A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

Benjamin D. Goddard; Tim D. Hurst; Mark Wilkinson

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A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

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摘要

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using two examples.

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《Proceedings of the Royal Society of Edinburgh, Section A. Mathematics》 |2021年第3期|1040-1074|共35页
作者
Benjamin D. Goddard; Tim D. Hurst; Mark Wilkinson;
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作者单位

School of Mathematics and the Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK;

Department of Mathematics, Nottingham Trent University, Nottingham, NG11 8NS, UK;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
Liouville equation; Hard particles; BBGKY hierarchy; Inelastic collisions;

A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

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