which are common in shots that have the shells inserted.
Video 3 - In this video of the raw data from Shot 77537, the shells are retracted. The
smooth non-reflective Acktar black background can be seen between the shells.
Video 4 - The dominant BD mode from Shot 77537 shows pinwheel-like behavior. With
the shells retracted, the plasma encounters fewer physical structures for neutral recycling
and this affects the light emissions.
Video 5 - This video shows the dominant BD modes from Shot 78029 during which a
phase-flip RMP was used to influence the plasma. The mode seems to slow in its rotation
as it resonates with the externally-applied field.Plasma physicsApplied Physics and Applied MathematicsDissertationsProbabilistic Approaches to Partial Differential Equations with Large Random Potentials
http://academiccommons.columbia.edu/catalog/ac:175891
Gu, Yuhttp://dx.doi.org/10.7916/D82R3PTDMon, 07 Jul 2014 11:40:10 +0000The thesis is devoted to an analysis of the heat equation with large random potentials in high dimensions. The size of the potential is chosen so that the large, highly oscillatory, random field is producing non-trivial effects in the asymptotic limit. We prove either homogenization, i.e., the random potential is replaced by some deterministic constant, or convergence to a stochastic partial differential equation, i.e., the random potential is replaced by some stochastic noise, depending on the correlation property. When the limit is deterministic, we provide estimates of the error between the heterogeneous and homogenized solutions when certain mixing assumption of the random potential is satisfied. We also prove a central limit type of result when the random potential is Gaussian or Poissonian. Lower dimensional and time-dependent cases are also treated. Most of the ingredients in the analysis are probabilistic, including a Feynman-Kac representation, a Brownian motion in random scenery, the Kipnis-Varadhan's method, and a quantitative martingale central limit theorem.Mathematicsyg2254Applied Physics and Applied MathematicsDissertationsHow Rotation affects Instabilities and the Plasma Response to Magnetic Perturbations in a Tokamak Plasma
http://academiccommons.columbia.edu/catalog/ac:175361
DeBono, Bryanhttp://dx.doi.org/10.7916/D8J964HRMon, 07 Jul 2014 11:29:36 +0000This thesis presents the systematic study of the multimode external kink mode structure and dynamics in the High-Beta Tokamak Extended-Pulse experiment (HBT-EP) when the plasma rotation is externally controlled using a source of toroidal momentum input. The capabilities of the HBT-EP tokamak to study rotation physics was greatly extended during a 2009-2010 major upgrade, when a new adjustable conducting wall, a high-power modular control coil array system, and an extensive set of 216 poloidal and radial magnetic sensors were installed on the machine. HBT-EP was additionally equipped with a biased edge electrode which made it possible to adjust the plasma ion and plasma magnetohydrodynamics (MHD) mode rotation frequencies by imparting an electromagnetic torque on the plasma. The design of this biased edge electrode, and its capability to torque the plasma is described. The rotation frequency of the helical kink modes was directly inferred from analysis of the magnetics dataset. To directly measure the plasma ion acceleration as the plasma was torqued by the biased electrode, a novel high-throughput and fast-response spectroscopic rotation diagnostic was installed on HBT-EP. This spectroscopic rotation diagnostic was designed to measure the velocity of He ions, therefore when conducting experiments using the spectroscopic rotation diagnostic a gas mixture of 90%D and 10%He was used. With its current power supplies the bias probe is capable of accelerating the primary m/n=3/1 helical kink mode (which has a natural rotation frequency between +7-+9kHz) to somewhere between -50kHz-+25kHz depending on the probe bias. At a probe voltage of +175V the He impurity ions were seen to accelerate by 3km/sec. Biorthogonal decomposition (BD) analysis was applied to the large magnetics dataset and used to determine the multimode m/n spectrum of the helical kink modes present in HBT-EP. The dominant helicities present as revealed by the BD are the m/n=3/1 and m/n=6/2 modes, which represent about 85% and 8% of the total MHD activity respectively. This percentages remain consistent across the entire range of 3/1 mode rotation frequencies obtainable from the bias probe, (-50kHz-25kHz). The Hilbert transform technique was also applied to magnetic sensor data to determine the instantaneous amplitude and frequency of the total MHD activity. The total MHD amplitude was seen to decrease with increasing plasma rotation, a 35% reduction as the 3/1 mode was accelerated from +6-+24kHz. Active MHD spectroscopy experiments using a resonant magnetic perturbation (RMP) are able to excite a clear three-dimensional plasma response. Plasma rotation is theoretically expected to increase plasma stability to external resonant error elds, and in HBT-EP the plasma amplitude response to a m/n=3/1 RMP increases by a factor of 2.7 when the plasma rotation is decreased from +25kHz to +-2kHz. As the RMP amplitude increases, slower plasmas are seen to disrupt at a lower perturbation amplitude than unperturbed or rapidly rotating modes. The 6/2 helical kink mode also shows an amplitude and phase response to the 3/1 RMP, and like the 3/1 mode the amplitude response is largest when the plasma is slowly rotating. The ratio between the plasma 6/2 amplication and the 3/1 amplication to a 3/1 RMP is nearly constant, regardless of the plasma rotation or the RMP amplitude.Plasma physics, Physicsbad2115Applied Physics and Applied MathematicsDissertationsPortfolio optimization with transaction costs and capital gain taxes
http://academiccommons.columbia.edu/catalog/ac:197100
Shen, Weiweihttp://dx.doi.org/10.7916/D8PK0D76Fri, 11 Apr 2014 16:41:52 +0000This thesis is concerned with a new computational study of optimal investment decisions with proportional transaction costs or capital gain taxes over multiple periods. The decisions are studied for investors who have access to a risk-free asset and multiple risky assets to maximize the expected utility of terminal wealth. The risky asset returns are modeled by a discrete-time multivariate geometric Brownian motion. As in the model in Davis and Norman (1990) and Lynch and Tan (2010), the transaction cost is modeled to be proportional to the amount of transferred wealth. As in the model in Dammon et al. (2001) and Dammon et al. (2004), the taxation rule is linear, uses the weighted average tax basis price, and allows an immediate tax credit for a capital loss. For the transaction costs problem, we compute both lower and upper bounds for optimal solutions. We propose three trading strategies to obtain the lower bounds: the hyper-sphere strategy (termed HS); the hyper-cube strategy (termed HC); and the value function optimization strategy (termed VF). The first two strategies parameterize the associated no-trading region by a hyper-sphere and a hyper-cube, respectively. The third strategy relies on approximate value functions used in an approximate dynamic programming algorithm. In order to examine their quality, we compute the upper bounds by a modified gradient-based duality method (termed MG). We apply the new methods across various parameter sets and compare their results with those from the methods in Brown and Smith (2011). We are able to numerically solve problems up to the size of 20 risky assets and a 40-year-long horizon. Compared with their methods, the three novel lower bound methods can achieve higher utilities. HS and HC are about one order of magnitude faster in computation times. The upper bounds from MG are tighter in various examples. The new duality gap is ten times narrower than the one in Brown and Smith (2011) in the best case. In addition, I illustrate how the no-trading region deforms when it reaches the borrowing constraint boundary in state space. To the best of our knowledge, this is the first study of the deformation in no-trading region shape resulted from the borrowing constraint. In particular, we demonstrate how the rectangular no-trading region generated in uncorrelated risky asset cases (see, e.g., Lynch and Tan, 2010; Goodman and Ostrov, 2010) transforms into a non-convex region due to the binding of the constraint.For the capital gain taxes problem, we allow wash sales and rule out "shorting against the box" by imposing nonnegativity on portfolio positions. In order to produce accurate results, we sample the risky asset returns from its continuous distribution directly, leading to a dynamic program with continuous decision and state spaces. We provide ingredients of effective error control in an approximate dynamic programming solution method. Accordingly, the relative numerical error in approximating value functions by a polynomial basis function is about 10E-5 measured by the l1 norm and about 10E-10 by the l2 norm. Through highly accurate numerical solutions and transformed state variables, we are able to explain the optimal trades through an associated no-trading region. We numerically show in the new state space the no-trading region has a similar shape and parameter sensitivity to that of the transaction costs problem in Muthuraman and Kumar (2006) and Lynch and Tan (2010). Our computational results elucidate the impact on the no-trading region from volatilities, tax rates, risk aversion of investors, and correlations among risky assets. To the best of our knowledge, this is the first time showing no-trading region of the capital gain taxes problem has such similar traits to that of the transaction costs problem. We also compute lower and upper bounds for the problem. To obtain the lower bounds we propose five novel trading strategies: the value function optimization (VF) strategy from approximate dynamic programming; the myopic optimization and the rolling buy-and-hold heuristic strategies (MO and RBH); and the realized Merton's and hyper-cube strategies (RM and HC) from policy approximation. In order to examine their performance, we develop two upper bound methods (VUB and GUB) based on the duality technique in Brown et al. (2009) and Brown and Smith (2011). Across various sets of parameters, duality gaps between lower and upper bounds are smaller than 3% in most examples. We are able to solve the problem up to the size of 20 risky assets and a 30-year-long horizon.Applied mathematicsws2215Applied Physics and Applied Mathematics, BusinessDissertationsMaterials Optimization and GHz Spin Dynamics of Metallic Ferromagnetic Thin Film Heterostructures
http://academiccommons.columbia.edu/catalog/ac:168924
Chenghttp://dx.doi.org/10.7916/D81V5BZJWed, 22 Jan 2014 12:13:44 +0000Metallic ferromagnetic (FM) thin film heterostructures play an important role in emerging magnetoelectronic devices, which introduce the spin degree of freedom of electrons into conventional charge-based electronic devices. As the majority of magnetoelectronic devices operate in the GHz frequency range, it is critical to understand the high-frequency magnetization dynamics in these structures. In this thesis, we start with the static magnetic properties of FM thin films and their optimization via the field-sputtering process incorporating a specially designed in-situ electromagnet. We focus on the origins of anisotropy and hysteresis/coercivity in soft magnetic thin films, which are most relevant to magentic susceptibility and power dissipation in applications in the sub-GHz frequency regime, such as magnetic-core integrated inductors. Next we explore GHz magnetization dynamics in thin-film heterostructures, both in semi-infinite samples and confined geometries. All investigations are rooted in the Landau-Lifshitz-Gilbert (LLG) equation, the equation of motion for magnetization. The phenomenological Gilbert damping parameter in the LLG equation has been interpreted, since the 1970's, in terms of the electrical resistivity. We present the first interpretation of the size effect in Gilbert damping in single metallic FM films based on this electron theory of damping. The LLG equation is intrinsically nonlinear, which provides possibilities for rf signal processing. We analyze the frequency doubling effect at small-angle magnetization precession from the first-order expansion of the LLG equation, and demonstrate second harmonic generation from Ni81 Fe19 (Permalloy) thin film under ferromagnetic resonance (FMR), three orders of magnitude more efficient than in ferrites traditionally used in rf devices. Though the efficiency is less than in semiconductor devices, we provide field- and frequency-selectivity in the second harmonic generation. To address further the relationship between the rf excitation and the magnetization dynamics in systems with higher complexity, such as multilayered thin films consisting of nonmagnetic (NM) and FM layers, we employ the powerful time-resolved x-ray magnetic circular dichroism (TR-XMCD) spectroscopy. Soft x-rays have element-specific absorption, leading to layer-specific magnetization detection provided the FM layers have distinctive compositions. We discovered that in contrast to what has been routinely assumed, for layer thicknesses well below the skin depth of the EM wave, a significant phase difference exists between the rf magnetic fields Hrf in different FM layers separated by a Cu spacer layer. We propose an analysis based on the distribution of the EM waves in the film stack and substrate to interpret this striking observation. For confined geometries with lateral dimensions in the sub-micron regime, there has been a critical absence of experimental techniques which can image small-amplitude dynamics of these structures. We extend the TR-XMCD technique to scanning transmission x-ray microscopy (STXM), to observe directly the local magnetization dynamics in nanoscale FM thin-film elements, demonstrated at picosecond temporal, 40 nm spatial and less than 6° angular resolution. The experimental data are compared with our micromagnetic simulations based on the finite element analysis of the time-dependent LLG equation. We resolve standing spin wave modes in nanoscale Ni81 Fe19 thin film ellipses (1000 nm × 500 nm × 20 nm) with clear phase information to distinguish between degenerate eigenmodes with different symmetries for the first time. With the element-specific imaging capability of soft x-rays, spatial resolution up to 15 nm with improved optics, we see great potential for this technique to investigate functional devices with multiple FM layers, and provide insight into the studies of spin injection, manipulation and detection.Materials sciencecc3043Materials Science and Engineering, Applied Physics and Applied MathematicsDissertationsLarge Scale Simulation of Spinodal Decomposition
http://academiccommons.columbia.edu/catalog/ac:189103
Zheng, Xianghttp://dx.doi.org/10.7916/D89W0DZ9Thu, 07 Nov 2013 14:32:38 +0000Spinodal decomposition is a process in which a system of binary mixture eventually evolves to the separation of two macroscopic phases. Such phase separation occurs in a thermodynamically unstable state. A number of binary mixture experiments have demonstrated the phenomenon of spinodal decomposition. Many models have been proposed to describe the evolution of the spinodal decomposition. The Cahn-Hilliard (CH) partial differential equation, which includes an order parameter and a free energy, and evolves to minimize the energy, has frequently been used as a phase field model. Due to random thermal fluctuations that are inevitable in physical systems, the CH equation might be unrealistic for the overall decomposition process. Experimental results demonstrate the existence of Brownian motion in the spinodal decomposition, which suggests that diffusion (deterministic contribution) and the noise (stochastic contribution) both have an essential influence on the rate of spinodal decomposition. Therefore, a stochastic process should be part of a realistic mathematical model of the overall decomposition process. In order to overcome the disadvantage that the CH equation ignores physically significant thermal fluctuation, the CH equation with a thermal fluctuation term has been proposed, where the thermal fluctuation is modeled by a time-space Brownian motion. The CH equation with the thermal fluctuation was first considered by Cook, so the extended CH equation is also known as the Cahn-Hilliard-Cook (CHC) equation. For studying the CHC equation, we are primarily interested in the properties of steady state, such as the energies, statistical moments, and morphology. This motivates our choices for the numerical frameworks for analyzing the CHC equation. The CHC equation is a stochastic partial differential equation involving a biharmonic form and a noise forcing term. When the potential term is a polynomial, the CHC equation is split into a lower order PDE system of two harmonic equations. The space is discretized by the standard finite element method. The evolution of the spinodal decomposition and the effect of the thermal fluctuation are studied in 2D. For obtaining numerical results of the CHC equation with a more realistic logarithmic potential efficiently, especially in 3D, a fully implicit, cell-centered, finite difference scheme in the original biharmonic form, and an adaptive time-stepping strategy are combined to discretize the space and time. The numerical scheme is verified by a comparison with an explicit scheme. At each time step, the parallel NKS algorithm is used to solve a nonlinear spatially discretized system. We discuss various numerical and computational challenges associated with the cell-centered finite difference-based, massively parallel implementation of this framework. We present steady state solutions of the CHC equation in 2D and, for the first time, in 3D. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We demonstrate that the thermal fluctuation is able to accelerate the spinodal decomposition process, and change the final steady morphology. We study the evolution of energies and statistical moments, from the initial stage to the steady state. Next, we study the CHC equation from the statistical perspective. A parallel domain decomposition method, based on the Wiener chaos expansion (WCE) and the Karhunen-Loeve expansion (KLE), is presented. Applying the two expansions to time-space white noise, we transform the CHC equation into a deterministic form. The main advantage of the Wiener chaos approach is that it separates deterministic and random effects, and factors the latter out of the primary stochastic partial differential equation effectively and rigorously. Therefore, the stochastic partial differential equation can be reduced to its propagator: a system of deterministic equations for the coefficients of the Wiener chaos expansion. Formulae for the expansion of high order nonlinear terms are presented, which involve the solutions of the propagator. Compared to the Monte Carlo (MC) method, the Wiener chaos approach does not require the generation of random numbers. The Karhunen-Loeve expansion is able to capture the principal component of the random field. A domain decomposition method is used to solve the equation system, which is discretized by a stabilized implicit cell-centered finite difference scheme. An NKS algorithm is applied to solve the nonlinear system of equations at each time step. The evolution of the spinodal decomposition and respective variances are demonstrated. Numerical results demonstrate that the parallel domain decomposition method scales well to a thousand processor cores. For short time, the Wiener chaos Karhunen-Loeve expansion (WCKLE) method is more efficient than the Monte Carlo simulation. We simulate the whole spinodal decomposition process by the Wiener chaos Karhunen-Loeve expansion Monte Carlo (WKCLE-MC) hybrid method, and obtain the distinctive separation stage for long time.Applied mathematicsApplied Physics and Applied MathematicsDissertationsHomogenization of Partial Differential Equations with Random, Large Potential
http://academiccommons.columbia.edu/catalog/ac:165171
Zhang, Ningyaohttp://hdl.handle.net/10022/AC:P:21626Fri, 13 Sep 2013 15:56:38 +0000Partial differential equations with highly oscillatory, random coefficients describe many applications in applied science and engineering such as porous media and composite materials. Homogenization of PDE states that the solution of the initial model converges to the solution to a macro model, which is characterized by the PDE with homogenized coefficients. Particularly, we study PDEs with a large potential, a class of PDEs with a potential properly scaled such that the limiting equation has a non-trivial (non-zero) potential.
This thesis consists of the investigation of three issues. The first issue is the convergence of Schodinger equation to a deterministic homogenized PDE in high dimension. The second issue is the convergence of the same equation to a stochastic PDE in low dimension. The third issue is the convergence of elliptic equation with an imaginary potential.Applied mathematicsnz2164Applied Physics and Applied MathematicsDissertationsInterplay between Mechanics, Electronics, and Energetics in Atomic-Scale Junctions
http://academiccommons.columbia.edu/catalog/ac:188963
Aradhya, Sriharsha Veerabhadraiahhttp://dx.doi.org/10.7916/D8PG1R4BFri, 13 Sep 2013 14:01:40 +0000The physical properties of materials at the nanoscale are controlled to a large extent by their interfaces. While much knowledge has been acquired about the properties of material in the bulk, there are many new and interesting phenomena at the interfaces that remain to be better understood. This is especially true at the scale of their constituent building blocks - atoms and molecules. Studying materials at this intricate level is a necessity at this point in time because electronic devices are rapidly approaching the limits of what was once thought possible, both in terms of their miniaturization as well as our ability to design their behavior. In this thesis I present our explorations of the interplay between mechanical properties, electronic transport and binding energetics of single atomic contacts and single-molecule junctions. Experimentally, we use a customized conducting atomic force microscope (AFM) that simultaneously measures the current and force across atomic-scale junctions. We use this instrument to study single atomic contacts of gold and silver and single-molecule junctions formed in the gap between two gold metallic point contacts, with molecules with a variety of backbones and chemical linker groups. Combined with density functional theory based simulations and analytical modeling, these experiments provide insight into the correlations between mechanics and electronic structure at the atomic level.
