Addendum to "Variational principles for solving nonlinear Poisson equations for the potential of impurity ions in semiconductors with spatially variable dielectric constants"

1979 ◽  
Vol 20 (10) ◽  
pp. 4372-4374 ◽  
Author(s):  
P. Csavinszky
Keyword(s):  
Variational Principles ◽  
Dielectric Constants ◽  
Poisson Equations ◽  
Impurity Ions

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

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210167
Author(s):  
Tomasz M. Tyranowski
Keyword(s):  
Maxwell Equations ◽  
Variational Principles ◽  
Particle Method ◽  
Variational Characterization ◽  
Particle In Cell ◽  
Poisson Equations ◽  
Stochastic Variational Principles ◽  
Further Development ◽  
Stochastic Particle

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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