Projects per year
Abstract
We will revisit the classical questions of understanding the statistics of various deterministic dynamics of $N$ hard spheres of diameter $\varepsilon$ with random initial data in the Boltzmann-Grad scaling as $\varepsilon$ tends to zero and $N$ tends to infinity. The convergence of the empiric particle dynamics to the Boltzmann-type dynamics is shown using semigroup methods to describe probability measures on collision trees associated to physical trajectories in the case of a Rayleigh gas. As an application we derive the diffusion equation by a further rescaling.
Original language | English |
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Publisher | London Mathematical Society |
Publication status | Acceptance date - 3 May 2024 |
Publication series
Name | London Mathematical Society Lecture Note Series |
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Bibliographical note
To appear in LMS lecture notes for conference 'Dynamics, Bifurcations and Numerics', University of Surrey, July 2023Keywords
- math.AP
- math.DS
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Dive into the research topics of 'Derivation of kinetic and diffusion equations from a hard-sphere Rayleigh gas using collision trees and semigroups'. Together they form a unique fingerprint.Projects
- 1 Finished
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Derivation of kinetic equation: From Newton to Boltzmann via trees
Matthies, K. (PI)
1/10/20 → 31/03/24
Project: UK charity