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Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neutrino emission during the gravitational collapse.

Kinetic theory of matter. --- Relativistic mechanics. --- Mechanics --- Relativity (Physics) --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics

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The world is governed by motions. The term kinetics partially originated from the Greek word ""kinisis,"" which means motion. How important is motion in our life is easily understood. But, how the kinetic theories have been developed during years? Which are the new kinetic theories and updates in recent years? This question and many others can be answered with this book. Some important areas discussed in this book are the kinetic theory of gases, kinetic theory of liquids and vapors, thermodynamic aspects, transportation phenomena, adsorption-kinetic theories, linear and nonlinear kinetic equations, quantum kinetic theory, kinetic theory of nucleation, plasma kinetic theory, and relativistic kinetic theory.

Kinetic theory of matter. --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics --- Physical Sciences --- Engineering and Technology --- Classical Mechanics --- Kinematics --- Physics

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Thermodynamics --- Matter, Kinetic theory of --- Thermodynamique --- Kinetic theory of matter --- 536.7 --- Matter --- Molecular theory --- Statistical mechanics --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Thermodynamics. Energetics --- 536.7 Thermodynamics. Energetics --- Kinetic theory of matter.

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This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions. Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

Maxwell-Boltzmann distribution law. --- Kinetic theory of matter --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics --- Boltzmann distribution law --- Maxwell-Boltzmann density function --- Maxwell distribution --- Distribution (Probability theory) --- Kinetic theory of gases --- Mathematical models.

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Initial value problems --- Kinetic theory of matter --- 517.958 --- Boundary value problems --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics --- Problems, Initial value --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Differential and integral equations of mathematical physics --- Boundary value problems. --- Initial value problems. --- Kinetic theory of matter. --- 517.958 Differential and integral equations of mathematical physics