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Physical Sciences and Mathematics Commons™
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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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Full-Text Articles in Physical Sciences and Mathematics
Low Regularity Solutions To A Gently Stochastic Nonlinear Wave Equation In Nonequilibrium Statistical Mechanics, L Rey-Bellet, Le Thomas
Low Regularity Solutions To A Gently Stochastic Nonlinear Wave Equation In Nonequilibrium Statistical Mechanics, L Rey-Bellet, Le Thomas
Mathematics and Statistics Department Faculty Publication Series
We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regularity, including spaces with norm beneath the energy norm. For the special case of thermal equilibrium, we also show the existence of an invariant measure (Gibbs state).
Error Analysis Of Coarse-Grained Kinetic Monte Carlo Method, Ma Katsoulakis, P Plechac, A Sopasakis
Error Analysis Of Coarse-Grained Kinetic Monte Carlo Method, Ma Katsoulakis, P Plechac, A Sopasakis
Mathematics and Statistics Department Faculty Publication Series
In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We provide both analytical and numerical evidence that the hierarchy of the coarse models is built in a systematic way that allows for error control in both transient and long-time simulations. We demonstrate that the numerical accuracy of the CGMC algorithm as an approximation of stochastic lattice spin flip dynamics is of order two in terms of the coarse-graining ratio and that the natural small parameter is the coarse-graining ratio over the range of particle/particle interactions. The error …