Academic Commons Search Results
http://academiccommons.columbia.edu/catalog.rss?f%5Bsubject_facet%5D%5B%5D=Theoretical+physics&q=&rows=500&sort=record_creation_date+desc
Academic Commons Search Resultsen-usIntrinsic properties of a Burridge-Knopoff model of an earthquake fault
http://academiccommons.columbia.edu/catalog/ac:162401
Carlson, Jean M.; Langer, James S.; Shaw, Bruce E.; Tang, Chaohttp://hdl.handle.net/10022/AC:P:20765Mon, 17 Jun 2013 10:13:43 +0000We present a detailed numerical study of certain fundamental aspects of a one-dimensional homogeneous, deterministic Burridge-Knopoff model. The model is described by a massive wave equation, in which the key nonlinearity is associated with the stick-slip velocity-weakening friction force at the interface between tectonic plates. In this paper, we present results for the statistical distribution of slipping events in the limit of a very long fault and infinitesimally slow driving rates. Typically, we find that the magnitude distribution of smaller events is consistent with the Gutenberg-Richter law, while the larger events occur in excess of this distribution. The crossover from smaller to larger events is identified with a correlation length describing the transition from localized to delocalized events. We also find that there is a sharp upper cutoff describing the maximum large event. We identify how the correlation length and this upper cutoff scale with the parameters in the model. We find that both are independent of system size, while both do depend on the spatial discretization. In addition to the magnitude distribution, we present a series of measurements of other seismologically relevant quantities, including the event duration, the size of the rupture zone, and the energy release, and discuss the relationship between our measurements and the corresponding empirical laws in seismology.Theoretical physics, Plate tectonicsbes11Lamont-Doherty Earth ObservatoryArticlesUniversality in selection with local perturbations in the Saffman-Taylor problem
http://academiccommons.columbia.edu/catalog/ac:162398
Shaw, Bruce E.http://hdl.handle.net/10022/AC:P:20764Mon, 17 Jun 2013 09:55:40 +0000An analytic theory using WKBJ methods for selection with local perturbations in the SaffmanTaylor [Proc. R. Soc. London, Ser. A 245, 312 (1958)] problem is presented. I obtain qualitative agreement with previously published phenomenology, including symmetric narrowed fingers for local reductions in the surface-tension parameter, narrowed asymmetric fingers for local increases,
and scaling of the tip curvature and asymmetry with the square root of the surface-tension parameter. The source of the universality in the perturbed problem is discussed, giving some explanation of why the experimental perturbations can be modeled by locally varying surface tension. Very good quantitative agreement between theory and a numerical simulation of the same perturbation is shown, with no adjustable parameters to fit. Finally, I outline experiments to test new behavior predicted by the theory; a quantitative prediction observable experimentally is given.Theoretical physics, Mechanicsbes11Lamont-Doherty Earth ObservatoryArticlesFinger narrowing under local perturbations in the Saffman-Taylor problem
http://academiccommons.columbia.edu/catalog/ac:162376
Zocchi, Giovanni; Shaw, Bruce E.; Libchaber, Albert; Kadanoff, Leo P.http://hdl.handle.net/10022/AC:P:20749Fri, 14 Jun 2013 11:45:56 +0000We present an experimental study and a numerical simulation of the effect of time-independent, localized perturbations applied to the interface in the Saffman-Taylor fingering problem. When the perturbation is applied at a specific spot near the tip of the finger, the selection of the steady-state shape is drastically changed. In particular, one can obtain fingers with a width well below λ=1/2. A perturbation applied far away from the tip has no effect. We observe the same behavior in the simulation and in the experiment.Theoretical physics, Mechanicsbes11Lamont-Doherty Earth ObservatoryArticlesThe Effective Field Theory Approach to Fluid Dynamics
http://academiccommons.columbia.edu/catalog/ac:161458
Endlich, Solomonhttp://hdl.handle.net/10022/AC:P:20419Thu, 23 May 2013 11:24:11 +0000In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that "lives in the fluid'', which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized, allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and---in the presence of a conserved charge---heat conduction. Using our methods we re-derive the Kubo relations for these transport coefficients.Theoretical physics, Physics, Condensed matter physicssge2104PhysicsDissertationsPrecision Lattice Calculation of Kaon Decays with Möbius Domain Wall Fermions
http://academiccommons.columbia.edu/catalog/ac:161136
