On the causality of a dilute gas as a dissipative relativistic fluid theory of divergence type

1995 ◽  
Vol 28 (23) ◽  
pp. 6943-6959 ◽  
Author(s):  
G B Nagy ◽  
O A Reula
Keyword(s):  
Relativistic Fluid ◽  
Dilute Gas ◽  
Fluid Theory ◽  
Divergence Type

Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron–positron–ion plasmas: Modulational instability and rogue waves

2013 ◽  
Vol 79 (6) ◽  
pp. 1089-1094 ◽  
Author(s):  
IOANNIS KOURAKIS ◽  
MICHAEL MC KERR ◽  
ATA UR-RAHMAN
Keyword(s):  
Fluid Model ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Relativistic Electrons ◽  
Relativistic Fluid ◽  
Ion Plasma ◽  
Electron Positron ◽  
Electrons And Positrons ◽  
Perturbative Method ◽  
Fluid Theory

AbstractA fluid model is used to describe the propagation of envelope structures in an ion plasma under the influence of the action of weakly relativistic electrons and positrons. A multiscale perturbative method is used to derive a nonlinear Schrödinger equation for the envelope amplitude. Criteria for modulational instability, which occurs for small values of the carrier wavenumber (long carrier wavelengths), are derived. The occurrence of rogue waves is briefly discussed.

Dissipative relativistic fluid theories of divergence type

1990 ◽  
Vol 41 (6) ◽  
pp. 1855-1861 ◽  
Author(s):  
Robert Geroch ◽  
Lee Lindblom
Keyword(s):  
Relativistic Fluid ◽  
Divergence Type

scholarly journals Corrigendum on Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron–positron–ion plasmas: Modulational instability & rogue waves

2014 ◽  
Vol 80 (4) ◽  
pp. 653-653
Author(s):  
IOANNIS KOURAKIS ◽  
MICHAEL MC KERR ◽  
ATA UR-RAHMAN
Keyword(s):  
Modulational Instability ◽  
Rogue Waves ◽  
Algebraic Expression ◽  
Typographical Error ◽  
Relativistic Fluid ◽  
Electron Positron ◽  
Formula Group ◽  
Fluid Theory ◽  
Image Position ◽  
Published Paper

There is a typographical error in our recently published paper (Kourakis et al. 2014), namely, in the algebraic expression for the quantity C210 provided in the Appendix.The correct expression for C210 should read: ${C}_{2_1}^0=\frac{c_1\left(\frac{c_1+k^2}{b}\right)^2\left(\frac{2v_g\omega}{k}+\frac{\omega^2}{k^2}\right)-2ac_2}{c_1v_g^2-ab} \, .\$The modification is limited to the presentation of the algebraic calculation, hence the plots presented in the paper are not affected by the typographical error.

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Sign in / Sign up

Export Citation Format

Share Document