Thisbookdealswith theclassicalkinetictheoryofgases.Itsaimisto present the basic principles of this theory within an elementary framework and from a more rigorous approach based on the Boltzmann equation. The subjects are presented in a self-contained manner such that the readers can und- stand and learn some methods used in the kinetic theory of gases in order to investigate the Boltzmann equation. In Chapter 1, a sketch on the evolution of the ideas of the kinetic theory is presented. Afterwards, the basic principles of an elementary kinetic theory areintroduced,which arebasedonthe concepts ofmean freepath, molecular mean velocity and mean free time. The Maxwellian distribution function is determinedfromstatisticalarguments,andthetransportcoe?cients ofshear viscosity, thermal conductivity and self-di?usion are obtained from the e- mentary theory. The most common interaction potentials used in the kinetic theory of gases are also introduced in this chapter, and the dynamics of a binary collision is analyzed. Chapter 2 is dedicated to the study of the Boltzmann equation. First, the BoltzmannequationisderivedandtheequationsoftheBBGKYhierarchyare determined.Fromtheknowledgeofthetransferequation-whichfollowsfrom theBoltzmannequation-themacroscopicbalanceequationsforthemoments ofthedistributionfunctionarederived.
Theequilibriumdistributionfunction is determined from the Boltzmann equation and the equilibrium states of a rare?ed gas are also analyzed. In this chapter, theH-theorem and the paradoxes of Loschmidt and Zermelo are discussed. The chapter ends with an analysis of the di?erent forms of the entropy which are used in statistical mechanics to describe the canonical and microcanonical ensembles.
Basic Principles of the Kinetic Theory.- The Boltzmann Equation.- The Chapman-Enskog Method.- Moment Methods.- Polyatomic Gases.- Dense Gases.- Granular Gases.- Mixtures of Monatomic Gases.- Chemically Reacting Gas Mixtures.
From the reviews: "Kremer has written a book with a focus on engineering perspectives and applications of the nonlinear Boltzmann equation, well suited for an advanced course. ... this book is very well suited as a graduate introduction to the Boltzmann equation and its variants. It is also a good reference for those who wish to apply kinetic theory to, say, chemically reacting gases, or who are looking for a good way to comprehend standard closure procedures for the macroscopic balance equations, like Chapman-Enskog or moment methods." (Reinhard Illner, SIAM Review, Vol. 53 (4), 2011)
INTRO TO THE BOLTZMANN EQUATIO
Interaction of Mechanics and Mathematics
Gilberto Medeiros Kremer
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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