Generalized Boltzmann Physical Kinetics

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Author: Boris V. Alexeev
Publisher: Elsevier
ISBN: 9780080478012
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Generalized Boltzmann Physical Kinetics by Boris V. Alexeev


Original Title: Generalized Boltzmann Physical Kinetics

The most important result obtained by Prof. B. Alexeev and reflected in the book is connected with new theory of transport processes in gases, plasma and liquids. It was shown by Prof. B. Alexeev that well-known Boltzmann equation, which is the basement of the classical kinetic theory, is wrong in the definite sense. Namely in the Boltzmann equation should be introduced the additional terms which generally speaking are of the same order of value as classical ones. It leads to dramatic changing in transport theory. The coincidence of experimental and theoretical data became much better. Particularly it leads to the strict theory of turbulence and possibility to calculate the turbulent flows from the first principles of physics. · Boltzmann equation (BE) is valid only for particles, which can be considered as material points, generalized Boltzmann equation (GBE) removes this restriction. · GBE contains additional terms in comparison with BE, which cannot be omitted · GBE leads to strict theory of turbulence · GBE gives all micro-scale turbulent fluctuations in tabulated closed analytical form for all flows · GBE leads to generalization of electro-dynamic Maxwell equations · GBE gives new generalized hydrodynamic equations (GHE) more effective than classic Navier-Stokes equations · GBE can be applied for description of flows for intermediate diapason of Knudsen numbers · Asymptotical solutions of GBE remove contradictions in the theory of Landau damping in plasma

Unified Non Local Theory Of Transport Processes

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Author: Boris V. Alexeev
Publisher: Elsevier
ISBN: 0444634878
Size: 40.69 MB
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Unified Non Local Theory Of Transport Processes by Boris V. Alexeev


Original Title: Unified Non Local Theory Of Transport Processes

Unified Non-Local Theory of Transport Processess, 2nd Edition provides a new theory of transport processes in gases, plasmas and liquids. It is shown that the well-known Boltzmann equation, which is the basis of the classical kinetic theory, is incorrect in the definite sense. Additional terms need to be added leading to a dramatic change in transport theory. The result is a strict theory of turbulence and the possibility to calculate turbulent flows from the first principles of physics. Fully revised and expanded edition, providing applications in quantum non-local hydrodynamics, quantum solitons in solid matter, and plasmas Uses generalized Boltzmann kinetic theory as an highly effective tool for solving many physical problems beyond classical physics Addresses dark matter and energy Presents non-local physics in many related problems of hydrodynamics, gravity, black holes, nonlinear optics, and applied mathematics

Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models

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Author: N. Bellomo
Publisher: World Scientific
ISBN: 9789810240783
Size: 69.46 MB
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Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models by N. Bellomo


Original Title: Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models

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.

An Introduction To The Theory Of The Boltzmann Equation

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Author: Stewart Harris
Publisher: Courier Corporation
ISBN: 0486143821
Size: 52.46 MB
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An Introduction To The Theory Of The Boltzmann Equation by Stewart Harris


Original Title: An Introduction To The Theory Of The Boltzmann Equation

This introductory graduate-level text emphasizes physical aspects of the theory of Boltzmann's equation in a detailed presentation that doubles as a practical resource for professionals. 1971 edition.

Mathematical Models Of Granular Matter

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Author: Gianfranco Capriz
Publisher: Springer Science & Business Media
ISBN: 3540782761
Size: 80.97 MB
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Mathematical Models Of Granular Matter by Gianfranco Capriz


Original Title: Mathematical Models Of Granular Matter

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Kinetic Theory Of Gases In Shear Flows

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Author: Vicente Garzó
Publisher: Springer Science & Business Media
ISBN: 9781402014369
Size: 29.71 MB
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Kinetic Theory Of Gases In Shear Flows by Vicente Garzó


Original Title: Kinetic Theory Of Gases In Shear Flows

The kinetic theory of gases as we know it dates to the paper of Boltzmann in 1872. The justification and context of this equation has been clarified over the past half century to the extent that it comprises one of the most complete examples of many-body analyses exhibiting the contraction from a microscopic to a mesoscopic description. The primary result is that the Boltzmann equation applies to dilute gases with short ranged interatomic forces, on space and time scales large compared to the corresponding atomic scales. Otherwise, there is no a priori limitation on the state of the system. This means it should be applicable even to systems driven very far from its eqUilibrium state. However, in spite of the physical simplicity of the Boltzmann equation, its mathematical complexity has masked its content except for states near eqUilibrium. While the latter are very important and the Boltzmann equation has been a resounding success in this case, the full potential of the Boltzmann equation to describe more general nonequilibrium states remains unfulfilled. An important exception was a study by Ikenberry and Truesdell in 1956 for a gas of Maxwell molecules undergoing shear flow. They provided a formally exact solution to the moment hierarchy that is valid for arbitrarily large shear rates. It was the first example of a fundamental description of rheology far from eqUilibrium, albeit for an unrealistic system. With rare exceptions, significant progress on nonequilibrium states was made only 20-30 years later.

Modeling In Applied Sciences

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Author: Nicola Bellomo
Publisher: Springer Science & Business Media
ISBN: 9780817641023
Size: 20.58 MB
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Modeling In Applied Sciences by Nicola Bellomo


Original Title: Modeling In Applied Sciences

A survey book providing an authoritative and comprehensive presentation of Boltzmann models (i.e., nonlinear kinetic theory) and computational methods. This new survey book provides a comprehensive and authoritative presentation of current methods and applications for Boltzmann models and computational methods. Selected applications address topics in complex fluid flows, geophysical problems, communications, and biochemical processes. The book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex

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