In carrying out these experimental studies, we repeatedly form and pull apart nanoscale junctions between a metallized AFM cantilever tip and a metal-coated substrate. The force and conductance of the contact are simultaneously measured as each junction evolves through a series of atomic-scale rearrangements and bond rupture events, frequently resulting in single atomic contacts before rupturing completely. The AFM is particularly optimized to achieve high force resolution with stiff probes that are necessary to create and measure forces across atomic-size junctions that are otherwise difficult to fabricate using conventional lithographic techniques. In addition to the instrumentation, we have developed new algorithmic routines to perform statistical analyses of force data, with varying degrees of reliance on the conductance signatures.
The key results presented in this thesis include our measurements with gold metallic contacts, through which we are able to rigorously characterize the stiffness and maximum forces sustained by gold single atomic contacts and many different gold-molecule-gold single-molecule junctions. In our experiments with silver metallic contacts we use statistical correlations in conductance to distinguish between pristine and oxygen-contaminated silver single atomic contacts. This allows us to separately obtain mechanical information for each of these structural motifs. The independently measured force data also provides new insights about atomic-scale junctions that are not possible to obtain through conductance measurements alone. Using a systematically designed set of molecules, we are able to demonstrate that quantum interference is not quenched in single-molecule junctions even at room temperature and ambient conditions. We have also been successful in conducting one of the first quantitative measurements of van der Waals forces at the metal-molecule interface at the single-molecule level. Finally, towards the end of this thesis, we present a general analytical framework to quantitatively reconstruct the binding energy curves of atomic-scale junctions directly from experiments, thereby unifying all of our mechanical measurements. I conclude with a summary of the work presented in this thesis, and an outlook for potential future studies that could be guided by this work.Physics, Nanoscience, Nanotechnologysva2107Applied Physics and Applied MathematicsDissertationsFunctional Nanocomposites Formed by Two-step Back-filling Methods
http://academiccommons.columbia.edu/catalog/ac:165145
Kramer, Theodore Jerveyhttp://hdl.handle.net/10022/AC:P:21605Fri, 13 Sep 2013 13:36:17 +0000This thesis investigates the synthesis and properties of nanocomposite materials comprised of inorganic nanocrystals (NCs) combined with a complementary organic compound utilizing sequential two-step synthesis methods. We demonstrate an enhancement in the mechanical and optical properties of electrophoreticially deposited (EPD) cadmium selendide (CdSe) nanocrystal (NC) films through post-deposition addition of organic ligand molecules and polymeric precursor molecules (monomers). Specifically we show that when these organic compounds are added (i.e. back-filled) into the as-deposited, wet EPD NC film, that fracture in the dried film is suppressed and photoluminscent (PL) efficiency of the inorganic NC phase is greatly increased. We go on to study the synthesis and properties of a novel nanocomposite comprised of inorganic NCs back-filled into a mat of semiconducting poly(3-hexylthiophene) [P3HT] nanowires. P3HT nanowire films are synthesized using a novel method developed as part of this thesis; where P3HT is blended with a sacrificial polymer (polystyrene, PS), leading to spontaneous demixing of the two polymers upon casting, and upon selective removal of the PS phase exposes a dense mat of P3HT nanowires. When back filled with CdSe NCs the composite material exhibits photovoltaic (PV) performance and provides a flexible platform for low-cost, hybrid organic/inorganic NC PV device fabrication. We conclude by showing how the above methods, in conjunction with novel ligand chemistry and lithographic techniques, can be utilized to create a photo-active nanocomposite consisting of lithographically defined, micron-scale, electrodes that are selectively decorated with electron-accepting NCs using EPD, and subsequently back-filled with a complementary electron-donating NC phase. The device architecture and resulting nanocomposite material is capable of lateral exciton separation on a potentially low-cost substrate.Materials sciencetjk2111Applied Physics and Applied MathematicsDissertationsProbing Electronic and Thermoelectric Properties of Single Molecule Junctions
http://academiccommons.columbia.edu/catalog/ac:165142
Widawsky, Jonathan R.http://hdl.handle.net/10022/AC:P:21604Fri, 13 Sep 2013 13:30:57 +0000In an effort to further understand electronic and thermoelectric phenomenon at the nanometer scale, we have studied the transport properties of single molecule junctions. To carry out these transport measurements, we use the scanning tunneling microscope-break junction (STM-BJ) technique, which involves the repeated formation and breakage of a metal point contact in an environment of the target molecule. Using this technique, we are able to create gaps that can trap the molecules, allowing us to sequentially and reproducibly create a large number of junctions. By applying a small bias across the junction, we can measure its conductance and learn about the transport mechanisms at the nanoscale. The experimental work presented here directly probes the transmission properties of single molecules through the systematic measurement of junction conductance (at low and high bias) and thermopower. We present measurements on a variety of molecular families and study how conductance depends on the character of the linkage (metal-molecule bond) and the nature of the molecular backbone. We start by describing a novel way to construct single molecule junctions by covalently connecting the molecular backbone to the electrodes. This eliminates the use of linking substituents, and as a result, the junction conductance increases substantially. Then, we compare transport across silicon chains (silanes) and saturated carbon chains (alkanes) while keeping the linkers the same and find a stark difference in their electronic transport properties. We extend our studies of molecular junctions by looking at two additional aspects of quantum transport - molecular thermopower and molecular current-voltage characteristics. Each of these additional parameters gives us further insight into transport properties at the nanoscale. Evaluating the junction thermopower allows us to determine the nature of charge carriers in the system and we demonstrate this by contrasting the measurement of amine-terminated and pyridine-terminated molecules (which exhibit hole transport and electron transport, respectively). We also report the thermopower of the highly conducting, covalently bound molecular junctions that we have recently been able to form, and learn that, because of their unique transport properties, the junction power factors, GS2, are extremely high. Finally, we discuss the measurement of molecular current-voltage curves and consider the electronic and physical effects of applying a large bias to the system. We conclude with a summary of the work discussed and an outlook on related scientific studies.Physics, Nanotechnology, Quantum physicsjrw2139Applied Physics and Applied MathematicsDissertationsProbing Electronic and Thermoelectric Properties of Single Molecule Junctions
http://academiccommons.columbia.edu/catalog/ac:164391
Widawsky, Jonathan R.http://hdl.handle.net/10022/AC:P:21389Tue, 20 Aug 2013 17:01:35 +0000In an effort to further understand electronic and thermoelectric phenomenon at the nanometer scale, we have studied the transport properties of single molecule junctions. To carry out these transport measurements, we use the scanning tunneling microscope-break junction (STM-BJ) technique, which involves the repeated formation and breakage of a metal point contact in an environment of the target molecule. Using this technique, we are able to create gaps that can trap the molecules, allowing us to sequentially and reproducibly create a large number of junctions. By applying a small bias across the junction, we can measure its conductance and learn about the transport mechanisms at the nanoscale. The experimental work presented here directly probes the transmission properties of single molecules through the systematic measurement of junction conductance (at low and high bias) and thermopower. We present measurements on a variety of molecular families and study how conductance depends on the character of the linkage (metal-molecule bond) and the nature of the molecular backbone. We start by describing a novel way to construct single molecule junctions by covalently connecting the molecular backbone to the electrodes. This eliminates the use of linking substituents, and as a result, the junction conductance increases substantially. Then, we compare transport across silicon chains (silanes) and saturated carbon chains (alkanes) while keeping the linkers the same and find a stark difference in their electronic transport properties. We extend our studies of molecular junctions by looking at two additional aspects of quantum transport - molecular thermopower and molecular current-voltage characteristics. Each of these additional parameters gives us further insight into transport properties at the nanoscale. Evaluating the junction thermopower allows us to determine the nature of charge carriers in the system and we demonstrate this by contrasting the measurement of amine-terminated and pyridine-terminated molecules (which exhibit hole transport and electron transport, respectively). We also report the thermopower of the highly conducting, covalently bound molecular junctions that we have recently been able to form, and learn that, because of their unique transport properties, the junction power factors, GS², are extremely high. Finally, we discuss the measurement of molecular current-voltage curves and consider the electronic and physical effects of applying a large bias to the system. We conclude with a summary of the work discussed and an outlook on related scientific studies.Physics, Nanotechnology, Quantum physicsjrw2139Applied Physics and Applied MathematicsDissertationsMonte Carlo Simulations of Powder Diffraction at Time-of-Flight Neutron Sources
http://academiccommons.columbia.edu/catalog/ac:168858
LiFri, 28 Jun 2013 10:56:49 +0000Measured powder diffraction patterns contain contributions from the sample and the instrument. Most available data analysis software operates on the measured data to extract sample parameters, however, few programs can take sample parameters and rigorously simulate the expected diffraction profile for a given instrument. In this work Monte Carlo methods, within the framework of McStas software, are used for the simulation of neutron diffraction at the SMARTS (Spectrometer for Materials Research at Temperature and Stress) diffractometer in the Los Alamos Neutron Science Center. The simulations include all the instrumental components, such as the moderator, guide system, collimator, detector banks and sample. The results of the simulations are in excellent agreement with the experimental data for different ideal powder samples. The simulations also yield information on the line broadening introduced into the diffraction profile as a function of energy and are used to predict the size and strain limit above which line broadening studies cannot be performed on this instrument. Theoretical derivations of line profile analysis are presented to provide an accurate explanation of the formation of diffraction peaks from the powder sample. This thesis demonstrates how rigorous scattering theory can be used to design optimal diffraction instruments.Materials scienceMaterials Science and Engineering, Applied Physics and Applied MathematicsDissertationsPressure profiles of plasmas confined in the field of a dipole magnet
http://academiccommons.columbia.edu/catalog/ac:161877
Davis, Matthew Stileshttp://hdl.handle.net/10022/AC:P:20570Tue, 04 Jun 2013 15:43:57 +0000Understanding the maintenance and stability of plasma pressure confined by a strong magnetic field is a fundamental challenge in both laboratory and space plasma physics. Using magnetic and X-ray measurements on the Levitated Dipole Experiment (LDX), the equilibrium plasma pressure has been reconstructed, and variations of the plasma pressure for different plasma conditions have been examined. The relationship of these profiles to the magnetohydrodynamic (MHD) stability limit, and to the enhanced stability limit that results from a fraction of energetic trapped electrons, has been analyzed. In each case, the measured pressure profiles and the estimated fractional densities of energetic electrons were qualitatively consistent with expectations of plasma stability. LDX confines high temperature and high pressure plasma in the field of a superconducting dipole magnet. The strong dipole magnet can be either mechanically supported or magnetically levitated. When the dipole was mechanically supported, the plasma density profile was generally uniform while the plasma pressure was highly peaked. The uniform density was attributed to the thermal plasma being rapidly lost along the field to the mechanical supports. In contrast, the strongly peaked plasma pressure resulted from a fraction of energetic, mirror trapped electrons created by microwave heating at the electron cyclotron resonance (ECRH). These hot electrons are known to be gyrokinetically stabilized by the background plasma and can adopt pressure profiles steeper than the MHD limit. X-ray measurements indicated that this hot electron population could be described by an energy distribution in the range 50-100 keV. Combining information from the magnetic reconstruction of the pressure profile, multi-chord interferometer measurements of the electron density profile, and X-ray measurements of the hot electron energy distribution, the fraction of energetic electrons at the pressure peak was estimated to be about 35% of the total electron population. When the dipole was magnetically levitated the plasma density increased substantially because particle losses to the mechanical supports were eliminated so particles could only be lost via slower cross-field transport processes. The pressure profile was observed to be broader during levitated operation than it was during supported operation, and the pressure appeared to be contained in both a thermal population and an energetic electron population. X-ray spectra indicated that the X-rays came from a similar hot electron population during levitated and supported operation; however, the hot electron fraction was an order of magnitude smaller during levitated operation (<3% of the total electron population). Pressure gradients for both supported and levitated plasmas were compared to the MHD limit. Levitated plasmas had pressure profiles that were (i) steeper than, (ii) shallower than, or (iii) near the MHD limit dependent on plasma conditions. However, those profiles that exceeded the MHD limit were observed to have larger fractions of energetic electrons. When the dipole magnet was supported, high pressure plasmas always had profiles that exceeded the MHD interchange stability limit, but the high pressure in these plasmas appeared to arise entirely from a population of energetic trapped electrons.Plasma physicsmsd2133Applied Physics and Applied MathematicsDissertationsSymmetry Breaking and the Inverse Energy Cascade in a Plasma
http://academiccommons.columbia.edu/catalog/ac:161865
Worstell, Matthewhttp://hdl.handle.net/10022/AC:P:20566Tue, 04 Jun 2013 14:45:25 +0000The application of electrostatic bias to both low density plasma with coherent fluctuations and high density plasma with turbulent fluctuations confined by a magnetic dipole are investigated. Previously, electrostatic biasing of low density plasma was symmetric, drove rapid plasma rotation, and excited the centrifugal interchange instability. This research investigates the application of non-symmetric bias and the influence of broken symmetry on strongly turbulent plasmas. Non- symmetric bias is applied through either point biasing or an equatorial array spanning the device. In both cases, the spatial symmetry of applied bias dramatically effects the plasma fluctuations. With bias applied, the plasma achieves a new equilibrium characterized by amplified low order modes and diminished amplitude of higher order modes. Although the turbulent spectrum changes, the RMS fluctuation level is unchanged by the bias. Bias also causes the turbulent electrostatic fluctuations to coalesce into a quasi-coherent mode and the appearance of increased coherence. The effect of bias configuration is also seen to change the measured levels of nonlinear coupling. Non-symmetric biasing increases nonlinear coupling while symmetric biasing leaves the coupling unchanged. These results represent the first experimental demonstration of symmetry breaking driving the inverse energy cascade in a quasi-two dimensional plasma system. The application of dynamic and rotating electrostatic bias as well as plans for applying turbulent feedback are discussed.Plasma physicsApplied Physics and Applied MathematicsDissertationsWhat is Driving Changes in the Tropospheric Circulation? New Insights from Simplified Models
http://academiccommons.columbia.edu/catalog/ac:161494
Tandon, Neil Francishttp://hdl.handle.net/10022/AC:P:20441Thu, 23 May 2013 13:13:16 +0000This thesis seeks an improved understanding of what has been driving changes in the large scale tropospheric circulation. First, we consider the effects of stratospheric water vapor levels, which exhibit significant changes on both interannual and decadal timescales. It is shown that idealized thermal forcings mimicking increases in stratospheric water vapor produce poleward expansion of the Hadley cells (HCs) and poleward shifts of the midlatitude jets. Quantitatively, the circulation responses are comparable to those produced by increased well-mixed greenhouse gases. This suggests that stratospheric water vapor may be a significant contribution to past and projected changes in the tropospheric circulation. The second part of this thesis focuses on the response to idealized thermal forcings in the troposphere. It is found that zonally uniform warming confined to a narrow region around the equator produces contraction of the HCs and equatorward shifts of the midlatitude jets. Forcings with wider meridional extent produce the opposite effect: HC expansion and poleward shifts of the jets. If the forcing is confined to the midlatitudes, the amount of HC expansion is more than three times that of a forcing of comparable amplitude that is spread over the tropics. This finding may be relevant to recently observed trends of amplified warming in the midlatitudes. Furthermore, a simple diffusive model is constructed to explain the sensitivity of the circulation response to the meridional structure of the thermal forcing. The final part of this thesis considers the possible influence of solar forcing on the tropospheric circulation. Of particular interest is the steady state response to a 0.1% increase in total solar irradiance (TSI), the approximate amplitude of the 11-year solar cycle. Using a comprehensive atmospheric general circulation model coupled to a mixed layer ocean, it is found that a 0.1% TSI increase produces a circulation response that has a high dependence on the background state. Specifically, a TSI perturbation applied to a present day climate produces an equatorward shift of the Southern Hemisphere (SH) midlatitude jet, while the same forcing applied to a warmer climate produces a poleward shift of the SH jet. Opposite-signed responses are also evident in regions of the sea surface temperature, sea level pressure, and precipitation fields. These divergent responses may help to explain why earlier studies reach highly disparate conclusions about the influence of solar variations on climate.Atmospheric sciences, Climate changenft2104Applied Physics and Applied MathematicsDissertationsZonal flow driven by convection and convection driven by internal heating
http://academiccommons.columbia.edu/catalog/ac:161452
Goluskin, Davidhttp://hdl.handle.net/10022/AC:P:20415Thu, 23 May 2013 10:51:47 +0000In the first part, Rayleigh-Benard convection is studied in a two-dimensional, horizontally periodic domain with free-slip top and bottom boundaries. This configuration encourages mean horizontal flows of zero horizontal wavenumber, which we study as an idealization of zonal flows in tokamaks, planetary atmospheres, and annular cylindrical convection experiments. These systems often satisfy free-slip conditions on at least one boundary and are approximately two-dimensional. Stable steady states with zonal flow are found for Prandtl numbers up to 0.3. Stable and unstable steady states with horizontal periods up to six times the layer height are computed for a Prandtl number of 0.1 and Rayleigh numbers, Ra, up to 2*10^5. Concurrently stable states with and without zonal flow are found where the state without zonal flow convects heat over 10 times faster. Steady zonal flow arises subcritically whenever the horizontal period is not forced to be narrow, contrary to most prior predictions by truncated models. Steady states and their bifurcations are studied in a truncated model that does predict subcriticality. Direct numerical simulations are performed with a horizontal period twice the layer height, Prandtl numbers between 1 and 10, and Ra between 5*10^5 and 2*10^8.. Zonal flow arises subcritically as Ra is raised but is seen in all quasi-steady states at large Ra. The fraction of the total kinetic energy comprised by zonal flow approaches unity as Ra grows. At a Prandtl number of 1, vertical convective heat transport occurs in temporal bursts, nearly vanishing in between, and is non-monotonic in Ra. At Prandtl numbers of 3 and 10, convective transport at no time nearly vanishes, and time-averaged Nusselt numbers scale as Ra^0.077 and Ra^0.19, respectively. Both growth rates are below the range accepted for Rayleigh-Benard convection without zonal flow. In the second part, two-dimensional direct numerical simulations are conducted for convection sustained by uniform internal heating in a horizontal fluid layer. Top and bottom boundary temperatures are fixed and equal. Prandtl numbers range from 0.01 to 100. A control parameter, R, that is similar to the usual Rayleigh number is varied up to 5*10^5 times its critical value at the onset of convection. The asymmetry between upward and downward heat fluxes is non-monotonic in R. In a broad high-R regime, dimensionless mean temperature scales as R^-1/5. We discuss the scaling of mean temperature and heat-flux-asymmetry, which we find to be better diagnostic quantities than the conventionally used top and bottom Nusselt numbers.Applied mathematicsdg2422Applied Physics and Applied Mathematics, AstronomyDissertationsTracer-Independent Approaches to Stratosphere-Troposphere Exchange and Tropospheric Air Mass Composition
