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Statistical mechanics

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This book describes advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. Chaotic Scattering is illustrated with disk scatterers and with examples of unimolecular chemical reactions and then generalized to transport in spatially extended systems. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.

Statistical mechanics --- Chaotic behavior in systems --- Scattering (Physics)

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Chaotic behavior in systems. --- Statistical mechanics. --- Scattering (Physics) --- Chaos (théorie des systèmes) --- Mécanique statistique. --- Diffusion (physique nucléaire)

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In the modern theory of boundary value problems the following ap­ proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob­ the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob­ lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].

Transport theory --- Boundary value problems. --- Mathematical physics. --- Problèmes aux limites --- Physique mathématique --- Mathematics. --- Problèmes aux limites --- Physique mathématique --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Mathematics, general. --- Math --- Science --- 517.1 Mathematical analysis --- Mathematical analysis --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Statistical mechanics --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Initial value problems --- Physical mathematics --- Physics --- Mathematics

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Énergie --- energy --- Chaleur --- Heat --- Transfert de masse --- Mass transfer --- Échange thermique --- Heat transfer --- Rayonnement thermique --- Thermal radiation --- Mécanique des fluides --- Fluid mechanics --- Mécanique du sol --- soil mechanics --- Échange d'énergie --- energy exchange --- Convection --- Transport theory --- Chemical engineering --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Engineering --- Chemistry, Technical --- Metallurgy --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Statistical mechanics --- Fluid mechanics. --- Mass transfer. --- Transmission. --- Transport theory. --- Chemical engineering. --- Convection. --- energy exchange. --- energy. --- Heat transfer. --- Heat. --- soil mechanics. --- Thermal radiation. --- Théorie du transport. --- Génie chimique. --- Transfert de masse. --- Creep --- Diffusion --- Laminar flow --- Transport properties --- Turbulent flow