# Mathematics Colloquia and Seminars

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### Enskog Equation and Particle Systems

Optimization

 Speaker: Prof. Fraydoun Rezakhanlou, UC Berkeley Location: 593 Kerr Start time: Thu, Apr 11 2002, 4:10PM

Boltzmann equation provides a successful description for dilute gases and can be derived from a Hamiltonian system. The simplest example of such a system is the hard sphere model. In this model, one starts with $N$ balls of diameter $\epsilon$ that travel according to their velocities in between elastic collisions. A long-standing open problem asserts that in a Boltzmann--Grad limit ($N$ goes to infinity and $N(\epsilon)^{d-1}$ converges to a nonzero constant) the particle densities converge to solutions of the Boltznmann equation. We change the hard sphere model in two ways. The number $\epsilon$ does not go to zero but instead a collision takes place with probabiliy $1/N$. We then show that the particle densities converge to the solutions of the so-called Enskog equation.