http://academiccommons.columbia.edu/catalog/ac:161531
Orbe, Clarahttp://hdl.handle.net/10022/AC:P:20400Wed, 22 May 2013 14:56:18 +0000Two transport processes are examined. The first addresses the interaction between the stratosphere and the troposphere. We perform the first analyses of stratosphere-troposphere exchange using one-way flux distributions; diagnostics are illustrated in both idealized and comprehensive contexts. By partitioning the one-way flux across the thermal tropopause according to stratospheric residence time τ and the regions where air enters and exits the stratosphere, the one-way flux is quantified robustly without being rendered ill-defined by the short-τ eddy-diffusive singularity. Diagnostics are first computed using an idealized circulation model that has topography only in the Northern Hemisphere (NH) and is run under perpetual NH winter conditions; suitable integrations are used to determine the stratospheric mean residence time and the mass fraction of the stratosphere in any given residence-time interval. For the idealized model we find that air exiting the stratosphere in the winter hemisphere has significantly longer mean residence times than air exiting in the summer hemisphere because the winter hemisphere has a deeper circulation and stronger eddy diffusion. The complicated response of mean residence times to increased topography underlines the fact that flux distributions capture the integrated advective-diffusive tropopause-to-tropopause transport, and not merely advection by the residual-mean circulation. Extending one-way flux distributions to non-stationary flow we quantify the seasonal ventilation of the stratosphere using the state-of-the-art GEOSCCM general circulation model subject to fixed present-day climate forcings. From the one-way flux distributions, we determine the mass of the stratosphere that is in transit from the tropical tropopause back to the troposphere, partitioned according to stratospheric residence time and exit location. We find that poleward of 45N, the cross-tropopause flux of air that has resided in the stratosphere three months or less is 34 ± 10 % larger for air that enters the stratosphere in July compared to air that enters in January. During late summer and early fall the stratosphere contains about six times more air of tropical origin that is destined to exit poleward of 45S/N in both hemispheres, after an entry-to-exit residence time of six months or less, than is the case during other times of year. We find that 51 ± 1 % and 39 ± 2 % of the stratospheric air mass of tropical origin, annually averaged and integrated over all residence times, exits poleward of 10N/S in the NH and SH, respectively, with most of the mass exiting downstream of the Pacific and Atlantic storm tracks. The mean residence time of this air is found to be ~ 5.1 years in the NH and ~ 5.7 years in the SH. The second transport process addresses new diagnostics of tropospheric transport. We introduce rigorously defined air masses as a diagnostic of tropospheric transport in the context of an idealized model. The fractional contribution from each air mass partitions air at any given point according to either where it was last in the planetary boundary layer (PBL), or where it was last in contact with the tropopause. The utility of these air-mass fractions in isolating the climate change signature on transport alone is demonstrated for the climate of a dynamical-core circulation model and its response to a specified heating. For an idealized warming that produces dynamical responses that are typical of end-of-century comprehensive model projections, changes in air-mass fractions are order 10% and reveal the model's climate change in tropospheric transport: poleward shifted jets and surface intensified eddy kinetic energy lead to more efficient stirring of air out of the midlatitude boundary layer, suggesting that in the future there may be increased transport of industrial pollutants to the Arctic upper troposphere. Correspondingly, air is less efficiently mixed away from the subtropical boundary layer. The air-mass fraction that had last stratosphere contact at midlatitudes increases all the way to the surface, in part due to increased isentropic eddy transport across the tropopause. A weakened Hadley circulation leads to decreased interhemispheric transport in the model's future climate.Applied mathematics, Atmospheric sciencesco2203Applied Physics and Applied Mathematics, Earth and Environmental SciencesDissertationsIncorporation of Nonconventional Crystalline Materials onto the Integrated Photonics Platform
http://academiccommons.columbia.edu/catalog/ac:156940
Gaathon, Ophirhttp://hdl.handle.net/10022/AC:P:19125Wed, 20 Feb 2013 10:24:55 +0000Applications that span from sensing, to large bandwidth communication, to acoustic filtering, to high-resolution imaging and display, to quantum information processing (QIP) and to advance electronics have a growing need for new device types and materials. These advanced devices require electrical and optical properties that, in some cases, can only be provided by truly single-crystal thin-films of nonconventional materials, such as lithium niobate (LN, LiNbO3), yttrium aluminum garnet (YAG, Y3Al5O12) and diamond. In order to incorporate those crystals into existing multi-scale integrated system platforms, new technologies must be developed that can supply high-quality, single-crystal, thin-films in the desired thin-film architecture. Unfortunately, production of thin-films of single-crystals is not always possible via growth. Here, the use of Crystal Ion Slicing (CIS) technique to realize single-crystal thin-films of three of the nonconventional crystals is described. The fabrication techniques vary greatly between different crystals. Thus, new exfoliation chemistries must be developed for each material system. Detailed description of the investigation into exfoliation of LN, YAG and diamond is presented. The most mature CIS application is for LN crystals. Here, the development of several important complementary fabrication methods is presented. This includes description of polishing and bonding techniques that are necessary for successful incorporation of thin-films. Further, a lateral patterning technology of thin-films using femtosecond laser ablation is demonstrated. In addition, an ion-implantation patterning method and its application in nonlinear optics is presented. Finally, a novel polarization dependent plasmonic filter is described. In addition, a detailed description of the fabrication methods of single-crystal thin-films of YAG for acoustical and optical applications is presented. It is shown that the thermal exfoliation is the preferred method for YAG. After the thermal exfoliation, the films are subject to additional thermal cycle to anneal the films. This process high-temperature annealing is introduced to promote relaxation of film by eliminating residual strain and increasing the films' radius of curvature, both attributed to the ion-implantation process. Thus, detailed description of the post-exfoliation process is presented. The mechanical quality of the films is investigated with specific attention to the annealing behavior. Finally, the fabrication process and optical characterization of single-crystal thin-films of diamond is described. The work on diamond is focused on developing a parallel fabrication process for high-optical-quality single-crystal diamond membranes for quantum information processing (QIP) applications. The diamond membranes, with thickness as small as 200 nm and over 100 μm on their side, exhibit nitrogen-vacancy emission spectra including the zero phonon line (ZPL) peak of negatively charged centers. The films are patterned and sliced in parallel from a single-crystal diamond sample. The compatibility of the membrane with planar optical devices is demonstrated by the formation of two-dimensional photonic crystal patterns in 200 nm films. The films are produced by a combination of thermal annealing, chemical etching and oxygen plasma. Analysis of the films quality and optimization of the exfoliation process is evaluated by a verity of experimental techniques including: Atomic force microscope (AFM), optical microscopy, scanning electron microscopy (SEM), Raman and fluorescence spectroscopy, optical profilometry and nanoindentation.Physics, Engineeringog2126Applied Physics and Applied Mathematics, Electrical EngineeringDissertationsInterfacial Studies of Organic Field-Effect Transistors
http://academiccommons.columbia.edu/catalog/ac:156934
Jia, Zhanghttp://hdl.handle.net/10022/AC:P:19101Mon, 18 Feb 2013 13:21:44 +0000Organic field-effect transistors (OFETs) are potential components for large-area electronics because of their attractive advantages: light weight, cost-effective and large-area processability, flexibility and resonable performance potential. However, the commercialization of OFETs faces several technical obstacles. Low mobility of organic semiconductors limits the current-carrying capacity; high operation voltage restricts their use in many applications; easy degradation in air and instability under electrical stress usually make the lifetime too short to be useful; and contact resistance and contact matching also limit the charge injection to the semiconductor. Many of the above problems relate to interfaces in OFETs. There are two important interfaces in OFETs. The interface between organic semiconductor and the dielectric layer is of crucial importance since it is the location where charge transport in the channel occurs. The other important interface in OFETs is between the semiconductor and the contacts, where the charge injection and removal happen during device operation. Surface treatment of the contacts for bottom-contact devices is usually necessary to achieve both a good semiconductor microstructure and excellent contact performance. Great effort has been applied to improving device performance, primarily by focusing on enhancing device mobility to increase current capacity and improving subthreshold behavior to reduce the operation voltage. One approach to improving both figures of merit is to use a high-capacitance gate dielectric, which reduces the operating voltage and increases the mobile charge carrier density for a given gate voltage. Operating at a higher channel charge density improves the effective mobility in OFETs. I first demonstrate the use of nanoscale high-$kappa$ materials based on barium titanate (BT) which are normally ferroelectric as gate dielectrics where their high dielectric constant is desirable but ferroelectric hysteresis is not. Self-assembled monolayer (SAM) treatment of the dielectric has been used to improve the morphology of subsequent deposition of organic semiconductor. The dipoles within the SAM, however, dramatically change the electrical performance in terms of threshold voltage and mobility. This thesis reviews the SAM treatment and explains why there is a substantial change in threshold voltage. During the fabrication, reactive agents can also reside at the interface between the semiconductor and the dielectric layer. Their chemical and structural effects are minor but their effect on electrical performance can be significant. This problem is studied using spectral photocurrent and $1/f$ noise measurement by comparing OFETs whose polymer gate dielectric is exposed to UV ozone prior to semiconductor deposition with control OFETs whose semiconductor/dielectric interface is produced in a nearly oxygen-free environment. Both of the techniques have shown that the interfacial trapping sites created by oxygen treatment play an important role in electrical performance. One approach developed to improve the performance of bottom contact source/drain electrodes is to treat the contacts with thiols before deposition of the semiconductor. Especially suggestive evidence shows that thiols that increase the effective work function of the contacts (textsl{e.g.} fluorinatedthiols) yield better device performance than work function decreasing thiols (textsl{e.g.} alkane thiols). We compare two technologically relevant thiol treatments, an alkane thiol (1-hexadecanethiol), and a fluorinated thiol (pentafluorobenzenethiol), in pentacene organic field effect transistors. Using textit{in-situ} semiconductor deposition, X-ray photoemission, and X-ray absorption spectroscopy, we were able to directly observe the interaction between the semiconductor and the thiol-treated gold layers. Our spectroscopic analysis suggests that there is not a site-specific chemical reaction between the pentacene and the thiol molecules. A homogeneous standing-up pentacene orientation was observed in both treated substrates, consistent with the morphological improvement expected from thiol treatment in both samples.Our study shows that both the HOMO-Fermi level offset and C $1s$ binding energy are shifted in the two thiol systems, which can be explained by varied dipole direction within the two thiols, causing a change in surface potential. The additional improvement of the electrical performance in the pentafluorobenzenethiol case is originated by a reduced hole injection barrier that is also associated with an increase of the density of states in the LUMO. In OFETs, the accumulated charges are not evenly distributed along the channel especially when the OFETs are operated in the saturation region, where the drain side has much fewer accumulated charges than the source side due to the cancellation of effective gate voltage by the drain voltage. Thus the carriers should be less mobile on the drain side where the trap states are filled less adequately, and one should expect a varied mobility across the channel. For the same reason, the saturation current formula $I_{DS} = frac{W}{2L}mu C_{i}(V_{GS}-V_{th})^{2}$ for silicon MOSFETs is not suitable for OFETs, and the mobility calculation based on linear fitting of $sqrt{I_{DS}}$ to $V_{GS}$ is problematic. In the last part of this thesis, I have reviewed the curve fitting method and quasi-static capacitance-voltage (QSCV) method for deriving linear mobility in OFETs. Further, we have measured spatially resolved photocurrent in OFETs operated in the linear and saturation regions. Because the photogenerated charge is constant as a function of bias, spatially resolved photocurrent measurement locally measures the product of channel field and mobility. This product can be used to derive the local mobility across the channel. Our results directly show that in the saturation region, mobility decreases from source contact to drain contact due to the decreased density of carriers on the drain side.Materials science, Electrical engineeringzj2108Materials Science and Engineering, Electrical Engineering, Applied Physics and Applied MathematicsDissertationsGPU-based, Microsecond Latency, Hecto-Channel MIMO Feedback Control of Magnetically Confined Plasmas
http://academiccommons.columbia.edu/catalog/ac:155493
Rath, Nikolaushttp://hdl.handle.net/10022/AC:P:15779Mon, 14 Jan 2013 15:39:32 +0000Feedback control has become a crucial tool in the research on magnetic confinement of plasmas for achieving controlled nuclear fusion. This thesis presents a novel plasma feedback control system that, for the first time, employs a Graphics Processing Unit (GPU) for microsecond-latency, real-time control computations. This novel application area for GPU computing is opened up by a new system architecture that is optimized for low-latency computations on less than kilobyte sized data samples as they occur in typical plasma control algorithms. In contrast to traditional GPU computing approaches that target complex, high-throughput computations with massive amounts of data, the architecture presented in this thesis uses the GPU as the primary processing unit rather than as an auxiliary of the CPU, and data is transferred from A-D/D-A converters directly into GPU memory using peer-to-peer PCI Express transfers. The described design has been implemented in a new, GPU-based control system for the High-Beta Tokamak -- Extended Pulse (HBT-EP) device. The system is built from commodity hardware and uses an NVIDIA GeForce GPU and D-TACQ A-D/D-A converters providing a total of 96 input and 64 output channels. The system is able to run with sampling periods down to 4 μs and latencies down to 8 μs. The GPU provides a total processing power of 1.5 x 10^12 floating point operations per second. To illustrate the performance and versatility of both the general architecture and concrete implementation, a new control algorithm has been developed. The algorithm is designed for the control of multiple rotating magnetic perturbations in situations where the plasma equilibrium is not known exactly and features an adaptive system model: instead of requiring the rotation frequencies and growth rates embedded in the system model to be set a priori, the adaptive algorithm derives these parameters from the evolution of the perturbation amplitudes themselves. This results in non-linear control computations with high computational demands, but is handled easily by the GPU based system. Both digital processing latency and an arbitrary multi-pole response of amplifiers and control coils is fully taken into account for the generation of control signals. To separate sensor signals into perturbed and equilibrium components without knowledge of the equilibrium fields, a new separation method based on biorthogonal decomposition is introduced and used to derive a filter that performs the separation in real-time. The control algorithm has been implemented and tested on the new, GPU-based feedback control system of the HBT-EP tokamak. In this instance, the algorithm was set up to control four rotating n=1 perturbations at different poloidal angles. The perturbations were treated as coupled in frequency but independent in amplitude and phase, so that the system effectively controls a helical n=1 perturbation with unknown poloidal spectrum. Depending on the plasma's edge safety factor and rotation frequency, the control system is shown to be able to suppress the amplitude of the dominant 8 kHz mode by up to 60% or amplify the saturated amplitude by a factor of up to two. Intermediate feedback phases combine suppression and amplification with a speed up or slow down of the mode rotation frequency. Increasing feedback gain results in the excitation of an additional, slowly rotating 1.4 kHz mode without further effects on the 8 kHz mode. The feedback performance is found to exceed previous results obtained with an FPGA- and Kalman-filter based control system without requiring any tuning of system model parameters. Experimental results are compared with simulations based on a combination of the Boozer surface current model and the Fitzpatrick-Aydemir model. Within the subset of phenomena that can be represented by the model as well as determined experimentally, qualitative agreement is found.Plasma physics, Computer sciencenr2303Applied Physics and Applied MathematicsDissertationsTropical Cyclone Risk Assessment Using Statistical Models
http://academiccommons.columbia.edu/catalog/ac:168327
Yonekura, EmmiFri, 14 Dec 2012 15:15:19 +0000Tropical cyclones (TC) in the western North Pacific (WNP) pose a serious threat to the coastal regions of Eastern Asia when they make landfall. The limited amount of observational data and the high computational cost of running TC-permitting dynamical models indicate a need for statistical models that can simulate large ensembles of TCs in order to cover the full range of possible activity that results from a given climate change. I construct and apply a statistical track model from the 1945-2007 observed "best tracks" in the IBTrACS database for the WNP. The lifecycle components--genesis, track propagation, and death--of each simulated track is determined stochastically based on the statistics of historical occurrences. The length scale that dictates what historical data to consider as "local" for each lifecycle component is calculated objectively through optimization. Overall, I demonstrate how a statistical model can be used as a tool to translate climate-induced changes in TC activity into implications for risk.
In contrast to other studies, I show that the El Niño/Southern Oscillation (ENSO) has an effect on track propagation separate from the genesis effect. The ENSO effect on genesis results in higher landfall rates during La Niña years due to the shift in genesis location to the northeast. The effect on tracks is more geographically and seasonally varied due to local changes in the mid-level winds. I use local regression techniques to capture the relationship between ENSO, cyclogenesis, and track propagation. Stationary climate simulations are run for extreme ENSO states in order to better understand changes in TC activity and their implication for regional landfall. Additionally, Several diagnostics are performed on model realizations of the historical period, confirming the model's ability to capture the geographical distribution and interannual variability of observed TCs.
