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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
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 3 , June 2021 , pp. 1040 - 1074
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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