Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

Tomasz M. Tyranowski

doi:10.1098/rspa.2021.0167

Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

Tomasz M. Tyranowski^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

5 Citations (Scopus)

19 Downloads (Pure)

Abstract

In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.

Original language	English
Article number	20210167
Number of pages	23
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	477
Issue number	2252
DOIs	https://doi.org/10.1098/rspa.2021.0167
Publication status	Published - 25 Aug 2021
Externally published	Yes

Keywords

stochastic variational principles
Vlasov-Maxwell equation
Vlasov-Poisson equation
collisions
Fokker-Planck equation
particle methods

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10.1098/rspa.2021.0167Licence: CC BY

ArticleFinal published version, 427 KBLicence: CC BY

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abstract = "In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.",

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AB - In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.

KW - stochastic variational principles

KW - Vlasov-Maxwell equation

KW - Vlasov-Poisson equation

KW - collisions

KW - Fokker-Planck equation

KW - particle methods

U2 - 10.1098/rspa.2021.0167

DO - 10.1098/rspa.2021.0167

M3 - Article

SN - 1364-5021

VL - 477

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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ER -

Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

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Keywords

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