Lastly, as a step to connect synthetic TC track simulations to economic damage risk assessment, I use a Damage Index and total damage data for U.S. landfalling hurricanes and fit generalized Pareto distributions (GPD) to them. The Damage Index uniquely separates out the effects of the physical damage capacity of a TC and the local economic vulnerability of a coastal region. GPD fits are also performed using covariates in the scale parameter, where bathymetric slope and landfall intensity are found to be useful covariates for the Damage Index. Using the Damage Index with covariates model, two examples are shown of assessing damage risk for different climates. The first takes landfall data input from a statistical-deterministic TC model downscaled from GFDL and ECHAM model current and future climates. The second takes landfall data from a fully statistical track model with different values of relative sea surface temperature given as a statistical predictor.Atmospheric sciences, Statistics, Climate changeey2111Earth and Environmental Sciences, Applied Physics and Applied Mathematics, Goddard Institute for Space StudiesDissertationsTropical Cyclone Risk Assessment Using Statistical Models
http://academiccommons.columbia.edu/catalog/ac:167904
Yonekura, EmmiMon, 26 Nov 2012 10:36:56 +0000Tropical cyclones (TC) in the western North Pacific (WNP) pose a serious threat to the coastal regions of Eastern Asia when they make landfall. The limited amount of observational data and the high computational cost of running TC-permitting dynamical models indicate a need for statistical models that can simulate large ensembles of TCs in order to cover the full range of possible activity that results from a given climate change. I construct and apply a statistical track model from the 1945-2007 observed "best tracks" in the IBTrACS database for the WNP. The lifecycle components--genesis, track propagation, and death--of each simulated track is determined stochastically based on the statistics of historical occurrences. The length scale that dictates what historical data to consider as "local" for each lifecycle component is calculated objectively through optimization. Overall, I demonstrate how a statistical model can be used as a tool to translate climate-induced changes in TC activity into implications for risk.In contrast to other studies, I show that the El Niño/Southern Oscillation (ENSO) has an effect on track propagation separate from the genesis effect. The ENSO effect on genesis results in higher landfall rates during La Niña years due to the shift in genesis location to the northeast. The effect on tracks is more geographically and seasonally varied due to local changes in the mid-level winds. I use local regression techniques to capture the relationship between ENSO, cyclogenesis, and track propagation. Stationary climate simulations are run for extreme ENSO states in order to better understand changes in TC activity and their implication for regional landfall. Additionally, Several diagnostics are performed on model realizations of the historical period, confirming the model's ability to capture the geographical distribution and interannual variability of observed TCs. Lastly, as a step to connect synthetic TC track simulations to economic damage risk assessment, I use a Damage Index and total damage data for U.S. landfalling hurricanes and fit generalized Pareto distributions (GPD) to them. The Damage Index uniquely separates out the effects of the physical damage capacity of a TC and the local economic vulnerability of a coastal region. GPD fits are also performed using covariates in the scale parameter, where bathymetric slope and landfall intensity are found to be useful covariates for the Damage Index. Using the Damage Index with covariates model, two examples are shown of assessing damage risk for different climates. The first takes landfall data input from a statistical-deterministic TC model downscaled from GFDL and ECHAM model current and future climates. The second takes landfall data from a fully statistical track model with different values of relative sea surface temperature given as a statistical predictor.Atmospheric sciences, Statistics, Climate changeey2111Earth and Environmental Sciences, Applied Physics and Applied MathematicsDissertationsMixed-Phase Solidification of of Thin Silicon Films on Silicon Dioxide
http://academiccommons.columbia.edu/catalog/ac:153534
Chahal, Monicahttp://hdl.handle.net/10022/AC:P:14983Wed, 17 Oct 2012 11:37:46 +0000In this thesis, we present a new beam-induced melt-mediated crystallization process called mixed-phase solidification (MPS) that can produce defect-free, large-grain polycrystalline-Si films with strong (100)-surface texture (>99%) on SiO2. Such a combination of microstructural attributes makes the resulting MPS material well-suited for high-performance electronic and photovoltaic applications. The MPS method was conceived based on a well-known phenomenon of coexisting solid-liquid regions in radiatively-melted Si films on SiO2. Through our investigations, we have discovered that multiple exposures (of an initially amorphous precursor) in air within the solid-liquid coexistence regime can lead to the generation of such a material. In the course of this thesis, we have also identified the optimal processing conditions for obtaining such a microstructure, as well as the physical factors that control the process. A systematic parametric study of the single- and multi-scan MPS process is performed using thin Si films on SiO2 irradiated via a continuous-wave (CW) laser system. We employ an in situ microscopic viewing system to directly observe and understand melting and solidification during the MPS process. Additionally, in order to investigate the grain boundary melting phenomenon, we have conducted "rapid-quench" demarcation experiments and established a one-to-one correspondence between the in situ data and the single-/multi-scan MPS processed microstructure. The experimental results show an incremental increase in grain size and (100)-surface texture with an increase in scan number. The grain size is found to reach an apparent soft saturation value as the number of scans increases. For a given number of scans, a decrease in power or an increase in velocity is found to decrease the grain size and (100)-surface texture. Increases in film thickness lead to an increase in grain size, but a reduction in (100)-surface texturing. Based on what we have experimentally observed, as well as what has been previously established regarding the radiative-melting of Si, we propose a thermodynamic model to account for the microstructural evolution observed in the MPS process (i.e., partial-melting and solidification of polycrystalline-Si films). The model is built on two fundamental considerations: (1) the near-equilibrium environment within which thermodynamic factors dominate the transitions, and (2) the dynamically balanced, yet continuously changing, thermal surroundings. According to our model, the physical melting-solidification sequence for an MPS cycle of polycrystalline-Si films can be described in terms of the melt being initiated first at grain boundaries, and melting and solidification subsequently proceeding primarily laterally at interface-location specific rates as determined by the local curvature and local temperature at a point in the solid/liquid interface. By analyzing the cross-sectional profile of solid/liquid interface, we correlate the local curvature of the interface to the solid-Si/SiO2 interfacial energy and the resulting local equilibrium melting temperature using the Gibbs-Thomson relationship. This local-interface-curvature analysis reveals how the anisotropic nature of the Si/SiO2 interfacial energy and the film thickness affect the surface texture evolution observed during the MPS processing of Si films on SiO2. Our model of MPS is noteworthy in that it is in contrast to the "variable-grain-melting-temperature" argument which has been previously invoked in order to explain similar observations of texture selection; we suggest that such an argument is not thermodynamically consistent, and furthermore, cannot account for the evolution of the microstructure observed in the multi-scan MPS of polycrystalline films. Based on (1) our understanding of the MPS process as interpreted by the above model, and (2) the experimental results, we have also deduced fundamental thermodynamic details of the system. Specifically, by scrutinizing the evolution of the distribution of solid surface orientations in the MPS processed samples, we have extracted the hierarchical order of the Si/SiO2 interfacial energies as a function of grain orientation. We propose, in accordance with our model, that the experimentally observed soft saturation grain size values can be determined from the considerations related to the stable coexistence of solid-liquid mixtures. We substantiate this argument by performing a Mullins- Sekerka-type interface-instability analysis. Specifically, the maximum allowed solid-liquid coexistence distances, which were calculated with an explicit consideration given to the accompanying emissivity changes, were found to correlate well to the experimentally measured grain size value obtained after multi-scan MPS processing. Also, we discuss certain factors encountered during the MPS process (such as slow solidification rates, stable interfaces, and the highly unusual inverted thermal profile) as being responsible for the formation of defect-free grains. Finally, recognizing that the MPS process requires neither the laser nor the scanning of a highly localized beam, we also demonstrate how the MPS process can potentially be implemented in a practical manner using an incoherent light source. Using a xenon-arc flash-lamp system we show how the MPS method can be liberated from the challenges and constraints that are associated with laser-based systems, and thus represents a potentially cost-effective and scalable option.Materials sciencemd2528Applied Physics and Applied Mathematics, Earth and Environmental Engineering, Materials Science and EngineeringDissertationsPulsed-Laser-Induced Melting and Solidification of Thin Metallic Films
http://academiccommons.columbia.edu/catalog/ac:153531
Choi, Min Hwanhttp://hdl.handle.net/10022/AC:P:14982Wed, 17 Oct 2012 11:30:45 +0000This thesis focused on investigating excimer-laser induced melting and solidification of thin metallic films on SiO2. Two distinct topics were pursued: (1) microstructural manipulation and optimization of Cu films via SLS of as-deposited Cu films on SiO2, and (2) investigation of oriented heterogeneous nucleation via complete melting and subsequent nucleation-initiated solidification of Ni films on SiO2. The work on SLS of Cu films is motivated in large part by the need to improve the properties of Cu films which, among other applications, constitute an essential element in the continued evolution of microelectronic products. The experiments we have conducted show clearly that the film can be, without much difficulty, melted and solidified using pulsed-laser irradiation. Based on the findings from a series of systematic single-shot experiments, we show that SLS can be properly implemented to obtain large-grained Cu films with controlled microstructures and restricted textures. The lateral growth distance was found to increase as a function of increasing incident energy density. This observation is consistent with the findings that were made previously using other materials, and basically indicates that lateral solidification continues until the interface is halted by the interfaces growing from nucleated solids, which are triggered within the liquid matrix ahead of the growing interface. Close examination of the laterally grown grains, which quickly develop 100 rolling direction crystallographic orientation texture due to occlusion of differently oriented grains, reveal, furthermore, that low-angle grain boundaries as well as twins can be generated during the growth. These intra-grain defects are found to appear in a systematic manner (as they are located at specific regions and observed under specific incident energy densities). Significantly longer lateral growth distances observed in Cu films (compared to that of Si films) was attributed to the fact that substantially higher growth rates are expected with simple metallic films at a given interfacial undercooling. The implementation of SLS using Cu films was accomplished quite effectively, as can be expected from the above lateral-growth-related results involving single-shot experiments. We were able to achieve a variety of large-grained, grain-boundary location and grain-orientation controlled Cu films via various SLS techniques. When performed optimally in accordance with the findings made in chapter 2, the resulting microstructure exhibits large grains, which are primarily devoid of intra-grain defects. For example, 2-shot SLS processed Cu films led to strong 100 rolling direction orientation, while avoiding the formation of low-angle grain boundaries and twin-boundaries. The highlight of SLS on Cu films correspond to a version of SLS (referred to as "2-Shot plus 2-Shot" SLS) in which the second 2-shot SLS is performed in the direction perpendicular to the first one. Through this approach, we were able to achieve grain-boundary-location controlled microstructure with a strong 100 orientation texture in all three dimensions (forming, effectively, an ultra-large quasi-single crystal material). Nucleation of solids in laser-quenched Ni films was investigated using EBSD analysis. The surface orientation analysis of nucleated grains obtained within the complete melting regime reveal a clear sign of texture. From these and additional findings from previous work involving Al films, we were able to conclude that systematic heterogeneous nucleation has taken place, and, furthermore, that oriented nucleation of the solids must have taken place. Although always suspected to be the case, it is typically extremely challenging to prove with certainty, in conventional nucleation experiments, that the mechanism of nucleation corresponds to that of a heterogeneous one. Furthermore, although it has been suspected theoretically for over 50 years, experimental results that clearly show that oriented nucleation actually transpires have not been obtained until our work involving Al films; the present findings involving Ni films further strengthen this conclusion as the Ni system removes some of the experimental uncertainties that are associated with Al films, and, furthermore, suggests that the process of oriented nucleation is a general and rather pervasive phenomenon. Additionally, it was observed that the selected orientation changed as a function of incident energy density; in the low energy density regime (above the completed melting threshold) {110}-surface texture was observed, while {111}-surface texture became more dominent at higher densities. Motivated by our experimental work involving Al and Ni that clearly indicates that oriented heterogeneous nucleation is a major path through which heterogeneous nucleation of solids occurs, we have also carried out a 2-dimensional Winterbottom-type thermodynamic analysis that can be used to obtain a better understanding of the phenomenon. In contrast to the previous work on the subject, we consider in our modelling the anisotropic nature of both the solid-liquid and solid-substrate interfacial energy; we advocate that this is the only physically consistent combination. The results show that oriented nucleation can be systematically accounted for as stemming from the expected anisotropic nature of the involved interfacial energies. Furthermore, the analysis also suggests possible reasons for observing a transition in surface texture from one orientation to another.Materials sciencemc2499Applied Physics and Applied Mathematics, Earth and Environmental EngineeringDissertationsLaser Crystallization of Silicon Thin Films for Three-Dimensional Integrated Circuits
http://academiccommons.columbia.edu/catalog/ac:153501
Ganot, Gabriel Sethhttp://hdl.handle.net/10022/AC:P:14972Wed, 17 Oct 2012 10:11:04 +0000The three-dimensional integration of microelectronics is a standard that has been actively pursued by numerous researchers in a variety of technical ways over the years. The primary aim of three-dimensional integration is to alleviate the well-known issues associated with device shrinking in conjunction with Moore's Law. In this thesis, we utilize laser-based and other melt-mediated crystallization techniques to create Si thin films that may be of sufficient microstructural quality for use in monolithic thin-film-based three-dimensional integrated circuits (3D-ICs). Beam-induced solidification of initially amorphous or polycrystalline Si films has been actively investigated over the years as an unconventional, yet often-effective, technical means to generate Si films with suitable microstructures for fabricating high-performance electronic devices. Two specific melt-mediated methods that are aimed at crystallizing Si thin films for 3D-ICs are presented. One is referred to as "advanced sequential lateral solidification (SLS)" while the other is referred to as "advanced mixed-phase solidification (MPS)" and we show that these approaches can provide a more 3D-IC-optimal microstructure than can be generated using previous deposition and/or crystallization-based techniques. Advanced SLS, as presented in this thesis, is a novel implementation of the previously-developed directional-SLS method, and is specifically aimed at addressing the microstructural non-uniformity issue that can be encountered in the directional solidification processing of continuous Si films. Films crystallized via the directional-SLS method, for instance, can contain physically distinct regions with varying densities of planar defects and/or crystallographic orientations. As a result, transistors fabricated within such films can potentially exhibit relatively poor device uniformity. To address this issue, we employ advanced SLS whereby Si films are prepatterned into closely-spaced, long, narrow stripes that are then crystallized via directional-SLS in the long-axis-direction of the stripe length. By doing so, one can create microstructurally distinct regions within each stripe, which are then placed within the active channel region of a device. It is shown that when the stripes are sufficiently narrow (less than 2 µm), a bi-crystal microstructure is observed. This is explained based on the change in the interface morphology as a consequence of enhanced heat flow at the edges of the stripe. It is suggested that this bi-crystal formation is beneficial to the approach, as it increases the effective number of stripes within the active channel region. One issue of fundamental and technological significance that is nearly always encountered in laser crystallization is the formation of structural defects, in general, and in particular, twins. Due to the importance of reducing the density of these defects in order to increase the performance of transistors, this thesis investigates the formation mechanism of twins in rapidly laterally solidified Si thin films. These defects have been characterized and examined in the past, but a physically consistent explanation has not yet been provided. To address this situation, we have carried out experiments using a particular version of SLS, namely dot-SLS. This specific technique is chosen because we identify that it is endowed with a fortuitous combination of experimental factors that enable the systematic examination of twinning in laterally grown Si thin films. Based on extensive microstructural analysis of dot-SLS-crystallized regions, we propose that it is the energetics associated with forming a new atomic layer (during growth) in either a twinned or non-twinned configuration heterogeneously at the oxide/film interface that dictate the formation (or absence) of twins. The second method presented in this thesis is that of advanced MPS. The basic MPS approach was originally conceived as a way to generate Si films for solar cells as it is capable of producing large, intragrain-defect-free regions that are predominantly (100) surface-textured. However, the location of the grain boundaries of these equiaxed grains is essentially random, and hence, transistors placed within the interior of the grains would exhibit differing performance compared to those that are place across the grain boundaries. To address this, advanced MPS is introduced and demonstrated as a means to manipulate solidification by seeding from {100} surface-oriented regions and to induce limited directional growth. This is accomplished using a continuous-wave laser with a Gaussian-shaped beam profile wherein a central, completely molten region is surrounded by a ``mixed-phase-region'' undergoing MPS. The technique creates quasi-directional material that consists of large, elongated, parallel, {100} surface-oriented grains. This material is an improvement over previously generated directionally solidified materials, and can allow one to build devices without high angle grain boundaries that are within, and oriented perpendicular to, the active channel. The resulting microstructure is explained in terms of the non-uniform energy density distribution generated by the Gaussian-shaped laser beam, and the corresponding shape and growth of the solid/liquid interface. Based on the observations and considerations from these results, we propose and demonstrate a related scheme whereby a flash-lamp annealing system is utilized in order to induce the advanced MPS condition. This method can potentially time-efficiently crystallize, and create in the process, well-defined regions that are microstructurally suitable for the fabrication of 3D-ICs.Materials sciencegsg2107Applied Physics and Applied Mathematics, Earth and Environmental Engineering, Materials Science and EngineeringDissertationsFabrication and Characterization of Optoelectronics Devices Based on III-V Materials for Infrared Applications by Molecular Beam Epitaxy
http://academiccommons.columbia.edu/catalog/ac:153295
