scholarly journals Transient Solution Determination of the Boltzmann Equation Using a Polynomial Expansion

1997 ◽  
Vol 7 (2) ◽  
pp. 281-289 ◽  
Author(s):  
S. Tabikh ◽  
C. Gontrand ◽  
J. P. Nougier
Keyword(s):  
Boltzmann Equation ◽  
Polynomial Expansion ◽  
Transient Solution ◽  
The Boltzmann Equation

A transient solution of the Boltzmann equation exposes energy overshoot in semiconductor devices

1999 ◽  
Vol 86 (1) ◽  
pp. 468-475 ◽  
Author(s):  
Chung-Kai Lin ◽  
Neil Goldsman ◽  
Isaak D. Mayergoyz ◽  
Chien-Hwa Chang
Keyword(s):  
Boltzmann Equation ◽  
Semiconductor Devices ◽  
Transient Solution ◽  
The Boltzmann Equation

A note on Mott-Smith's solution of the Boltzmann equation for a shock wave

1957 ◽  
Vol 3 (3) ◽  
pp. 255-260 ◽  
Author(s):  
Akira Sakurai
Keyword(s):  
Shock Wave ◽  
Boltzmann Equation ◽  
Mach Number ◽  
Interpolation Formula ◽  
Velocity Space ◽  
Unique Determination ◽  
Finite Region ◽  
Wave Problem ◽  
The Boltzmann Equation

After a Modification, the interpolation formula of Mott-Smith (1951) for the shock wave problem is found to be a solution of the Boltzmann equation at large Mach number in a finite region of molecular velocity space. This modification gives a unique determination of the shock wave thickness, removing the ambiguity for this in Mott-Smith's formula.

scholarly journals The determination of low energy electron-molecule cross sections via swarm analysis

2008 ◽  
Vol 6 (1) ◽  
pp. 57-69 ◽  
Author(s):  
S. Dujko ◽  
R.D. White ◽  
Z.Lj. Petrovic
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Boltzmann Equation ◽  
Electron Transport ◽  
Cross Sections ◽  
Low Energy ◽  
Energy Electron ◽  
The Boltzmann Equation ◽  
Low Energy Electron

In this paper we discuss the swarm physics based techniques including the Boltzmann equation analysis and Monte Carlo simulation technique for determination of low energy electron-molecule cross sections. A multi term theory for solving the Boltzmann equation and Monte Carlo simulation code have been developed and used to investigate some critical aspects of electron transport in neutral gases under the varying configurations of electric and magnetic fields when non-conservative collisions are operative. These aspects include the validity of the two term approximation and the Legendre polynomial expansion procedure for solving the Boltzmann equation, treatment of non-conservative collisions, the effects of a magnetic field on the electron transport and nature and difference between transport data obtained under various experimental arrangements. It was found that these issues must be carefully considered before unfolding the cross sections from swarms transport data.

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.

Approach to Equilibrium, the H-Theorem and Irreversibility

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Detailed Knowledge ◽  
Approach To Equilibrium ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underlying microdynamics.

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