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 Exercises2 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 3 The Lorentz model for the classical transport of charges3.1 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 3.8.4 Di usive behaviour3.8.5 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 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

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