scholarly journals A Comment on ‘‘On the corotating frame and evolution equations in kinetic theory’’

1986 ◽  
Vol 85 (4) ◽  
pp. 2341-2342 ◽  
Author(s):  
A. S. Lodge ◽  
R. B. Bird ◽  
C. F. Curtiss ◽  
M. W. Johnson
Keyword(s):  
Kinetic Theory ◽  
Evolution Equations ◽  
Corotating Frame

scholarly journals Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 907 ◽  
Author(s):  
Oğul Esen ◽  
Miroslav Grmela ◽  
Hasan Gümral ◽  
Michal Pavelka
Keyword(s):  
Kinetic Theory ◽  
Lie Algebra ◽  
Particle Motion ◽  
Evolution Equations ◽  
Poisson Brackets ◽  
Hamiltonian Approach ◽  
Symmetric Tensors ◽  
Field Equations ◽  
Algebra Homomorphisms

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

MATHEMATICAL METHODS AND TOOLS OF KINETIC THEORY TOWARDS MODELLING COMPLEX BIOLOGICAL SYSTEMS

2005 ◽  
Vol 15 (11) ◽  
pp. 1639-1666 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
MARCELLO DELITALA
Keyword(s):  
Kinetic Theory ◽  
Evolution Equations ◽  
Classical Mechanics ◽  
Mathematical Framework ◽  
Mathematical Approach ◽  
Biological Functions ◽  
Mathematical Methods ◽  
Research Perspectives ◽  
Large Systems ◽  
The One

This paper develops a variety of mathematical tools to model the dynamics of large systems of interacting cells. Interactions are ruled not only by laws of classical mechanics, but also by some biological functions. The mathematical approach is the one of kinetic theory and non-equilibrium statistical mechanics. The paper deals both with the derivation of evolution equations and with the design of specific models consistent with the above-mentioned mathematical framework. Various hints for research perspectives are proposed in the last part of the paper.

Relativistic Kinetic Theory

2017 ◽  
Author(s):  
Gregory V. Vereshchagin ◽  
Alexey G. Aksenov
Keyword(s):  
Kinetic Theory ◽  
Relativistic Kinetic Theory
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