Al Torfi, Aminhttp://hdl.handle.net/10022/AC:P:14908Thu, 11 Oct 2012 16:32:50 +0000Optoelectronic devices based on III-V materials operating in infrared wavelength range have been attracting intensive research effort due to their applications in optical communication, remote sensing, spectroscopy, and environmental monitoring. The novel semiconductor lasers and photodetectors structures and materials investigated in this thesis cover the spectral range from 1.3µm to 12µm. This spectral region includes near-infrared (NIR), mid-infrared (MIR) and long wavelength infrared. This thesis demonstrated infrared optoelectronic devices, based on III-V compound semiconductors grown by Molecular Beam Epitaxy (MBE,) utilizing various combinations of novel III-V materials, device structures and substrate orientations. This thesis will be presented in two parts; the first part focuses on two types of photodetectors; type-II InAs/GaSb superlattice IR detector and AlGaAsSb/InGaAsSb mid-infrared heterojunction p-i-n photodetector. The second part of this thesis focuses on the three types of quantum well (QW) lasers; phosphor-free1.3µm InAlGaAs strain-compensated multiple-quantum-well (SCMQW) lasers on InP (100), InGaAsNSb/GaAs quantum wells (QWs) grown on GaAs (411)A substrates and mid-infrared InGaAsSb lasers with digitally grown tensile-strained AlGaAsSb barriers. Type-II InAs/GaSb superlattice IR detectors with various spectral ranges were grown by MBE. Two superlattice structures with 15 monolayers (ML) of InAs/12ML GaSb and 17ML InAs/7ML GaSb are discussed. Based on X-ray diffraction (XRD) measurements both InAs/GaSb superlattices exhibit excellent material qualities with the full width at half maximum (FWHM) of the 0th-order peak about 20arcsec, which is among the narrowest ever reported. The 50% cutoff wavelengths at 80K of the two photodiodes with 15ML InAs/12ML GaSb and 17ML InAs/7ML GaSb superlattices are measured to be 10.2 µm and 6.6 µm, respectively. Mid-infrared heterojunction p-i-n photodetector, AlGaAsSb/InGaAsSb lattice-matched to GaSb grown by solid source molecular beam epitaxy using As and Sb valved crackers greatly facilitated the lattice-matching of the quaternary InGaAsSb absorbing layer to the GaSb substrates, as characterized by X-ray diffraction. The resulting device exhibited low dark current and a breakdown voltage of 32V at room temperature. A record Johnson-noise-limited detectivity of 9.0 × [10]^10 cm Hz^(1/2)/W was achieved at 290K. The 50% cutoff wavelength of the device was 2.57 µm. Thus, our result has clearly demonstrated the potential of very high-performance lattice-matched InGaAsSb p-i-n photodetectors for mid-infrared wavelengths. For phosphor-free1.3 µm InAlGaAs multiple-quantum-well (MQW) lasers, the substrate temperature has been found to be a critical growth parameter for lattice-matched InAl(Ga)As layers in the laser structures. As shown by X-ray diffraction measurements, in the temperature range of 485-520° C, spontaneously ordered superlattices (SLs) with periods around 7-10 nm were formed in the bulk InAl(Ga)As layers. Based on photoluminescence (PL) measurements, a large band gap reduction of 300 meV and a broadened PL peak were observed for the In_0.52 Al_0.48 As layers with SL, as compared to those without SL. The undesirable, spontaneously-ordered SL can be avoided by using MBE growth temperatures higher than 530 °C. This results in a high laser performance. Threshold-current density as low as 690 A/cm² and T_0 as high as 80 K were achieved for InAlGaAs laser bars emitting at 1310 nm. InGaAsNSb/GaAs QWs on GaAs (411)A exhibited remarkably enhanced photoluminescence efficiency compared with the same structures on conventional GaAs (100) substrates. It was further observed that the optimum growth temperature for (411)A was 30 °C higher than that for (100). To explain this phenomenon, a model based on the self-assembling of local rough surface domains into a unique global smooth surface at the lowest energy state of the system is proposed. Lastly, the digital-growth approach for tensile-strained AlGaAsSb barriers improved the reliability and controllability of MBE growth for the MQW active region in the mid-infrared InGaAsSb quantum well lasers. The optical and structural qualities of InGaAsSb MQW were improved significantly, as compared to those with random-alloy barriers due to the removal of growth interruption at the barrier/well interfaces in digital growth. As a result, high-performance devices were achieved in the InGaAsSb lasers with digital AlGaAsSb barriers. A low threshold current density of 163 A/cm² at room temperature was achieved for 1000-µm-long lasers emitting at 2.38 µm. An external differential quantum efficiency as high as 61% was achieved for the 880-µm-long lasers, the highest ever reported for any lasers in this wavelength range.Electrical engineering, Optics, Physicsaa2227Electrical Engineering, Applied Physics and Applied MathematicsDissertationsSearch for Excited Randall-Sundrum Gravitons with Semi-Leptonic Diboson Final States in 4.7 fb-1 of Proton-Proton Collisions using the ATLAS Detector at the Large Hadron Collider
http://academiccommons.columbia.edu/catalog/ac:153207
Williams, Eric Lloydhttp://hdl.handle.net/10022/AC:P:14878Wed, 10 Oct 2012 13:43:02 +0000This dissertation describes a search for resonant WW and WZ production in the lvjj decay channel using 4.701 fb-1 of sqrt(s) = 7 TeV LHC collision data collected by the ATLAS detector. Events with a single charged lepton, at least two jets and missing transverse energy are analyzed and no significant deviation from the Standard Model prediction is observed. Upper limits on the production cross section are interpreted as lower limits on the mass of a resonance and are derived assuming two warped extra-dimension production modes: the original Randall-Sundrum (RS1) model and the more recent "bulk" Randal-Sundrum (Bulk RS) model. The mass range for both models is excluded at 95% CL with a lower mass limit for an RS1 graviton of 936 GeV and 714 GeV for the Bulk RS graviton.Particle physicselw2113Applied Physics and Applied Mathematics, PhysicsDissertationsMultimode Structure of Resistive Wall Modes near the Ideal Wall Stability Limit
http://academiccommons.columbia.edu/catalog/ac:150384
Levesque, Jeffrey Peterhttp://hdl.handle.net/10022/AC:P:14171Fri, 20 Jul 2012 16:58:00 +0000This thesis presents the first systematic study of multimode external kink structure and dynamics in a tokamak using a high-resolution magnetic sensor set. Multimode effects are directly measured, rather than inferred from anomalies in single-mode behavior. In order to accomplish this, an extensive set of 216 poloidal and radial magnetic field sensors has been installed in the High Beta Tokamak -- Extended Pulse (HBT-EP) device for high-resolution measurements of three-dimensional mode activity. An analysis technique known as biorthogonal decomposition (BD) is described, and simulations are presented to justify its use for studying kink mode dynamics in HBT-EP data. Coherent activity of multiple simultaneous modes is observed using the BD without needing to define a mode structure basis beforehand. Poloidal mode numbers up to m=8 are observed via sensor arrays with full 360 degree coverage. Higher poloidal mode numbers are suggested by the data, but cannot be well-resolved with the available diagnostics. Toroidal mode numbers up to n=4 are observed. Non-rigid, multimode activity is observed for coexisting external kinks having m/n=3/1 and 6/2 structures. Despite sharing the same helicity and same resonant surface, rotation of 6/2 modes is independent of 3/1 mode rotation -- the n=2 mode does not simply rotate with double the frequency of the n=1 mode. During periods of 3/1-dominated activity, the 6/2 mode is observed to modulate the 3/1 amplitude, and in brief instances can overpower the 3/1. Statistical analysis over many shots reveals the multimode nature of the 3/1 kink to be more significant when the resonant q=3 surface begins internal, then is ejected from the plasma. This inference is based on the relative amplitudes of secondary modes during 3/1-dominated activity, as well as spectral content of the modes. Conformal conducting wall segments were also retracted away from the plasma surface using low-order poloidal and toroidal asymmetries to excite measurable differences in low m- and n-number modes. Kink mode amplitudes increase as the wall segments are withdrawn, and non-symmetric wall configurations modulate the amplitude and frequency of the rotating modes depending upon their toroidal orientation with respect to the non-symmetric wall. Modulations of mode amplitude and rotation are larger for the toroidal wall asymmetry than for the poloidal wall asymmetry.Plasma physicsjpl2131Applied Physics and Applied MathematicsDissertationsDynamics of Melt-mediated Crystallization of Amorphous Silicon Films
http://academiccommons.columbia.edu/catalog/ac:149824
Hu, Qiongyinghttp://hdl.handle.net/10022/AC:P:14058Mon, 16 Jul 2012 10:52:40 +0000This thesis reports on the new experimental findings and the corresponding conclusions that were made regarding the pulsed-laser-induced melting-and-solidification behavior of a-Si films. In particular, it focuses on investigating the melt-mediated crystallization details that are associated with the a-Si films, which presumably do not contain preexisting microcrystal clusters (as for instance can be formed via high-dose ion-irradiation of Si wafers and PECVD deposition of a-Si films). Whereas the behavior of microcrystalline-cluster-containing a-Si films within the partial-melting regime was well characterized and accounted for [1], a more intrinsic, and, therefore, more fundamentally important situation involving microcrystalline-cluster-deficient a-Si films in the partial melting regime has yet to be definitively resolved. The present thesis addresses this unsatisfactory situation. The samples used in this work consisted of 50nm to 200nm dehydrogenated PECVD a-Si films (with or without additional ion irradiation of the films) on SiO2-coated glass and quartz substrate. Single-shot irradiation experiments using an excimer-laser-based system were conducted at various pulse durations (30ns-Gaussian-profile beam to 250ns beam obtained via an optical pulse duration extender) and at various energy densities. Extensive in situ transformation analysis was performed using both front-side and back-side transient reflectance measurements also microstructural characterization of the irradiated films was conducted using TEM and AFM. The experimental findings obtained in this investigation reveal that these a-Si films can melt and solidify in ways that are quite distinct, more varied, and highly complex compared to those encountered in microcrystalline-cluster-rich a-Si films. Specifically: (1) spatially dispersed and temporally stochastic nucleation of crystalline solids occurring relatively effectively at the moving liquid-amorphous interface, (2) very defective crystal growth that leads to the formation of fine-grained Si proceeding, at least initially after the nucleation, at a sufficiently rapidly moving crystal solidification front, and (3) the propensity for local preferential re-melting of the defective regions and grain boundaries (while the beam is still on) are some of the fundamental factors that can participate and affect how these films melt and solidify. We discuss, by providing an extensive and critical review of the relevant papers, how the present conclusions are fundamentally distinct from those that have been made by the previous investigators in the field. The implications of these findings on the conventional ELA (i.e., excimer-laser annealing) method as well as the possibility of developing partial-melting-regime-based ultra-high-throughput crystallization methods are also discussed.Chemistry, Materials scienceChemistry, Applied Physics and Applied Mathematics, Earth and Environmental EngineeringDissertationsHigh-Resolution MHD Spectroscopy of External Kinks in a Tokamak Plasma
http://academiccommons.columbia.edu/catalog/ac:147680
Shiraki, Daisukehttp://hdl.handle.net/10022/AC:P:13437Thu, 07 Jun 2012 13:57:26 +0000This thesis describes the first results of passive and active MHD spectroscopy experiments on the High Beta Tokamak-Extended Pulse (HBT-EP) device using a new array of magnetic diagnostics and coils. The capabilities of the HBT-EP experiment are significantly extended with the installation of a new adjustable conducting wall, high-power modular control coil arrays, and an extensive set of 216 magnetic sensors that allow simultaneous high-resolution detection of multimode MHD phenomena. The design, construction, and calibration of this system are described. The capability of this new magnetic diagnostic set is demonstrated by biorthogonal decomposition analysis of passive measurements of rotating resistive wall modes (RWMs). A strong multimode effect is detected for the first time in HBT-EP plasmas consisting of the simultaneous existence of m/n=3/1 and 6/2 RWMs which cause the plasma to evolve in a non-rigid multimode manner. Additional mode numbers as high as n=3 are also observed. Active MHD spectroscopy experiments using a "phase-flip" resonant magnetic perturbation (RMP) are able to excite a clear three-dimensional response. By adjusting the helicity of the magnetic field applied by the control coils, the driven plasma response is shown to be predominantly resonant field amplification. When the amplitude of the applied field is not too large, the driven resonant response appears linear, independent of the presence of background MHD phenomena and consistent with the predictions of single-helicity modeling of kink mode dynamics. The spatial structures of both the naturally rotating kink mode and the externally driven response are observed to be identical, while the temporal evolutions are approximately independent. The phase-flip driven plasma response is measured as a function of edge safety factor, plasma rotation, and the amplitude of the applied magnetic perturbation. As the RMP amplitude increases, the plasma response is shown to be linear, saturated, and ultimately, disruptive.Plasma physicsds2552Applied Physics and Applied MathematicsDissertationsTaming unstable inverse problems: Mathematical routes toward high-resolution medical imaging modalities
http://academiccommons.columbia.edu/catalog/ac:146713
Monard, Francoishttp://hdl.handle.net/10022/AC:P:13162Mon, 07 May 2012 14:47:05 +0000This thesis explores two mathematical routes that make the transition from some severely ill-posed parameter reconstruction problems to better-posed versions of them. The general introduction starts by defining what we mean by an inverse problem and its theoretical analysis. We then provide motivations that come from the field of medical imaging. The first part consists in the analysis of an inverse problem involving the Boltzmann transport equation, with applications in Optical Tomography. There we investigate the reconstruction of the spatially-dependent part of the scattering kernel, from knowledge of angularly averaged outgoing traces of transport solutions and isotropic boundary sources. We study this problem in the stationary regime first, then in the time-harmonic regime. In particular we show, using techniques from functional analysis and stationary phase, that this inverse problem is severely ill-posed in the former setting, whereas it is mildly ill-posed in the latter. In this case, we deduce that making the measurements depend on modulation frequency allows to improve the stability of reconstructions. In the second part, we investigate the inverse problem of reconstructing a tensor-valued conductivity (or diffusion) coefficient in a second-order elliptic partial differential equation, from knowledge of internal measurements of power density type. This problem finds applications in the medical imaging modalities of Electrical Impedance Tomography and Optical Tomography, and the fact that one considers power densities is justified in practice by assuming a coupling of this physical model with ultrasound waves, a coupling assumption that is characteristic of so-called hybrid medical imaging methods. Starting from the famous Calderon's problem (i.e. the same parameter reconstruction problem from knowledge of boundary fluxes of solutions), and recalling its lack of injectivity and severe instability, we show how going from Dirichlet-to-Neumann data to considering the power density operator leads to reconstruction of the full conductivity tensor via explicit inversion formulas. Moreover, such reconstruction algorithms only require the loss of either zero or one derivative from the power density functionals to the unknown, depending on what part of the tensor one wants to reconstruct. The inversion formulas are worked out with the help of linear algebra and differential geometry, in particular calculus with the Euclidean connection. The practical pay-off of such theoretical improvements in injectivity and stability is twofold: (i) the lack of injectivity of CalderÃ³n's problem, no longer existing when using power density measurements, implies that future medical imaging modalities such as hybrid methods may make anisotropic properties of human tissues more accessible; (ii) the improvements in stability for both problems in transport and conductivity may yield practical improvements in the resolution of images of the reconstructed coefficients.Mathematics, Medical imaging and radiologyfm2234Applied Physics and Applied MathematicsDissertationsTransit Dosimetry for Patient Treatment Verification with an Electronic Portal Imaging Device
http://academiccommons.columbia.edu/catalog/ac:146689
Berry, Sean Lawrencehttp://hdl.handle.net/10022/AC:P:13155Mon, 07 May 2012 10:46:35 +0000\The complex and individualized photon fluence patterns constructed during intensity modulated radiation therapy (IMRT) treatment planning must be verified before they are delivered to the patient. There is a compelling argument for additional verification throughout the course of treatment due to the possibility of data corruption, unintentional modification of the plan parameters, changes in patient anatomy, errors in patient alignment, and even mistakes in identifying the correct patient for treatment. Amorphous silicon (aSi) Electronic Portal Imaging Devices (EPIDs) can be utilized for IMRT verification. The goal of this thesis is to implement EPID transit dosimetry, measurement of the dose at a plane behind the patient during their treatment, within the clinical process. In order to achieve this goal, a number of the EPID's dosimetric shortcomings were studied and subsequently resolved. Portal dose images (PDIs) acquired with an aSi EPID suffer from artifacts related to radiation backscattered asymmetrically from the EPID support structure. This backscatter signal varies as a function of field size (FS) and location on the EPID. Its presence can affect pixel values in the measured PDI by up to 3.6%. Two methods to correct for this artifact are offered: discrete FS specific correction matrices and a single generalized equation. The dosimetric comparison between the measured and predicted through-air dose images for 49 IMRT treatment fields was significantly improved (p << .001) after the application of these FS specific backscatter corrections. The formulation of a transit dosimetry algorithm followed the establishment of the backscatter correction and a confirmation of the EPID's positional stability with linac gantry rotation. A detailed characterization of the attenuation, scatter, and EPID response behind an object in the beam's path is necessary to predict transit PDIs. In order to validate the algorithm's performance, 49 IMRT fields were delivered to a number of homogeneous and heterogeneous slab phantoms. A total of 33 IMRT fields were delivered to an anthropomorphic phantom. On average, 98.1% of the pixels in the dosimetric comparison between the measured and predicted transit dose images passed a 3%/3mm gamma analysis. Further validation of the transit dosimetry algorithm was performed on nine human subjects under an institutional review board (IRB) approved protocol. The algorithm was shown to be feasible for patient treatment verification. Comparison between measured and predicted transit dose images resulted in an average of 89.1% of pixels passing a 5%/3mm gamma analysis. A case study illustrated the important role that EPID transit dosimetry can play in indicating when a treatment delivery is inconsistent with the original plan. The impact of transit dosimetry on the clinical workflow for these nine patients was analyzed to identify improvements that could be made to the procedure in order to ease widespread clinical implementation. EPID transit dosimetry is a worthwhile treatment verification technique that strikes a balance between effectiveness and efficiency. This work, which focused on the removal of backscattered radiation artifacts, verification of the EPID's stability with gantry rotation, and the formulation and validation of a transit dosimetry algorithm, has improved the EPID's dosimetric performance. Future research aimed at online transit verification would maximize the benefit of transit dosimetry and greatly improve patient safety.Physicsslb2006Applied Physics and Applied Mathematics, Radiation OncologyDissertationsAnalytical Solutions of the SABR Stochastic Volatility Model
http://academiccommons.columbia.edu/catalog/ac:174329
Wu, Qihttp://hdl.handle.net/10022/AC:P:12647Tue, 21 Feb 2012 11:54:55 +0000This thesis studies a mathematical problem that arises in modeling the prices of option contracts in an important part of global financial markets, the fixed income option market. Option contracts, among other derivatives, serve an important function of transferring and managing financial risks in today's interconnected financial world. When options are traded, we need to specify what the underlying asset an option contract is written on. For example, is it an option on IBM stock or on precious metal? Is it an option on Sterling-Euro exchange rate or on US dollar interest rates? Usually option markets are organized according to their underlying assets and they can be traded either on exchanges or over-the-counter. The scope of this thesis is the option markets on currency exchange rates and interest rates, which are less familiar to the general public than those of equities and commodities, and are mostly traded over-the-counter as bi-lateral agreements among large financial institutions such as investment banks, central banks, commercial banks, government agencies, and large corporations. Since early 1970's, the Black-Scholes-Merton option model has become the market standard of buying and selling standard option contracts of European style, namely calls and puts. Of particular importance is this ever more quantitative approach to the practice of option trading, in which the volatility parameter of the Black-Scholes-Merton's model has become the market "language'' of quoting option prices. Despite its tremendous success, the Black-Scholes-Merton model has exhibited a few well-known deficiencies, the most important of which are first, the assumption that the underlying asset is lognormally distributed and second, the volatility of the underlying asset's return is constant. In reality, the return distribution of an underlying asset can exhibit various level of tail behavior, ranging from "sub''-normal to normal, from lognormal to "super''-lognormal. Also the implied volatilities of liquidly traded options generally vary with both option strikes and option maturity. This variation with strike is termed the "volatility skew'' or the "volatility smile''. Naturally as market evolves, so does the model. People then start to look for the new standard. Among various successful extensions, models with constant elasticity of variance (CEV) prove to be able to generate enough range of return distributions while models with volatility itself being stochastic start to become popular in terms fitting the "smile'' or "skew'' phenomenon of option implied volatilities. In 2002, the combination of CEV model with stochastic volatility, particulary the SABR model, became the new market standard in fixed income option market. This is the starting point of this thesis. However, being the market standard also poses new challenges, which are speed and accuracy. Three mathematical aspects of the model prevent one from obtaining a strictly speaking closed form solution of its joint transition density, namely the nonlinearity from the CEV type local volatility function, the coupling between the underlying asset process and the volatility process, and finally the correlation between the two driving Brownian motions. We look at the problem from a PDE perspective where the joint transition density follows a linear second order equation of parabolic type in non-divergence form with coordinate-dependent coefficients. Particularly, we construct an expansion of the joint density through a hierarchy of parabolic equations after applying a financially justified scaling and a series of well designed transformations. We then derive accurate asymptotic formulas in both free-boundary conditions and absorbing-boundary conditions. We further establish an existence result to characterize the truncation error and examined extensively the derived formulas through various numerical examples. Finally we go back to the fixed income market itself and use our result to examine empirically whether today's option prices traded at different expiries contain information on predicting future levels of option prices, using ten-year over-the-counter FX option data from a major investment bank dealer desk. Our theoretical results for the joint density of the SABR model serve as a basis for banks and dealers to manage the forward smile risk of their fixed income option portfolio. Our empirical studies extend the forward concept from interest rate term structure modeling to interest rate volatility term structure modeling and examine the relationship between today's forward implied volatility and future spot implied volatility.Applied mathematics, Financeqw2107Applied Physics and Applied Mathematics, BusinessDissertationsNanomaterials from Nanocomponents: Synthesis and Properties of Hybrid Nanomaterials