Yin, Hantaohttp://hdl.handle.net/10022/AC:P:20325Tue, 14 May 2013 17:27:36 +0000We report our recent development in algorithms and progress in measurements in lattice QCD. The algorithmic development includes the forecasted force gradient integrator, and further theoretical development and implementation of the Möbius domain wall fermions. These new technologies make it practical to simulate large 48^3*96 and 64^3*128 lattice ensembles with (5.5fm)^3 boxes and 140MeV pion. The calculation was performed using the Möbius domain wall fermions and the Iwasaki gauge action. Simulated directly at physical quark masses, these ensembles are of great value for our ongoing and future lattice measurement projects. With the help of measurement techniques such as the eigCG algorithm and the all mode averaging method, we perform a direct, precise lattice calculation of the semileptonic kaon decay K→πlν using these newly generated high quality lattice ensembles. Our main result is the form factor f^+_{Kπ}(q^2) evaluated directly at zero momentum transfer q^2=0. Free of various systematic errors, this new result can be used to determine the CKM matrix element Vus to a very high precision when combined with experimental input. The calculation also provides results for various low energy strong interaction constants such as the pseudoscalar decay constants f_K and f_π, and the neutral kaon mixing matrix element B_K. These calculations are naturally performed by reusing the propagators calculated for the kaon semileptonic decay mentioned above. So they come with no or very low additional cost. The results allow us to also determine these important low energy constants on the lattice to unprecedented accuracy.Physics, Particle physics, Theoretical physicshy2242PhysicsDissertationsPrecision Lattice Calculation of Kaon Decays with Möbius Domain Wall Fermions
http://academiccommons.columbia.edu/catalog/ac:160818
Yin, Hantaohttp://hdl.handle.net/10022/AC:P:20151Wed, 01 May 2013 18:02:44 +0000We report our recent development in algorithms and progress in measurements in lattice QCD. The algorithmic development includes the forecasted force gradient integrator, and further theoretical development and implementation of the Möbius domain wall fermions. These new technologies make it practical to simulate large 48^3*96 and 64^3*128 lattice ensembles with (5.5fm)^3 boxes and 140MeV pion. The calculation was performed using the Möbius domain wall fermions and the Iwasaki gauge action. Simulated directly at physical quark masses, these ensembles are of great value for our ongoing and future lattice measurement projects.With the help of measurement techniques such as the eigCG algorithm and the all mode averaging method, we perform a direct, precise lattice calculation of the semileptonic kaon decay K→πlν using these newly generated high quality lattice ensembles. Our main result is the form factor f^+_{Kπ}(q^2) evaluated directly at zero momentum transfer q^2=0. Free of various systematic errors, this new result can be used to determine the CKM matrix element Vus to a very high precision when combined with experimental input. The calculation also provides results for various low energy strong interaction constants such as the pseudoscalar decay constants f_K and f_π, and the neutral kaon mixing matrix element B_K. These calculations are naturally performed by reusing the propagators calculated for the kaon semileptonic decay mentioned above. So they come with no or very low additional cost. The results allow us to also determine these important low energy constants on the lattice to unprecedented accuracy.Particle physics, Physics, Theoretical physicshy2242PhysicsDissertationsKaon to two pions decays from lattice QCD: ΔI=1/2 rule and CP violation
http://academiccommons.columbia.edu/catalog/ac:146416
Liu, Qihttp://hdl.handle.net/10022/AC:P:13068Mon, 30 Apr 2012 16:42:42 +0000We report a direct lattice calculation of the K to ππ decay matrix elements for both the ΔI = 1/2 and 3/2 amplitudes A0 and A2 on a 2+1 flavor, domain wall fermion, 163 × 32 × 16 lattice ensemble and a 243 × 64 × 16 lattice ensemble. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this work we take a major step towards the computation of the physical K → ππ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422MeV and 329MeV at rest in the kaon rest frame. With this simplification we are able to resolve Re(A0) from zero for the first time, with a 25% statistical error on the 163 lattice and 15% on the 243 lattice. The complex amplitude A2 is calculated with small statistical errors. We obtain the ΔI = 1/2 rule with an enhancement factor of 9.1(21) and 12.0(17) on these two ensembles. From the detailed analysis of the results we gain a deeper understanding of the origin of the ΔI = 1/2 rule. We also calculate the complex amplitude A0, a calculation central to understanding and testing the standard model of CP violation in the kaon system. The final result for the measure of direct CP violation, ε′, calculated at unphysical kinematics has an order of 100% statistical error, so this only serves as an order of magnitude check.Theoretical physicsql2142PhysicsDissertations