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arXiv · 1403.1621

On the Virial Series for a Gas of Particles with Uniformly Repulsive Pairwise Interaction

David Brydges·Domingos H. U. Marchetti
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Abstract

The pressure of a gas of particles with a uniformly repulsive pair interaction in a finite container is shown to satisfy (exactly as a formal object) a "viscous" Hamilton-Jacobi (H-J) equation whose solution in power series is recursively given by the variation of constants formula. We investigate the solution of the H-J and of its Legendre transform equation by the Cauchy-Majorant method and provide a lower bound to the radius of convergence on the virial series of the gas which goes beyond the threshold established by Lagrange's inversion formula. A comparison between the behavior of the Mayer and virial coefficients for different regimes of repulsion intensity is also provided.

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David Brydges, Domingos H. U. Marchetti. 2014-03-06. On the Virial Series for a Gas of Particles with Uniformly Repulsive Pairwise Interaction. https://arxiv.org/abs/1403.1621

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