http://academiccommons.columbia.edu/catalog/ac:144730
Akey, Austin Josephhttp://hdl.handle.net/10022/AC:P:12610Fri, 17 Feb 2012 14:55:08 +0000This thesis consists of two series of investigations into two different classes of hybrid nanomaterials, their formation and properties. In the first part of this thesis, hybrid nanomaterials composed of cadmium selenide nanoparticles and single-walled carbon nanotubes (SWNTs) are discussed; a novel synthetic method for these hybrids is presented, and an anomalous photoluminescence behavior is examined. Our experiments show that SWNTs can be decorated with CdSe nanoparticles at high loading densities, following the removal of the nanoparticle surface ligands and replacement with pyridine. The resulting hybrids are thermally stable up to 350ºC and mechanically stable against sonication. The photoluminescence Stokes shift in the bound nanoparticles is shown to be reduced relative to that of unbound nanoparticles. This difference is attributed to Forster resonance energy transfer from the nanoparticles to the nanotube, leading to hot luminescence in the nanoparticles. The second part of this thesis focuses on formation strategies and mechanisms for nanoparticle superlattices. Supercrystals, as they are called, are formed using lithographically-patterned reservoirs and capillary channels, giving control over both supercrystal dimensions and placement; these supercrystals form within a few hours, much faster than those previously reported. These results are extended to the formation of large-area (> 10 µm lateral dimension) thick (> 1 µm) supercrystals on substrates, and the formation mechanism probed by in situ small-angle x-ray scattering. Both monocomponent and binary supercrystals are examined.Materials science, PhysicsApplied Physics and Applied Mathematics, Materials Science and EngineeringDissertationsMidlatitude Storm Track Response to Increased Greenhouse Warming
http://academiccommons.columbia.edu/catalog/ac:144028
Wu, Yutianhttp://hdl.handle.net/10022/AC:P:12419Wed, 01 Feb 2012 12:38:53 +0000Storm tracks play a major role in regulating the precipitation and hydrological cycle in midlatitudes. The changes in the location and amplitude of the storm tracks in response to global warming will have significant impacts on the poleward transport of heat, momentum and moisture and on the hydrological cycle. Recent studies have indicated a poleward shift of the storm tracks and midlatitude precipitation zone in the warming world that will contribute to subtropical drying and higher latitude moistening. This dissertation is to investigate the storm track response to increased greenhouse warming and the dynamical mechanisms driving the changes in the storm tracks. First, by analyzing the eddy statistics simulated in the Geophysical Fluid Dynamics Laboratory (GFDL) CM2.1 model simulations (IPCC AR4 model), we confirm the poleward and upward shift and intensification of the storm tracks in the late 21st century. It has been found that this key feature is generally consistent with the change in Eady growth rate. Diagnosis of the latitude-by-latitude energy budget for the current and future climate demonstrates how the coupling between radiative and surface heat fluxes and eddy heat and moisture transport influences the midlatitude storm track response to global warming. Through radiative forcing by increased atmospheric carbon dioxide and water vapor, more energy is gained within the tropics and subtropics, while in the middle and high latitudes energy is reduced through increased outgoing terrestrial radiation in the Northern Hemisphere and increased ocean heat uptake in the Southern Hemisphere. This enhanced energy imbalance in the future climate requires larger poleward atmospheric energy transports in the midlatitudes which are partially accomplished by the intensified storm tracks. This strong connection between intensified storm track energy transports and intensified energy imbalance in the atmosphere is also confirmed in other IPCC AR4 models. We further explore the dynamical mechanisms inducing the changes in the general circulation of the atmosphere due to increased carbon dioxide (CO2) by looking into the transient step-by-step adjustment of the circulation. This allows an assessment of the causality sequence in the circulation and thermal structure response prior to establishment of a quasi-equilibrium state. The transient atmospheric adjustment is examined using the National Center for Atmospheric Research Community Atmospheric Model Version 3 coupled to a slab ocean model and the CO2 concentration in the atmosphere is uniformly and instantaneously doubled. The thermal structure and circulation response is well established after one year of integration with the magnitudes gradually increasing afterwards towards quasi-equilibrium. Tropical upper tropospheric warming occurs in the first month. The expansion of the warming in the middle and upper troposphere to the subtropics occurs later and is found to be primarily dynamically-driven due to the intensification of transient eddy momentum flux convergence and resulting anomalous descending motion in this region. This linkage between the eddy-driven vertical motion anomaly and the subtropical warming expansion in the middle and upper troposphere is also confirmed in the late 21st century in the IPCC AR4 simulations. The poleward displacement of the midlatitude tropospheric jet streams occurs together with the change in eddy momentum flux convergence but only after the intensification of the subpolar westerlies in the stratosphere. The results demonstrate the importance of the tropospheric eddies in setting up the extratropical tropospheric response to global warming. Our modeling results also show the sequence of the zonal wind anomaly in the vertical column of the atmosphere during the period of transient adjustment, indicating that the poleward displacement of the tropospheric jets follows the subpolar westerly anomaly in the stratosphere. It suggests the importance of the stratosphere and the coupling between the stratosphere and the troposphere in regulating the extratropical tropospheric circulation response to increasing CO2. Three phases are defined during this period of transient adjustment including a fast radiatively-induced thermal response in the stratosphere, a westerly acceleration in the stratosphere driven by stationary eddy anomaly, and a 'downward propagation' of westerly acceleration from the stratosphere to the troposphere followed by a poleward displacement of the tropospheric midlatitude jets. Diagnoses using wave spectra and linear index of refraction are used to understand the dynamics underlying the adjustment process.Applied mathematicsyw2225Applied Physics and Applied Mathematics, Earth Institute, Earth and Environmental SciencesDissertationsMidlatitude Storm Track Response to Increased Greenhouse Warming
http://academiccommons.columbia.edu/catalog/ac:161301
Wu, Yutianhttp://hdl.handle.net/10022/AC:P:12382Fri, 27 Jan 2012 15:27:50 +0000Storm tracks play a major role in regulating the precipitation and hydrological cycle in midlatitudes. The changes in the location and amplitude of the storm tracks in response to global warming will have significant impacts on the poleward transport of heat, momentum and moisture and on the hydrological cycle. Recent studies have indicated a poleward shift of the storm tracks and midlatitude precipitation zone in the warming world that will contribute to subtropical drying and higher latitude moistening. This dissertation is to investigate the storm track response to increased greenhouse warming and the dynamical mechanisms driving the changes in the storm tracks. First, by analyzing the eddy statistics simulated in the Geophysical Fluid Dynamics Laboratory (GFDL) CM2.1 model simulations (IPCC AR4 model), we confirm the poleward and upward shift and intensification of the storm tracks in the late 21st century. It has been found that this key feature is generally consistent with the change in Eady growth rate. Diagnosis of the latitude-by-latitude energy budget for the current and future climate demonstrates how the coupling between radiative and surface heat fluxes and eddy heat and moisture transport influences the midlatitude storm track response to global warming. Through radiative forcing by increased atmospheric carbon dioxide and water vapor, more energy is gained within the tropics and subtropics, while in the middle and high latitudes energy is reduced through increased outgoing terrestrial radiation in the Northern Hemisphere and increased ocean heat uptake in the Southern Hemisphere. This enhanced energy imbalance in the future climate requires larger poleward atmospheric energy transports in the midlatitudes which are partially accomplished by the intensified storm tracks. This strong connection between intensified storm track energy transports and intensified energy imbalance in the atmosphere is also confirmed in other IPCC AR4 models. We further explore the dynamical mechanisms inducing the changes in the general circulation of the atmosphere due to increased carbon dioxide (CO2) by looking into the transient step-by-step adjustment of the circulation. This allows an assessment of the causality sequence in the circulation and thermal structure response prior to establishment of a quasi-equilibrium state. The transient atmospheric adjustment is examined using the National Center for Atmospheric Research Community Atmospheric Model Version 3 coupled to a slab ocean model and the CO2 concentration in the atmosphere is uniformly and instantaneously doubled. The thermal structure and circulation response is well established after one year of integration with the magnitudes gradually increasing afterwards towards quasi-equilibrium. Tropical upper tropospheric warming occurs in the first month. The expansion of the warming in the middle and upper troposphere to the subtropics occurs later and is found to be primarily dynamically-driven due to the intensification of transient eddy momentum flux convergence and resulting anomalous descending motion in this region. This linkage between the eddy-driven vertical motion anomaly and the subtropical warming expansion in the middle and upper troposphere is also confirmed in the late 21st century in the IPCC AR4 simulations. The poleward displacement of the midlatitude tropospheric jet streams occurs together with the change in eddy momentum flux convergence but only after the intensification of the subpolar westerlies in the stratosphere. The results demonstrate the importance of the tropospheric eddies in setting up the extratropical tropospheric response to global warming. Our modeling results also show the sequence of the zonal wind anomaly in the vertical column of the atmosphere during the period of transient adjustment, indicating that the poleward displacement of the tropospheric jets follows the subpolar westerly anomaly in the stratosphere. It suggests the importance of the stratosphere and the coupling between the stratosphere and the troposphere in regulating the extratropical tropospheric circulation response to increasing CO2. Three phases are defined during this period of transient adjustment including a fast radiatively-induced thermal response in the stratosphere, a westerly acceleration in the stratosphere driven by stationary eddy anomaly, and a 'downward propagation' of westerly acceleration from the stratosphere to the troposphere followed by a poleward displacement of the tropospheric midlatitude jets. Diagnoses using wave spectra and linear index of refraction are used to understand the dynamics underlying the adjustment process.Applied mathematicsyw2225Applied Physics and Applied Mathematics, Earth and Environmental Sciences, Earth InstituteDissertationsForce and Conductance Spectroscopy of Single Molecule Junctions
http://academiccommons.columbia.edu/catalog/ac:143847
Frei, Michaelhttp://hdl.handle.net/10022/AC:P:12363Fri, 27 Jan 2012 12:41:35 +0000Investigation of mechanical properties of single molecule junctions is crucial to develop an understanding and enable control of single molecular junctions. This work presents an experimental and analytical approach that enables the statistical evaluation of force and simultaneous conductance data of metallic atomic point contacts and molecular junctions. A conductive atomic force microscope based break junction technique is developed to form single molecular junctions and collect conductance and force data simultaneously. Improvements of the optical components have been achieved through the use of a super luminescent diode, enabling tremendous increases in force resolution. An experimental procedure to collect data for various molecular junctions has been developed and includes deposition, calibration, and analysis methods. For the statistical analysis of force, novel approaches based on two dimensional histograms and a direct force identification method are presented. The two dimensional method allows for an unbiased evaluation of force events that are identified using corresponding conductance signatures. This is not always possible however, and in these situations, the force based identification of junction rearrangement events is an attractive alternative method. This combined experimental and analytical approach is then applied to three studies: First, the impact of molecular backbones to the mechanical behavior of single molecule junctions is investigated and it is found that junctions formed with identical linkers but different backbone structure result in junctions with varying breaking forces. All molecules used show a clear molecular signature and force data can be evaluated using the 2D method. Second, the effects of the linker group used to attach molecules to gold electrodes are investigated. A study of four alkane molecules with different linkers finds a drastic difference in the evolution of donor acceptor and covalently bonded molecules respectively. In fact, the covalent bond is found to significantly distort the metal electrode rearrangement such that junction rearrangement events can no longer be identified with a clean and well defined conductance signature. For this case, the force based identification process is used. Third, results for break junction measurements with different metals are presented. It is found that silver and palladium junctions rupture with forces different from those of gold contacts. In the case of silver experiments in ambient conditions, we can also identify oxygen impurities in the silver contact formation process, leading to force and conductance measurements of silver-oxygen structures. For the future, this work provides an experimental and analytical foundation that will enable insights into single molecule systems not previously accessible.Physics, Chemistrymf2433Applied Physics and Applied MathematicsDissertationsSpatial-Statistical Properties of Geochemical Variability as Constraints on Magma Transport and Evolution Processes at Ocean Ridges
http://academiccommons.columbia.edu/catalog/ac:143838
Collier, Martin Leehttp://hdl.handle.net/10022/AC:P:12359Fri, 27 Jan 2012 11:42:03 +0000The research presented in this thesis employs spatial and statistical properties of major element variability in basaltic lavas and mantle residues to constrain some of the processes and dynamics occurring beneath ocean ridge magmatic systems. Ocean ridges represent a critical setting for many geochemical fractionation processes involved in the chemical evolution of the silicate Earth, and are fundamental to the plate tectonic cycle. Because of the inherent inaccessibility, it remains an ongoing challenge to interpret the geochemistry of ocean ridge lavas and exposed mantle residues in order to extract information about the petrogenetic and geodynamic workings of ocean ridge magmatic systems. This endeavor continues to require a concerted effort, incorporating field work, laboratory experimentation and quantitative modeling, in which the identification of features in the spatial or statistical distribution of geochemical variability represents an important contribution. In the three main chapters of this thesis, I apply techniques of exploratory data analysis, computational statistics, and petrologic modeling to develop original ideas about the relationship between sampled major element variability and the effects of specific processes, both petrogenetic and scientific: crystallization, melt transport, and sampling. In Chapter 2, I use spatial patterns of mid-ocean ridge basalt (MORB) glass variability to test competing hypotheses about crystallization in the thermal boundary layer beneath ocean ridges. I develop the hypothesis that reactive crystallization (crystallization influenced by chemical exchange with surrounding peridotite) could result in a different geochemical evolution of crystallizing magmas than expected for fractional crystallization. According to this hypothesis, fractionation-corrected MORB variability could be caused largely by sample-to-sample variations in the relative extents of reactive versus fractional crystallization. I demonstrate that MORB major element variability observed within 30-km-scale spatial bins contains 40-70 percent of globally observed variability, consistent with the predicted effects of reactive crystallization, but inconsistent with mantle temperature variations. Chapter 3 considers the effect of spatially heterogeneous sampling on apparent variability in MORB glasses. I demonstrate that MORB variability, as represented by the PetDB MORB glass database, contains large variability in sampling density, leading to significant artifacts in the estimated relative frequency of different MORB compositions. I introduce a method for removing these artifacts, and show that the increase in MORB data availability over the past decades has not been sufficient to increase significantly the resolution with which major element variability systematics can be studied at global or regional length scales, at least in comparison to early syntheses of global MORB data. Chapter 4 examines statistical variability within spatially defined volumes of mantle residue exposed in the Oman ophiolite. I provide a preliminary map of intermediate-scale compositional variability within the southernmost Oman ophiolite massif, in which multiple, spatially coherent, compositionally distinctive, 20-100 sq. km regions are resolved, representing the first mapping of compositional mantle domains at this length scale anywhere in the world. I interpret the observations as the consequence of regionally distinctive internal proportions of different mantle lithologies (e.g., dunite versus harzburgite), in turn reflecting the organization of focused melt transport at mid-ocean ridges into channel-rich and channel-poor zones.Petrology, Geochemistrymlc2123Earth and Environmental Sciences, Applied Physics and Applied MathematicsDissertationsChip-scale Photonic Devices for Light-matter Interactions and Quantum Information Processing
http://academiccommons.columbia.edu/catalog/ac:143058
Gao, Jiehttp://hdl.handle.net/10022/AC:P:12160Tue, 10 Jan 2012 13:22:40 +0000Chip-scale photonic devices such as microdisks, photonic crystal cavities and slow-light photonic crystal waveguides possess strong light localization and long photon lifetime, which will significantly enhance the light-matter interactions and can be used to implement new functionalities for both classical and quantum information processing, optical computation and optical communication in integrated nanophotonic circuits. This thesis will focus on three topics about light matter interactions and quantum information processing with chip-scale photonic devices, including 1) Design and characterization of asymmetric resonate cavity with radiation directionality and air-slot photonic crystal cavity with ultrasmall effective mode volume, 2) Exciton-photon interactions between quantum dots and photonic crystal devices and non-classical photon source from a single quantum dot, and 3) Quantum controlled phase gate and phase switching based on quantum dots and photonic crystal waveguide. The first topic is engineered control of radiation directionality and effective mode volume for optical mode in chip-scale silicon micro-/nano-cavities. High quality factor (Q), subwavelength mode volume (V) and controllable radiation directionality are the major properties for optical cavities designs. In Chapter 2, asymmetric resonant cavities with rational caustics are proposed and interior whispering gallery modes in monolithic silicon mesoscopic microcavities are experimentally demonstrated. These microcavities possess unique robustness of cavity quality factor against roughness Rayleigh scattering. In Chapter 3, air-slot mode-gap photonic crystal cavities with quality factor of 10^4 and effective mode volume ~ 0.02 cubic wavelengths are experimentally demonstrated. The origin of the high Q air-slot cavity mode is the mode-gap effect from the slotted photonic crystal waveguide mode with negative dispersion. The second topic is exciton-photon coupling between quantum dots and twodimensional photonic crystal nanocavities and waveguide localized modes, including Purcell effect in weak coupling regime and vacuum Rabi splitting in strong coupling regime. In Chapter 4, micro-photoluminescence measurements of PbS quantum dots coupled to air-slot mode-gap photonic crystal cavities with potentially high qualify factor and small effective mode volume are presented. Purcell factor due to ultrahigh Q/V ratios are critical for applications in non-classical photon sources, cavity QED, nonlinear optics and sensing. In Chapter 5, the observation of subpoisson photon statistics from a single InAs quantum dot emission is presented from both continuous wave and pulsed Hanbury Brown and Twiss measurement. Furthermore, strong coupling between single quantum dot exciton line and photonic crystal waveguide localized mode is demonstrated experimentally and theoretically analyzed with master equations, which can be used as a great implementation platform for realizing future solid-state quantum computation. The third topic is quantum controlled phase gate and phase switching operations based on quantum dots and photonic crystal slow-light waveguide. In Chapter 6, we propose a scheme to realize controlled phase gate between two single photons through a single quantum dot embedded in a photonic crystal waveguide. Enhanced Purcell factor and large Î² factor lead to high gate fidelity over broadband frequencies compared to cavity-assisted system. The excellent physical integration of this photonic crystal waveguide system provides tremendous potential for large-scale quantum information processing. In Chapter 7, dipole induced transparency can be achieved in a system which consists of two quantum dots properly located in silicon photonic crystal waveguide. Furthermore, we describe how this effect can be useful for designing full Ï€ phase switching in a hetero-photonic crystal waveguide structure just by a small amount of photons.Optics, Nanosciencejg2499Applied Physics and Applied Mathematics, Mechanical Engineering, Electrical Engineering, Center for Integrated Science and EngineeringDissertationsSingle Molecule Junction Conductance and Binding Geometry
http://academiccommons.columbia.edu/catalog/ac:143055
Kamenetska, Mariahttp://hdl.handle.net/10022/AC:P:12159Tue, 10 Jan 2012 13:11:33 +0000This Thesis addresses the fundamental problem of controlling transport through a metal-organic interface by studying electronic and mechanical properties of single organic molecule-metal junctions. Using a Scanning Tunneling Microscope (STM) we image, probe energy-level alignment and perform STM-based break junction (BJ) measurements on molecules bound to a gold surface. Using Scanning Tunneling Microscope-based break-junction (STM-BJ) techniques, we explore the effect of binding geometry on single-molecule conductance by varying the structure of the molecules, metal-molecule binding chemistry and by applying sub-nanometer manipulation control to the junction. These experiments are performed both in ambient conditions and in ultra high vacuum (UHV) at cryogenic temperatures. First, using STM imaging and scanning tunneling spectroscopy (STS) measurements we explore binding configurations and electronic properties of an amine-terminated benzene derivative on gold. We find that details of metal-molecule binding affect energy-level alignment at the interface. Next, using the STM-BJ technique, we form and rupture metal-molecule-metal junctions ~104 times to obtain conductance-vs-extension curves and extract most likely conductance values for each molecule. With these measurements, we demonstrated that the control of junction conductance is possible through a choice of metal-molecule binding chemistry and sub-nanometer positioning. First, we show that molecules terminated with amines, sulfides and phosphines bind selectively on gold and therefore demonstrate constant conductance levels even as the junction is elongated and the metal-molecule attachment point is modified. Such well-defined conductance is also obtained with paracyclophane molecules which bind to gold directly through the Ã° system. Next, we are able to create metal-molecule-metal junctions with more than one reproducible conductance signatures that can be accessed by changing junction geometry. In the case of pyridine-linked molecules, conductance can be reliably switched between two distinct conductance states using sub-nanometer mechanical manipulation. Using a methyl sulfide linker attached to an oligoene backbone, we are able to create a 3-nm-long molecular potentiometer, whose resistance can be tuned exponentially with Angstom-scale modulations in metal-molecule configuration. These experiments points to a new paradigm for attaining reproducible electrical characteristics of metal-organic devices which involves controlling linker-metal chemistry rather than fabricating identically structured metal-molecule interfaces. By choosing a linker group which is either insensitive to or responds reproducibly to changes in metal-molecule configuration, one can design single molecule devices with functionality more complex than a simple resistor. These ambient temperature experiments were combined with UHV conductance measurements performed in a commercial STM on amine-terminated benzene derivatives which conduct through a non-resonant tunneling mechanism, at temperatures varying from 5 to 300 Kelvin. Our results indicate that while amine-gold binding remains selective irrespective of environment, conductance is not temperature independent, in contrast to what is expected for a tunneling mechanism. Furthermore, using temperature-dependent measurements in ambient conditions we find that HOMO-conducting amines and LUMO-conducting pyridines show opposite dependence of conductance on temperature. These results indicate that energy-level alignment between the molecule and the electrodes changes as a result of varying electrode structure at different temperatures. We find that temperature can serve as a knob with which to tune transport properties of single molecule-metal junctions.Physics, Nanosciencemk2743Applied Physics and Applied MathematicsDissertationsSpectroscopy of Two Dimensional Electron Systems Comprising Exotic Quasiparticles
http://academiccommons.columbia.edu/catalog/ac:143043
Rhone, Trevor David Nathanielhttp://hdl.handle.net/10022/AC:P:12155Tue, 10 Jan 2012 12:01:23 +0000In this dissertation I present inelastic and elastic light scattering studies of collective states emerging from interactions in electron systems confined to two dimensions. These studies span the first, second and third Landau levels. I report for the first time, high energy excitations of composite fermions in the quantum fluid at v = 1/3. The high energies discovered represent excitations across multiple composite fermion energy levels, demonstrating the topological robustness of the fractional quantum Hall state at v = 1/3. This study sets the ground work for similar measurements of states in the second Landau level, such as those at v = 5/2. I present the first light scattering studies of low energy excitations of quantum fluids in the second Landau level. The study of low energy excitations of the quantum fluid at 3 ≥ v ≥ 5/2 reveals a rapid loss of spin polarization for v ≤ 3, as monitored by the intensity of the spin wave excitation at the Zeeman energy. The emergence of a continuum of low-lying excitations for v ≤ 3 reveals competing quantum phases in the second Landau level with intriguing roles of spin degrees of freedom and phase inhomogeneity. The first light scattering studies of the electron systems in the third Landau level are reported here. Measurements of low energy excitations and their spin degrees of freedom reveal contrasting behavior of states in the second and third Landau levels. I discuss these measurements in the context of the charge density wave phases, that are believed, by some, to dominate the third Landau level, and suggest ways of verifying this belief using light scattering. Distinct behavior in the dispersion of the spin wave at v = 3 is measured for the first time. The study may highlight differences in the first and second Landau levels that are manifested through the electron wavefunctions. In addition to intra-Landau level measurements, inter-Landau level studies are also reported. The results of which reveal roles of spin degrees of freedom and many body interactions in odd denominator integer quantum Hall states.Condensed matter physics, Optics, Quantum physicstnr2103Physics, Applied Physics and Applied MathematicsDissertationsWorking Up Hills: Dynamics over Sloping Topography with Bottom-Enhanced Diffusion
http://academiccommons.columbia.edu/catalog/ac:143037
Diehl, Benjamin Williamhttp://hdl.handle.net/10022/AC:P:12153Tue, 10 Jan 2012 11:44:21 +0000The deep ocean circulation is known to have influence even at the surface, through means such as the Meridional Overturning Circulation (MOC). Initial theories on abyssal circulation and mixing have been improving, based on observation of both physical and numerical experiments. By tracing this progression, key aspects are identified but the explanations and relationships between them still contain gaps. Vertical diffusivity is one such component known to influence the strength of the MOC and is a part of the least understood leg of that circulation. Observations in particular have identified intense regions of mixing occurring near, and likely caused by, rough topography. Though the pieces are all present from this brief description, the exact relationships between them are still unclear, and observations cannot fully be generalized without more direct knowledge of how the phenomena interact. With these issues in mind, two models were used for simulating two dimensional abyssal canyons having constant sloping topography and bottom-intensified mixing acting on an initial uniform stratification. The first model uses finite volumes on a uniform z-coordinate grid, and it was set up and used to verify general sensitivity and confirm the choice of experimental variables while keeping the rest constant in a base state. The second model, developed specifically for use in this investigation, employed finite element techniques with a nonuniform mesh. A variational problem was created from derived streamfunction-vorticity equations plus advection-diffusion of a sole tracer, potential temperature. Preliminary simulations confirmed that both models were capable of simulating the desired phenomena, notably an upslope flow along the topography, and had otherwise comparable results. Two diagnostics were used for analyzing both models: the minimum value of streamfunction is a proxy for flux of a bottom boundary layer, and an estimate of thickness for the bottommost layer is a minimum length of communication into the fluid interior. These two diagnostics were studied in relation to changes in the amount of bottom enhanced mixing and also to changes in slope angle of the underlying topography. The boundary layer thickness increases with slope angle, a trend thought to continue well beyond tested values. Likewise, the streamfunction minima closely follow a linear relationship determined by the maximum diffusivity. Additionally, the variability within the values for both diagnostics are seen to decrease in response to either diffusivity decreases or slope length increases. Tangent investigations focusing on slope length and effects of periodic domains add support to the results as well as demonstrate potential robustness of the identified trends. With this restriction in mind, all slopes (0.0025-0.0075) and diffusivities (0.05-0.3 m2/s) generate intense layers over 100m high with over 0.1Sv of up-slope flow, comparable to that observed in along-canyon flows.Applied mathematicsbwd2104Applied Physics and Applied Mathematics, Lamont-Doherty Earth ObservatoryDissertationsState-Space Models and Latent Processes in the Statistical Analysis of Neural Data
http://academiccommons.columbia.edu/catalog/ac:142761
Vidne, Michaelhttp://hdl.handle.net/10022/AC:P:12050Tue, 20 Dec 2011 15:18:18 +0000This thesis develops and applies statistical methods for the analysis of neural data. In the second chapter we incorporate a latent process to the Generalized Linear Model framework. We develop and apply our framework to estimate the linear filters of an entire population of retinal ganglion cells while taking into account the effects of common-noise the cells might share. We are able to capture the encoding and decoding of visual stimulus to neural code. Our formalism gives us insight into the underlying architecture of the neural system. And we are able to estimate the common-noise that the cells receive. In the third chapter we discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. In the fourth chapter we develop a more general approach to the state-space filtering problem. Our method solves the same recursive set of Markovian filter equations as the particle filter, but we replace all importance sampling steps with a more general Markov chain Monte Carlo (MCMC) step. Our algorithm is especially well suited for problems where the model parameters might be misspecified.Applied mathematics, Statistics, Neurosciencesmv333Applied Physics and Applied MathematicsDissertationsLarge Scale Machine Learning in Biology
http://academiccommons.columbia.edu/catalog/ac:138449
Raj, Anilhttp://hdl.handle.net/10022/AC:P:11116Fri, 09 Sep 2011 11:22:11 +0000Rapid technological advances during the last two decades have led to a data-driven revolution in biology opening up a plethora of opportunities to infer informative patterns that could lead to deeper biological understanding. Large volumes of data provided by such technologies, however, are not analyzable using hypothesis-driven significance tests and other cornerstones of orthodox statistics. We present powerful tools in machine learning and statistical inference for extracting biologically informative patterns and clinically predictive models using this data. Motivated by an existing graph partitioning framework, we first derive relationships between optimizing the regularized min-cut cost function used in spectral clustering and the relevance information as defined in the Information Bottleneck method. For fast-mixing graphs, we show that the regularized min-cut cost functions introduced by Shi and Malik over a decade ago can be well approximated as the rate of loss of predictive information about the location of random walkers on the graph. For graphs drawn from a generative model designed to describe community structure, the optimal information-theoretic partition and the optimal min-cut partition are shown to be the same with high probability. Next, we formulate the problem of identifying emerging viral pathogens and characterizing their transmission in terms of learning linear models that can predict the host of a virus using its sequence information. Motivated by an existing framework for representing biological sequence information, we learn sparse, tree-structured models, built from decision rules based on subsequences, to predict viral hosts from protein sequence data using multi-class Adaboost, a powerful discriminative machine learning algorithm. Furthermore, the predictive motifs robustly selected by the learning algorithm are found to show strong host-specificity and occur in highly conserved regions of the viral proteome. We then extend this learning algorithm to the problem of predicting disease risk in humans using single nucleotide polymorphisms (SNP) -- single-base pair variations -- in their entire genome. While genome-wide association studies usually aim to infer individual SNPs that are strongly associated with disease, we use popular supervised learning algorithms to infer sufficiently complex tree-structured models, built from single-SNP decision rules, that are both highly predictive (for clinical goals) and facilitate biological interpretation (for basic science goals). In addition to high prediction accuracies, the models identify 'hotspots' in the genome that contain putative causal variants for the disease and also suggest combinatorial interactions that are relevant for the disease. Finally, motivated by the insufficiency of quantifying biological interpretability in terms of model sparsity, we propose a hierarchical Bayesian model that infers hidden structured relationships between features while simultaneously regularizing the classification model using the inferred group structure. The appropriate hidden structure maximizes the log-probability of the observed data, thus regularizing a classifier while increasing its predictive accuracy. We conclude by describing different extensions of this model that can be applied to various biological problems, specifically those described in this thesis, and enumerate promising directions for future research.Applied mathematics, Bioinformatics, Computer sciencear2384Applied Physics and Applied MathematicsDissertationsFingerprinting analysis of non-crystalline pharmaceutical compounds using high energy X-rays and the total scattering pair distribution function
http://academiccommons.columbia.edu/catalog/ac:136566
Davis, Timur D.http://hdl.handle.net/10022/AC:P:10800Tue, 02 Aug 2011 15:00:25 +0000In the development of new medicinal products, poor oral bioavailability, due to the low solubilities of many active pharmaceutical ingredients (APIs), is increasingly a barrier for treatments to be administered using tablet or capsule formulations and one of the main challenges facing the pharmaceutical industry. Non-crystalline phases such as the amorphous and nanostructured states can confer increased solubility to a drug, and therefore, have recently garnered a lot of interest from pharmaceutical researchers. However, little is known about local ordering in non-crystalline pharmaceuticals due to the lack of reliable experimental probes, hindering the clinical application of these compounds. The powerful tools of crystallography begin to lose their potency for structures on the nanoscale; conventional X-ray powder diffraction (XRPD) patterns become broad and featureless in these cases and are not useful for differentiating between different local molecular packing arrangements. In this thesis, we introduce the use of high energy X-rays coupled with total scattering pair distribution function (TSPDF) and fingerprinting analysis to investigate the local structures of non-crystalline pharmaceutical compounds. The high energy X-rays allow us to experimentally collect diffuse scattering intensities, which contain information about a sample's local ordering, in addition to the Bragg scattering available in conventional XRPD experiments, while the TSPDF allows us to view the intra- and inter-molecular correlations in real space. The goal of this study was to address some fundamental problems involving fingerprinting non-crystalline APIs using TSPDF in order to lay the groundwork for the proper use of the technique by the pharmaceutical community. We achieved this by developing the methodology as well as the exploring the scientific implications. On the methodology side, we introduced PDFGetX3, a new software program for calculating TSPDFs that simplifies the procedure and reduces user interaction. We also set a baseline for the minimum X-ray energy that is needed for fingerprinting analysis, which had implications on the type of X-ray diffractometers that can be used. On the science side, we investigated the local structures of nanocrystalline and amorphous materials as well mixtures containing crystalline and amorphous phases. First, we identified a non-crystalline sample of the mood-stabilizing drug carbamazepine as a nanocrystalline version of one of its polymorphs. Next, we found that amorphous forms created by spray drying and cryomilling a proprietary compound have the same local structure. Finally, we quantified the phase fractions of polymorphic and amorphous components in a sample of the antibiotic sulfamerazine that was recrystallizing from a cryomilling-induced amorphous state.Materials science, Condensed matter physics, Pharmaceutical sciencestd2218Applied Physics and Applied MathematicsDissertationsNonlinear Applications using Silicon Nanophotonic Wires
http://academiccommons.columbia.edu/catalog/ac:132924
Liu, Xiaopinghttp://hdl.handle.net/10022/AC:P:10443Thu, 26 May 2011 16:29:56 +0000This thesis is concerned with an emerging set of nonlinear-optical applications using silicon nanophotonic "wires" fabricated on a silicon-on-insulator photonic chip. These deeply scaled silicon nanophotonic wires are capable of confining the telecom and mid-infrared (mid-IR) light tightly into an optical-modal area ~ 0.1 μm2. The tight optical confinement leads to many advantageous physical properties including enhanced effective nonlinearity, flexible control of waveguide dispersion, and short free-carrier lifetime. All these advantages make silicon nanophotonic wires an ideal platform for a variety of nonlinear applications. The first part of my thesis study is focused on nonlinear applications in the telecom bands. In Chapter 3, I study the frequency dependence of optical nonlinearity in silicon nanophotonic wires, and its influence on the propagation of ultra-short optical pulses in such wires. I show that silicon nanophotonic wires possess a remarkably large characteristic time associated with the self-steepening effect and optical-shock formation. In Chapter 4, I present an experimental demonstration of an ultrafast cross-phase-modulation-based wavelength-conversion (XPM-WC) technique for telecom RZ-OOK data. I also investigate the effect of pump-probe detuning on the efficacy of this XPM-WC technique. In Chapter 5, I show a (primarily) numerical study of a method for dispersion-engineering of silicon nanophotonic wires using a conformal thin-silicon-nitride dielectric film deposited around the silicon wire core. My simulation results show that this approach may be used to achieve the dispersion characteristics required for broadband phase-matched four-wave-mixing processes, while simultaneously maintaining strong modal confinement within the silicon core for high effective nonlinearity. The second part of my thesis is devoted to investigations of nonlinear applications in mid-IR spectral region, in which nonlinear optical loss due to parasitic two-photon absorption can be significantly reduced and therefore a large nonlinear figure of merit can be achieved in order to facilitate efficient nonlinear processes. In Chapter 6, I present an experimental demonstration of a mid-IR-silicon-nanophotonic-wire optical parametric amplifier with 25.4 dB on-chip gain. This gain achieved with only a 4-mm-long silicon nanophotonic wire is sufficient enough to overcome all the insertion loss, resulting in 13 dB net off-chip amplification. In addition, I show, on the same waveguide, efficient generation of 4 orders of cascaded FWM products enabled by the large on-chip gain. In Chapter 7, I report a comprehensive study of the propagation characteristics of a picosecond pulse through a 4-mm-long silicon nanophotonic wire with normal dispersion with excitation wavelengths crossing the mid-infrared two-photon absorption edge at λ = 2200 nm. Significant reduction in nonlinear loss due to two-photon absorption is demonstrated as the excitation wavelengths approach 2200 nm. Self-phase modulation at high input power is also observed. Analysis of experimental data and comparison with numerical simulations illustrates that the two-photon absorption coefficient obtained from nanophotonic wire measurements is in reasonable agreement with prior measurements of bulk silicon crystals, and that bulk silicon values of the nonlinear refractive index can be confidently incorporated in the modeling of pulse propagation in deeply-scaled waveguide structures. In Chapter 8, I investigate a higher-order phase matching technique utilizing the 4th-order dispersion term for realizing a broadband or discrete band parametric process in silicon nanophotonic wires. I demonstrate experimentally, on a silicon nanophotonic wire designed to exhibit a desired 2nd-order and 4th-order dispersion, broadband/discrete-band modulation instability and 50 dB Raman assisted parametric gain.Optics, Nanotechnologyxl2165Electrical Engineering, Center for Integrated Science and Engineering, Applied Physics and Applied MathematicsDissertationsPlasmas of Arbitrary Neutrality
http://academiccommons.columbia.edu/catalog/ac:161386
Sarasola Martin, Xabierhttp://hdl.handle.net/10022/AC:P:10402Tue, 17 May 2011 13:08:26 +0000The physics of partially neutralized plasmas is largely unexplored, partly because of the difficulty of confining such plasmas. Plasmas are confined in a stellarator without the need for a plasma current, and regardless of the degree of neutralization. The Columbia Non-neutral Torus (CNT) is a stellarator dedicated to the study of non-neutral, and partially neutralized plasmas. This thesis describes the first systematic studies of plasmas of arbitrary neutrality. The degree of neutralization of the plasma can be parameterized through the quantity η ≡ |n_e - Z n_i|/|n_e + Z n_i|. In CNT, η can be varied continuously from pure electron (η = 1) to quasi-neutral (η ≈ 0) by adjusting the neutral pressure in the chamber, which controls the volumetric ionization rate. Pure electron plasmas are in macroscopically stable equilibria, and have strong self electric potentials dictated by the emitter filament bias voltage on the magnetic axis. As η decreases, the plasma potential decouples from the emitter, and spontaneous fluctuations begin to appear. Partially neutralized plasmas (10^-3 < η < 10^-1) generally exhibit multi-mode oscillations in CNT. However, when magnetized ions are present, the electron-rich plasma oscillates at a single dominant mode (20 - 100 kHz). As the plasma approaches quasi-neutrality (η < 10^-5), it also reverts to single mode behavior (1 - 20 kHz). A parametric characterization of the single mode fluctuations detected in plasmas of arbitrary neutrality is presented in this thesis along with measurements of the spatial structure of the oscillations. The single mode fluctuations observed for η ≈ 0.01 to 0.8 are identified as an ion resonant instability propagating close to the E × B velocity of the plasma. The experiments also show that these oscillations present a poloidal mode number m = 1, and a toroidal number n = 0, which is identical to the spatial structure of the diocotron instability in pure-toroidal traps, and implies that the ion-driven instability breaks parallel force balance and the conservation of poloidal flux in CNT. The low frequency oscillations detected in the quasi-neutral regime are a global instability convected by the E × B flow of the plasma. In this case, the mode aligns almost perfectly with the field lines, and presents a resonant m = 3 poloidal structure.Plasma physicsxs2126Applied Physics and Applied MathematicsDissertationsAccuracy, Precision, and Resolution in Strain Measurements on Diffraction Instruments
