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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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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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This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasi-static, controlled by a kinetic relation which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.

Phase transformations (Statistical physics) --- Continuum mechanics. --- Kinetic theory of matter. --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics

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This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems—comprised of large populations of interacting cells—whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. The authors propose a new biological model for the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Because the microscopic description of a biological system is far more complex than that of a physical system of inert matter, a higher level of analysis is needed to deal with such complexity. Mathematical models using kinetic theory may represent a way to deal with such complexity, allowing for an understanding of phenomena of nonequilibrium statistical mechanics not described by the traditional macroscopic approach. The proposed models are related to the generalized Boltzmann equation and describe the population dynamics of several interacting elements (kinetic population models). The particular models proposed by the authors are based on a framework related to a system of integro-differential equations, defining the evolution of the distribution function over the microscopic state of each element in a given system. Macroscopic information on the behavior of the system is obtained from suitable moments of the distribution function over the microscopic states of the elements involved. The book follows a classical research approach applied to modeling real systems, linking the observation of biological phenomena, collection of experimental data, modeling, and computational simulations to validate the proposed models. Qualitative analysis techniques are used to identify the prediction ability of specific models. The book will be a valuable resource for applied mathematicians as well as researchers in the field of biological sciences. It may be used for advanced graduate courses and seminars in biological systems modeling with applications to collective social behavior, immunology, and epidemiology. .

Biological systems --- Kinetic theory of matter --- Mathematical models. --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics --- Life sciences. --- Mathematics. --- Genetics --- Physiology --- Life Sciences, general. --- Mathematical Modeling and Industrial Mathematics. --- Mathematical and Computational Biology. --- Applications of Mathematics. --- Genetics and Population Dynamics. --- Physiological, Cellular and Medical Topics. --- Animal physiology --- Animals --- Biology --- Anatomy --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Math --- Science --- Biosciences --- Sciences, Life --- Biomathematics. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Models, Mathematical --- Simulation methods

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This lecture-style monograph is addressed to several categories of readers. First, it will be useful for graduate students studying theory. Second, the topics covered should be interesting for postgraduate students of various specializations. Third, the researchers who want to understand the background of modern theoretical issues in more detail can find a number of useful results here. The phenomena covered involve kinetics of electron, phonon, and photon systems in solids. The dynamical properties and interactions of electrons, phonons, and photons are briefly described in Chapter 1. Further, in Chapters 2-8, the authors present the main theoretical methods: linear response theory, various kinetic equations for the quasiparticles under consideration, and diagram technique. The presentation of the key approaches is always accompanied by solutions of concrete problems to illustrate ways to apply the theory. The remaining chapters are devoted to various manifestations of quantum transport in solids. The choice of particular topics is determined by their scientific importance and methodological value. The 267 supplementary problems presented in the ends of chapters are offered to guide the reader in self-study. Focusing attention on the methodological aspects and discussing a great diversity of kinetic phenomena, in keeping with the guiding principle "a method is more important than a result", the authors minimize both detailed discussion of physical mechanisms of the phenomena considered and comparison of theoretical results to experimental data.

Kinetic theory of matter. --- Matter, Kinetic theory of --- Matter --- Molecular theory --- Statistical mechanics --- Quantum theory. --- Materials. --- Solid State Physics. --- Spectroscopy and Microscopy. --- Elementary Particles, Quantum Field Theory. --- Quantum Optics. --- Materials Science, general. --- Quantum Physics. --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Materials --- Solid state physics. --- Spectroscopy. --- Microscopy. --- Elementary particles (Physics). --- Quantum field theory. --- Quantum optics. --- Materials science. --- Quantum physics. --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Analysis, Microscopic --- Light microscopy --- Micrographic analysis --- Microscope and microscopy --- Microscopic analysis --- Optical microscopy --- Optics --- Analysis, Spectrum --- Spectra --- Spectrochemical analysis --- Spectrochemistry --- Spectrometry --- Spectroscopy --- Chemistry, Analytic --- Interferometry --- Radiation --- Wave-motion, Theory of --- Absorption spectra --- Light --- Spectroscope --- Solids --- Material science --- Physical sciences --- Photons --- Quantum theory --- Relativistic quantum field theory --- Field theory (Physics) --- Relativity (Physics) --- Qualitative --- Analytical chemistry