Variational principles for solving nonlinear Poisson equations for the potential of impurity ions in semiconductors

1976 ◽  
Vol 14 (10) ◽  
pp. 4483-4487 ◽  
Author(s):  
P. Csavinszky
Keyword(s):  
Variational Principles ◽  
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.

Variational Principles in Mathematical Physics, Geometry, and Economics

2009 ◽  
Author(s):  
Alexandru Kristaly ◽  
Vicentiu D. Radulescu ◽  
Csaba Varga
Keyword(s):  
Variational Principles ◽  
Mathematical Physics

A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder

1988 ◽  
Vol 16 (1) ◽  
pp. 18-43 ◽  
Author(s):  
J. T. Oden ◽  
T. L. Lin ◽  
J. M. Bass
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Standing Waves ◽  
Rolling Contact ◽  
Finite Element Models ◽  
Viscoelastic Cylinder ◽  
Element Analysis ◽  
Elastic Rubber ◽  
Frictional Effects ◽  
Rough Foundation

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

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