http://academiccommons.columbia.edu/catalog/ac:132041
Polvino, Sean M.http://hdl.handle.net/10022/AC:P:10338Wed, 11 May 2011 18:02:24 +0000Diffraction stress analysis is a commonly used technique to evaluate the properties and performance of different classes of materials from engineering materials, such as steels and alloys, to electronic materials like Silicon chips. Often to better understand the performance of these materials at operating conditions they are also commonly subjected to elevated temperatures and different loading conditions. The validity of any measurement under these conditions is only as good as the control of the conditions and the accuracy and precision of the instrument being used to measure the properties. What is the accuracy and precision of a typical diffraction system and what is the best way to evaluate these quantities? Is there a way to remove systematic and random errors in the data that are due to problems with the control system used? With the advent of device engineering employing internal stress as a method for increasing performance the measurement of stress from microelectronic structures has become of enhanced importance. X-ray diffraction provides an ideal method for measuring these small areas without the need for modifying the sample and possibly changing the strain state. Micro and nano diffraction experiments on Silicon-on-Insulator samples revealed changes to the material under investigation and raised significant concerns about the usefulness of these techniques. This damage process and the application of micro and nano diffraction is discussed.Materials sciencesmp2007Applied Physics and Applied Mathematics, Earth and Environmental Engineering, Materials Science and EngineeringDissertationsConfinement of Non-neutral Plasmas in Stellarator Magnetic Surfaces
http://academiccommons.columbia.edu/catalog/ac:132089
Brenner, Paulhttp://hdl.handle.net/10022/AC:P:10353Wed, 11 May 2011 16:19:07 +0000The Columbia Non-neutral Torus (CNT) is the first experiment designed to create and study small Debye length non-neutral plasmas confined by magnetic surfaces. This thesis describes experimental confinement studies of non-neutral plasmas on magnetic surfaces in CNT. Open orbits exist in CNT resulting in electron loss rates that are much faster than initially predicted. For this reason a conforming boundary was designed and installed to address what is believed to be the primary cause of open orbits: the existence of a sizable mismatch between the electrostatic potential surfaces and the magnetic surfaces. After installation a record confinement time of 337 ms was measured, more than an order of magnitude improvement over the previous 20 ms record. This improvement was a combination of the predicted improvement in orbit quality, a reduced Debye length that resulted in decreased transport due to the perturbing insulated rods, and improved operating parameters not indicative of any new physics. The perturbation caused by the insulated rods that hold emitters on axis in CNT is a source of electron transport and would provide a loss mechanism for positrons in future positron-electron plasma experiments. For these reasons an emitter capable of creating plasmas then being removed faster than the confinement time was built and installed. Measurements of plasma decay after emitter retraction indicate that ion accumulation reduces the length of time that plasmas are confined. Plasmas have been measured after retraction with decay times as long as 92 ms after the emitter has left the last closed flux surface. Experimental observations show that obstructing one side of an emitting filament with a nearby insulator substantially improves confinement. As a result, experiments have been performed to determine whether a two stream instability affects confinement in CNT. Results indicate that the improvement is not caused by reducing a two stream instability. Instead, the improvement is a result of altering the sheath of the emitting filament which allows the plasma to reach an equilibrium state with improved confinement. These measurements agree with confinement times for plasmas created by unobstructed emission that are in the same improved confinement state.Plasma physicspwb2103Applied Physics and Applied MathematicsDissertationsSynthesis and electronic transport in single-walled carbon nanotubes of known chirality
http://academiccommons.columbia.edu/catalog/ac:132056
Caldwell, Robert Victorhttp://hdl.handle.net/10022/AC:P:10342Wed, 11 May 2011 14:31:49 +0000Since their discovery in 1991, carbon nanotubes have proven to be a very interesting material for its physical strength, originating from the pure carbon lattice and strong covalent sp2 orbital bonds, and electronic properties which are derived from the lattice structure lending itself to either a metallic or semiconducting nature among its other properties. Carbon nanotubes have been researched with an eye towards industry applications ranging from use as an alloy in metals and plastics to improve physical strength of the resulting materials to uses in the semiconductor industry as either an interconnect or device layer for computer chips to chemical or biological sensors. This thesis focuses on both the synthesis of individual single-walled carbon nanotubes as well as the electrical properties of those tubes. What makes the work herein different from that of other thesis is that the research has been performed on carbon nanotubes of known chirality. Having first grown carbon nanotubes with a chemical vapor deposition growth in a quartz tube using ethanol vapor as a feedstock to grow long individual single-walled carbon nanotubes on a silicon chip that is also compatible with Rayleigh scattering spectroscopy to identify the chiral indices of the carbon nanotubes in question, those tubes were then transferred with a mechanical transfer process specially designed in our research lab onto a substrate of our choosing before an electrical device was made out of those tubes using standard electron beam lithography. The focus in this thesis is on the work that went into designing and testing this process as well as the initial results of the electronic properties of those carbon nanotubes of known chirality, such as the first known electrical measurements on single individual armchair carbon nanotubes as well as the first known electrical measurements of a single semiconducting carbon nanotube on thin hexagonal boron nitride to study the effects of the surface optical phonons from the boron nitride on the electrical properties of the carbon nanotube. Finally a few research projects are discussed in which carbon nanotubes of known chirality were used in conjunction with first electrical tests on molecules, secondly on a prefabricated complementary metal-oxide-semiconductor integrated circuit as an inverter and lastly to study the photoconductivity generated by a synchrotron laser source to identify the values for the low energy excitonic peak.Physics, Nanotechnologyrvc2101Applied Physics and Applied Mathematics, Mechanical EngineeringDissertationsCorrector Theory in Random Homogenization of Partial Differential Equations
http://academiccommons.columbia.edu/catalog/ac:132034
Jing, Wenjiahttp://hdl.handle.net/10022/AC:P:10336Wed, 11 May 2011 13:51:51 +0000We derive systematically a theory for the correctors in random homogenization of partial differential equations with highly oscillatory coefficients, which arise naturally in many areas of natural sciences and engineering. This corrector theory is of great practical importance in many applications when estimating the random fluctuations in the solution is as important as finding its homogenization limit. This thesis consists of three parts. In the first part, we study some properties of random fields that are useful to control corrector in homogenization of PDE. These random fields mostly have parameters in multi-dimensional Euclidean spaces. In the second part, we derive a corrector theory systematically that works in general for linear partial differential equations, with random coefficients appearing in their zero-order, i.e., non-differential, terms. The derivation is a combination of the studies of random fields and applications of PDE theory. In the third part of this thesis, we derive a framework of analyzing multiscale numerical algorithms that are widely used to approximate homogenization, to test if they succeed in capturing the limiting corrector predicted by the theory.Mathematics, Applied mathematicswj2136Applied Physics and Applied MathematicsDissertationsEssays on the Social Impacts of Climate
http://academiccommons.columbia.edu/catalog/ac:161383
Hsiang, Solomon M.http://hdl.handle.net/10022/AC:P:10328Wed, 11 May 2011 12:37:55 +0000It has been hypothesized that local or global climatic conditions can affect societies in a variety of ways. However, to date, it has been difficult to measure the social impact of climate, so the scale and scope of its influence on populations remains mostly theoretical. This dissertation integrates data and quantitative methods from climate science, economics and political science to develop new techniques for empirically measuring the the social impacts of climate. These techniques are used to measure large-scale dynamical relationships between climatological conditions and the response of the societies that are exposed to them. In general, the response of societies to climatological forcing is found to be larger than previously thought. The concluding chapter discusses how these findings may inform policies that govern the global environment and economic development.Sustainability, Economics, Climate changesmh2137International and Public Affairs, Economics, Earth and Environmental Sciences, Applied Physics and Applied Mathematics, Sustainable DevelopmentDissertationsComplex-Analytic Methods in Reconstructive Integral Geometry
http://academiccommons.columbia.edu/catalog/ac:131980
Hoell, Nicholas McMurrayhttp://hdl.handle.net/10022/AC:P:10319Tue, 10 May 2011 16:40:13 +0000Each chapter is self-contained yet thematically dependent. A review of some of the main objectives and techniques in reconstructive integral geometry is presented. The inverse problem central to the author's work, namely reconstructing a function of position from its averages over a class of curves in the unit disc, is then introduced. We give several new results on that front and present explicit ltered backprojection inversion formulae for the attenuated and non-attenuated X-ray transform over a wide class of curves in a simply-connected region of 2-dimensional Euclidean space. The method used to derive these formulae is based on the complexication of the vector felds defing the particle transport,thereby making the problem amenable to complex-analytic techniques. The remainder of the thesis can largely be considered to be variations on this theme. The proof of the reconstruction procedure we give demands the vector fields governing the transport satisfy a somewhat stringent condition we call condition H. A thorough investigation of this condition is then presented culminating in results applicable to a certain subset of the space of vector fields with polynomial coecients. This is done by explicitly looking at the complexification and appealing to the logarithmic Poisson-Jensen formula as well as some results on quasi-conformal mapping theory. These results are used in establishing a stability estimate on a natural generalization of this polynomial space in real-analytic functions in an attempt to address approximation/truncation concerns. Finally, we take up a variant of this problem on 2-dimensional, simple and compact Riemannian manifolds with boundary. In this case, we deal with data that is of a fanbeam type and thereby have to concern ourselves with the boundary of the domain we are interested in probing. A related but somewhat less direct means of complexification is used in this case on local trivializations of the unitized bundle of Hamiltonian coordinates. A novel derivation of an existing formula is then presented using a similar approach as was considered in earlier chapters. This serves as a prelude to a new result for an explicit formula for inverting the attenuated ray transform in such settings modulo a Fredholm error. We close with an appendix on containing all useful geometrical jargon used throughout.Applied mathematicsnmh2111Applied Physics and Applied MathematicsDissertationsComplex-Analytic Methods in Reconstructive Integral Geometry
http://academiccommons.columbia.edu/catalog/ac:132096
Hoell, Nicholas McMurrayhttp://hdl.handle.net/10022/AC:P:10313Tue, 10 May 2011 13:33:46 +0000Each chapter is self-contained yet thematically dependent. A review of some of the main objectives and techniques in reconstructive integral geometry is presented. The inverse problem central to the author's work, namely reconstructing a function of position from its averages over a class of curves in the unit disc, is then introduced. We give several new results on that front and present explicit ltered backprojection inversion formulae for the attenuated and non-attenuated X-ray transform over a wide class of curves in a simply-connected region of 2-dimensional Euclidean space. The method used to derive these formulae is based on the complexication of the vector felds defing the particle transport, thereby making the problem amenable to complex-analytic techniques. The remainder of the thesis can largely be considered to be variations on this theme. The proof of the reconstruction procedure we give demands the vector fields governing the transport satisfy a somewhat stringent condition we call condition H. A thorough investigation of this condition is then presented culminating in results applicable to a certain subset of the space of vector fields with polynomial coecients. This is done by explicitly looking at the complexification and appealing to the logarithmic Poisson-Jensen formula as well as some results on quasi-conformal mapping theory. These results are used in establishing a stability estimate on a natural generalization of this polynomial space in real-analytic functions in an attempt to address approximation/truncation concerns. Finally, we take up a variant of this problem on 2-dimensional, simple and compact Riemannian manifolds with boundary. In this case, we deal with data that is of a fanbeam type and thereby have to concern ourselves with the boundary of the domain we are interested in probing. A related but somewhat less direct means of complexification is used in this case on local trivializations of the unitized bundle of Hamiltonian coordinates. A novel derivation of an existing formula is then presented using a similar approach as was considered in earlier chapters. This serves as a prelude to a new result for an explicit formula for inverting the attenuated ray transform in such settings modulo a Fredholm error. We close with an appendix on containing all useful geometrical jargon used throughout.Applied mathematicsnmh2111Applied Physics and Applied MathematicsDissertationsPrecision Tuning of Silicon Nanophotonic Devices through Post-Fabrication Processes
http://academiccommons.columbia.edu/catalog/ac:131585
Chen, Charlton J.http://hdl.handle.net/10022/AC:P:10282Thu, 05 May 2011 15:19:56 +0000This thesis investigates ways of improving the performance of fundamental silicon nanophotonic devices through post-fabrication processes. These devices include numerous optical resonator designs as well as slow-light waveguides. Optical resonators are used to confine photons both spatially and temporally. In recent years, there has been much research, both theoretical and experimental, into improving the design of optical resonators. Improving these devices through fabrication processes has generally been less studied. Optical waveguides are used to guide the flow of photons over chip-level distances. Slow-light waveguides have also been studied by many research groups in recent years and can applied to an increasingly wide-range of applications. The work can be divided into several parts: Chapter 1 is an introduction to the field of silicon photonics as well as an overview of the fabrication, experimental and computational techniques used throughout this work. Chapters 2, 3 and 4 describe our investigations into the precision tuning of nanophotonic devices using laser-assisted oxidation and atomic layer deposition. Chapters 5 and 6 describe our investigations into improving the sidewall roughness of silicon photonic devices using hydrogen annealing and excimer laser induced melting. Finally, Chapter 7 describes our investigations into the nonlinear properties of lead chalcogenide nanocrystals.Nanotechnology, Electromagneticscjc2106Applied Physics and Applied Mathematics, Mechanical Engineering, Earth and Environmental EngineeringDissertationsSpectral Optimization Problems Controlling Wave Phenomena
http://academiccommons.columbia.edu/catalog/ac:131510
Osting, BraxtonFri, 29 Apr 2011 14:32:19 +0000Design problems seek a material arrangement or shape which fully harnesses the physical properties of the material(s) to create an environment in which a particular phenomena is most (or least) pronounced. Mathematically, design problems are formulated as PDE-constrained optimization problems to find the material arrangement that maximizes an objective function which expresses the desired behavior. The PDE constraint describes the relationship between the material and the phenomena of interest. The focus of this thesis is four design problems where the PDE constraint is a time-independent wave equation and the objective function governs some aspect of wave motion. We consider the shape optimization of functions of Dirichlet-Laplacian eigenvalues associated with the set of star-shaped, symmetric, bounded planar regions with smooth boundary. The boundary of such a region is represented using a Fourier-cosine series and the optimization problem is solved numerically using a quasi-Newton method. The method is applied to maximizing two particular nonsmooth functions of the eigenvalues: (a) the ratio of the n-th to first eigenvalues and (b) the ratio of the n-th eigenvalue gap to first eigenvalue. Both are generalizations of the Payne-Pólya-Weinberger ratio. The optimal values of these ratios and regions for which they are attained, for n ≤ 13, are presented and interpreted as a study of the range of the Dirichlet-Laplacian eigenvalues. For both spectral functions and each n, the optimal region has multiplicity two n-th eigenvalue. We consider a system governed by the wave equation with index of refraction n(x), taken to be variable within a bounded region of d-dimensional space and constant outside. The solution of the time-dependent wave equation with spatially-localized initial data spreads and decays with advancing time. The rate of spatially localized energy decay can be measured in terms of the eigenvalues of the scattering resonance problem, a non-selfadjoint eigenvalue problem consisting of the time-harmonic wave (Helmholtz) equation with outgoing radiation condition at infinity. Specifically, the rate of energy escape is governed by the complex scattering eigenfrequency which is closest to the real axis. We study the structural design problem: Find a refractive index profile n* within an admissible class which has a scattering frequency with minimal imaginary part. The admissible class is defined in terms of the compact support of n(x)-1 and pointwise upper and lower (material) bounds on n(x): 0 < n- ≤ n(x) ≤ n+ < ∞. We formulate this problem as a constrained optimization problem and prove that an optimal structure, n* exists. Furthermore, n*(x) is piecewise constant and achieves the material bounds, i.e., n*(x) is n- or n+ almost everywhere. In one dimension, we establish a connection between n*(x) and the well-known class of Bragg structures, where n(x) is constant on intervals whose length is one-quarter of the effective wavelength. Consider a system governed by the time-dependent Schroedinger equation in its ground state. When subjected to weak parametric forcing by an "ionizing field" (time-varying), the state decays with advancing time due to coupling of the bound state to radiation modes. The decay-rate of this metastable state is governed by Fermi's Golden Rule (FGR), which depends on the potential V and the details of the forcing. We pose the potential design problem: find V* which minimizes FGR (maximizes the lifetime of the state) over an admissible class of potentials with fixed spatial support. We formulate this problem as a constrained optimization problem and prove that an admissible optimal solution exists. Then, using quasi-Newton methods, we compute locally optimal potentials. These have the structure of a truncated periodic potential with a localized defect. In contrast to optimal structures for other spectral optimization problems, the optimizing potentials appear to be interior points of the constraint set and to be smooth. The multi-scale structures that emerge incorporate the physical mechanisms of energy confinement via material contrast and interference effects. An analysis of locally optimal potentials reveals local optimality is attained via two mechanisms: (i) decreasing the density of states near a resonant frequency in the continuum and (ii) tuning the oscillations of extended states to make FGR, an oscillatory integral, small. Finally, we explore the performance of optimal potentials via simulations of the time-evolution. We consider a general class of two-dimensional passive propagation media, represented as a planar graph where nodes are capacitors connected to a common ground and edges are inductors. Capacitances and inductances are fixed in time but vary in space. Kirchhoff's laws give the time dynamics of voltage and current in the system. By harmonically forcing input nodes and collecting the resulting steady-state signal at output nodes, we obtain a linear, analog device that transforms the inputs to outputs. We pose the lattice synthesis problem: given a linear transformation, find the inductances and capacitances for an inductor-capacitor circuit that can perform this transformation. Formulating this as an optimization problem, we numerically demonstrate its solvability using gradient-based methods. By solving the lattice synthesis problem for various desired transformations, we design several devices that can be used for signal processing and filtering. In addition to these spectral optimization problems, we study several problems on wave propagation, diffraction, and scattering. The focus is on the behavior of time-harmonic solutions to continuous and discrete wave equations.Applied mathematics, Physics, Materials sciencebro2103Applied Physics and Applied MathematicsDissertations