Statistical equilibrium of the Coulomb/vortex gas on the unbounded 2-dimensional plane
type: Item
instance of: scholarly article
title: Statistical equilibrium of the Coulomb/vortex gas on the unbounded 2-dimensional plane
zbMATH Open document ID: 1115.82033
author: Syed M. Assad
author: Chjan C. Lim
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2005-04-18T00:00:00Z
review text: This paper presents the statistical equilibrium distributions of single-species vortex gases and cylindrical electron plasmas on the unbounded plane obtained by Monte Carlo simulations. We present detailed numerical evidence that at high values of \(\beta>0\) and \(\mu>0\), where \(\beta\) is the inverse temperature and \(mu\) is the Lagrange multiplier associated with the conservation of the moment of vorticity, the equilibrium vortex gas distribution is centered about a regular crystalline distribution with very low variance. This equilibrium crystalline structure has the form of several concentric nearly regular polygons within a bounding circle of radius \(R\). When \(\beta\sim O(1)\), the mean vortex distributions have nearly uniform vortex density inside a circular disk of radius \(R\). In all the simulations, the radius \(R=\sqrt{\beta\Omega/2\mu}\) where \(\Omega\) is the total vorticity of the point vortex gas or number of identical point charges. Using a continuous vorticity density model and assuming that the equilibrium distribution is a uniform one within a bounding circle of radius \(R\), we show that the most probable value of \(R\) scales with inverse temperature \(\beta>0\) and chemical potential \(\mu>0\) as in \(R=\sqrt{\beta\Omega/2\mu}\).
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 82B80
zbMATH DE Number: 2157837
MaRDI profile type: Publication
full work available at URL: dcdsb.2005.5.1
OpenAlex ID: W2078247350
DOI: 10.3934/DCDSB.2005.5.1
description: scientific article; zbMATH DE number 2157837