We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting...
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A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically ge...
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A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.
The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity mode...
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The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.
The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that data...
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We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evol...
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We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this scale separation, an efficient hybrid fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability—and temporal scale separation—is maintained. For 2D systems, the fluctuation eigenfunctions are labeled by their Fourier wave numbers characterizing spatial variability in that extended spatial direction, and the marginal mode(s) must coincide with the fastest-growing mode(s) over all admissible Fourier wave numbers. Here we derive an ordinary differential equation governing the slow evolution of the wave number of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows and other strongly constrained forms of geophysical turbulence in extreme parameter regimes. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasicoherent structures in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows in which scale separation justifies a QL approximation of the dynamics.
The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limit...
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The temperature dependence of the static penetration lambda(T) has been used as a guide to the nature of the superconducting state in high-T-c materials. It has been argued that an algebraic temperature dependence in ...
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The temperature dependence of the static penetration lambda(T) has been used as a guide to the nature of the superconducting state in high-T-c materials. It has been argued that an algebraic temperature dependence in the ratio Delta lambda(T)/lambda(0) = [lambda(T) - lambda(0)]/lambda(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon lambda(T) and finds an algebraic dependence over a broad range of temperature.
We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or -1) and these block spin values are kept fixed. We then impo...
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We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or -1) and these block spin values are kept fixed. We then impose the majority rule and look at the effect on the phase transition that was present in the original unconstrained spin system. We find that for the checkerboard block-spin configuration, Monte Carlo simulations show that beta(c) is close to 1, which, compared to the original nearest neighbor Ising beta(c) = 0.44..., shows that the critical temperature has been reduced by more than one half For none of the other 11 block-spin configurations that ive have considered is there any indication of a phase transition in the constrained system of original spins.
In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle...
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Fractional-order stochastic gradient descent (FOSGD) leverages a fractional exponent to capture long-memory effects in optimization, yet its practical impact is often constrained by the difficulty of tuning and stabil...
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