Kinetic theory and transport phenomena / Rodrigo Soto.

Author/creator Soto, Rodrigo author.
Format Electronic
PublicationNew York, NY : Oxford University Press, 2016.
Copyright Date©2016
Description1 online resource : illustrations.
Supplemental ContentClick here to view book
Subjects

SeriesOxford master series in statistical, computational, and theoretical physics
Oxford master series in statistical, computational, and theoretical physics. ^A710977
Contents Cover; Half-Title; Series page; Kinetic Theory and Transport Phenomena; Copyright; Preface; Acknowledgements; Contents; 1 Basic concepts; 1.1 Velocity distribution function; 1.2 The Maxwell-Boltzmann distribution function; 1.3 Densities and fluxes; 1.3.1 Stress tensor and energy flux; 1.3.2 Stress tensor and heat flux in equilibrium; 1.3.3 Flux distribution; 1.4 Collision frequency; 1.5 Mean free path; 1.6 Transport properties in the mean free path approximation; 1.6.1 Thermal conductivity; 1.6.2 Viscosity; 1.6.3 Wall slip; 1.6.4 Self-diffusion; 1.7 Drude model for electric transport
Contents Exercises; 2 Distribution functions; 2.1 Introduction; 2.2 Hamiltonian dynamics; 2.3 Statistical description of the phase space; 2.4 Equilibrium distribution; 2.5 Reduced distributions; 2.6 Microscopic and average observables; 2.6.1 Global observables; 2.6.2 Densities; 2.6.3 Fluxes; 2.6.4 Conservation equations; 2.7 BBGKY hierarchy; 2.7.1 Equation for the one-particle distribution; 2.8 Generalisation to mixtures; 2.9 Reduced distributions in equilibrium and the pair distribution function; 2.10 Master equations; 2.11 Application: systems with overdamped dynamics; Further reading; Exercises
Contents 3 The Lorentz model for the classical transport of charges; 3.1 Hypothesis of the model; 3.2 Lorentz kinetic equation; 3.3 Ion distribution function; 3.4 Equilibrium solution; 3.5 Conservation laws and the collisional invariants; 3.6 Kinetic collision models; 3.6.1 Rigid hard spheres; 3.6.2 Thermalising ions: the BGK model; 3.7 Electrical conduction; 3.7.1 Conservation equation; 3.7.2 Linear response; 3.7.3 Ohm's law; 3.7.4 Electrical conductivity; 3.7.5 Frequency response; 3.8 Relaxation dynamics; 3.8.1 Properties of the linear operator; 3.8.2 Kinetic gap; 3.8.3 Spectrum of the linear operator
Contents 3.8.4 Di usive behaviour; 3.8.5 Rigid hard spheres; 3.8.6 Time scales; 3.9 The Chapman-Enskog method; 3.10 Application: bacterial suspensions, run-and-tumble motion; Further reading; Exercises; 4 The Boltzmann equation for dilute gases; 4.1 Formulation of the Boltzmann model; 4.1.1 Hypothesis; 4.1.2 Kinematics of binary collisions; 4.2 Boltzmann kinetic equation; 4.2.1 General case; 4.2.2 Hard sphere model; 4.3 General properties; 4.3.1 Balance equations and collisional invariants; 4.3.2 H-theorem; 4.3.3 On the irreversibility problem; 4.4 Dynamics close to equilibrium
Contents 4.4.1 Linear Boltzmann operator4.4.2 Spectrum of the linear Boltzmann equation; 4.4.3 Time scales; 4.5 BGK model; 4.6 Boundary conditions; 4.7 Hydrodynamic regime; 4.7.1 The hydrodynamic equations; 4.7.2 Linear response; 4.7.3 Variational principle; 4.7.4 The Chapman-Enskog method; 4.8 Dense gases; 4.8.1 The Enskog model for hard sphere gases; 4.8.2 Virial expansion; 4.9 Application: granular gases; 4.10 Application: the expanding universe; Further reading; Exercises; 5 Brownian motion; 5.1 The Brownian phenomenon; 5.2 Derivation of the Fokker-Planck equation; 5.3 Equilibrium solutions
Summary This title presents the fundamentals of kinetic theory, considering classical paradigmatic examples as well as modern applications. It covers the most important systems where kinetic theory is applied, explaining their major features. The text is balanced between exploring the fundamental concepts of kinetic theory (irreversibility, transport processes, separation of time scales, conservations, coarse graining, distribution functions, etc.) and the results and predictions of the theory, where the relevant properties of different systems are computed.
Bibliography noteIncludes bibliographical references and index.
Source of descriptionOnline resource; title from PDF title page (Oxford, viewed Aug. 02, 2016).
Issued in other formPrint version: Soto, Rodrigo. Kinetic theory and transport phenomena. New York, NY : Oxford University Press, 2016 0198716052 9780198716051
Genre/formElectronic books.
ISBN0191025143 (electronic bk.)
ISBN9780191025143 (electronic bk.)
ISBN9780191824401 (electronic bk.)
ISBN0191824402 (electronic bk.)
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