Search results for "Linear Boltzmann equation"
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Non Markovian Behavior of the Boltzmann-Grad Limit of Linear Stochastic Particle Systems
2007
We will review some results which illustrate how the distribution of obstacles and the shape of the characteristic curves influence the convergence of the probability density of linear stochastic particle systems to the one particle probability density associated with a Markovian process in the Boltzmann-Grad asymptotics.
On the derivation of a linear Boltzmann equation from a periodic lattice gas
2004
We consider the problem of deriving the linear Boltzmann equation from the Lorentz process with hard spheres obstacles. In a suitable limit (the Boltzmann-Grad limit), it has been proved that the linear Boltzmann equation can be obtained when the position of obstacles are Poisson distributed, while the validation fails, also for the "correct" ratio between obstacle size and lattice parameter, when they are distributed on a purely periodic lattice, because of the existence of very long free trajectories. Here we validate the linear Boltzmann equation, in the limit when the scatterer's radius epsilon vanishes, for a family of Lorentz processes such that the obstacles have a random distributio…