The Boltzmann Equation: Theory and Applications

ISBN-13: 9783709183380 / Angielski / Miękka / 2012 / 642 str.

E. G. D. Cohen; W. Thirring

Opis

In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D.

Spis treści

Welcome Speech.- Life and Personality of Ludwig Boltzmann.- Philosophical Biography of Ludwig Boltzmann.- The Development of Boltzmann’s Statistical Ideas.- The Validity and the Limitations of the Boltzmann Equation.- Comment to Professor Uhlenbeck’s Paper.- On Higher Order Hydrodynamic Theories of Shock Structure.- Sound From the Boltzmann Equation.- The Generalization of the Boltzmann Equation to Higher Densities.- The Three-Particle Collision Term in the Generalized Boltzmann Equation.- Velocity Correlation Functions for Moderately Dense Gases.- On Kinetic Equations for Particles with Internal Degrees of Freedom.- Flow-Birefringence in Gases, An Example of the Kinetic Theory Based on the Boltzmann Equation for Rotating Particles.- Non-Equilibrium Angular Momentum Polarization in Rotating Molecules.- The Boltzmann Equation in Solid State Physics.- Experimental and Theoretical Investigations in Semiconductors Concerning the Boltzmann Equation.- Some Probabilistic Aspects of the Boltzmann Equation.- The Statistical Interpretation of Non-Equilibrium Entropy.- A Review of Computer Studies in the Kinetic Theory of Fluids.- A Survey of Neutron Transport Theory.- Relativistic Boltzmann Theory.- Kinetic Equation for Elementary Excitations in Quantum Systems.- Ergodic Theory.- Ergodic Theory.- Ergodic Theory and Approach to Equilibrium for Finite and Infinite Systems.- Erinnerungen an Boltzmanns Vorlesungen.