On the number of collisions in a hard sphere particle system in all space

DOI10.1080/00411458908214499zbMath0723.58031OpenAlexW2051576749MaRDI QIDQ3210577

Reinhard Illner

Publication date: 1989

Published in: Transport Theory and Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00411458908214499

Mathematics Subject Classification ID

Kinetic theory of gases in equilibrium statistical mechanics (82B40) Ergodic theory (37A99) Collision of rigid or pseudo-rigid bodies (70F35)

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Finite-range repulsive systems of finitely many particles ⋮ Hard spheres dynamics: weak vs strong collisions ⋮ Finiteness of the number of collisions in a hard sphere particle system in all space, II: Arbitrary diameters and masses ⋮ On pinned billiard balls and foldings ⋮ Long‐time correlations for a hard‐sphere gas at equilibrium ⋮ On the number of hard ball collisions ⋮ Long-time derivation at equilibrium of the fluctuating Boltzmann equation ⋮ Structure of correlations for the Boltzmann-Grad limit of hard spheres ⋮ New proof of Sinai's formula for the entropy of hyperbolic billard systems. Application to Lorentz gases and Bunimovich stadiums ⋮ The \(K\)-property of \(N\) billiard balls. I ⋮ A lower bound for the number of elastic collisions ⋮ The propagation of chaos for a rarefied gas of hard spheres in the whole space ⋮ The Boltzmann Equation over $${{\mathbb R}^{{\mathrm {D}}}}$$ R D : Dispersion Versus Dissipation ⋮ Virial estimates for hard spheres ⋮ Protecting billiard balls from collisions ⋮ A ``transversal fundamental theorem for semi-dispersing billiards ⋮ An improved upper bound on the number of billiard ball collisions

Cites Work

• Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum
• Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum