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

Published online by Cambridge University Press:  28 December 2020

Benjamin D. Goddard
Affiliation:
School of Mathematics and the Maxwell Institute for Mathematical Sciences, University of Edinburgh, EdinburghEH9 3FD, UK ([email protected])
Tim D. Hurst
Affiliation:
School of Mathematics and the Maxwell Institute for Mathematical Sciences, University of Edinburgh, EdinburghEH9 3FD, UK ([email protected])
Mark Wilkinson
Affiliation:
Department of Mathematics, Nottingham Trent University, Nottingham, NG11 8NS, UK ([email protected])

Abstract

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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