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Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation

Journal article
Authors Mattias Sundén
Bernt Wennberg
Published in Journal of Statistical Physics
Volume 130
Issue 2
Pages 295-312
ISSN 0022-4715
Publication year 2008
Published at Department of Mathematical Sciences, Mathematical Statistics
Department of Mathematical Sciences, Mathematics
Pages 295-312
Language en
Keywords Diffusion approximation; Direct simulation Monte Carlo; Kac equation; Markov jump process; Non-equilibrium stationary state; Thermostat
Subject categories Mathematics


The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.

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