Kinetic Boltzmann Vlasov and Related Equations

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions

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  • Author : Alexander Sinitsyn
  • Publisher : Elsevier
  • Pages : 320 pages
  • ISBN : 0123877806
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKKinetic Boltzmann Vlasov and Related Equations

Kinetic Boltzmann, Vlasov and Related Equations

Kinetic Boltzmann, Vlasov and Related Equations
  • Author : Alexander Sinitsyn,Eugene Dulov,Victor Vedenyapin
  • Publisher : Elsevier
  • Release : 17 June 2011
GET THIS BOOKKinetic Boltzmann, Vlasov and Related Equations

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation

Kinetic Boltzmann, Vlasov and Related Equations

Kinetic Boltzmann, Vlasov and Related Equations
  • Author : Alexander Sinitsyn,Victor Vedenyapin,Eugene Dulov
  • Publisher : Elsevier
  • Release : 16 May 2022
GET THIS BOOKKinetic Boltzmann, Vlasov and Related Equations

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation

Toward General Theory Of Differential-operator And Kinetic Models

Toward General Theory Of Differential-operator And Kinetic Models
  • Author : Sidorov Denis,Sidorov Nikolay,Sinitsyn Alexander V
  • Publisher : World Scientific
  • Release : 13 March 2020
GET THIS BOOKToward General Theory Of Differential-operator And Kinetic Models

This volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov-Maxwell, Fredholm, Lyapunov-Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.

Hyperbolic and Kinetic Models for Self-organised Biological Aggregations

Hyperbolic and Kinetic Models for Self-organised Biological Aggregations
  • Author : Raluca Eftimie
  • Publisher : Springer
  • Release : 07 January 2019
GET THIS BOOKHyperbolic and Kinetic Models for Self-organised Biological Aggregations

This book focuses on the spatio-temporal patterns generated by two classes of mathematical models (of hyperbolic and kinetic types) that have been increasingly used in the past several years to describe various biological and ecological communities. Here we combine an overview of various modelling approaches for collective behaviours displayed by individuals/cells/bacteria that interact locally and non-locally, with analytical and numerical mathematical techniques that can be used to investigate the spatio-temporal patterns produced by said individuals/cells/bacteria. Richly

Statistical Mechanics And The Physics Of Many-particle Model Systems

Statistical Mechanics And The Physics Of Many-particle Model Systems
  • Author : Kuzemsky Alexander Leonidovich
  • Publisher : World Scientific
  • Release : 24 February 2017
GET THIS BOOKStatistical Mechanics And The Physics Of Many-particle Model Systems

The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main

Differential Equations on Measures and Functional Spaces

Differential Equations on Measures and Functional Spaces
  • Author : Vassili Kolokoltsov
  • Publisher : Springer
  • Release : 20 June 2019
GET THIS BOOKDifferential Equations on Measures and Functional Spaces

This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard,

The Cauchy Problem in Kinetic Theory

The Cauchy Problem in Kinetic Theory
  • Author : Robert T. Glassey
  • Publisher : SIAM
  • Release : 01 January 1996
GET THIS BOOKThe Cauchy Problem in Kinetic Theory

Studies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.

Topics in Kinetic Theory

Topics in Kinetic Theory
  • Author : Thierry Passot,Catherine Sulem,P. L. Sulem
  • Publisher : American Mathematical Soc.
  • Release : 16 May 2022
GET THIS BOOKTopics in Kinetic Theory

This book covers a variety of topics related to kinetic theory in neutral gases and magnetized plasmas, with extensions to other systems such as quantum plasmas and granular flows. A comprehensive presentation is given for the Boltzmann equations and other kinetic equations for a neutral gas, together with the derivations of compressible and incompressible fluid dynamical systems, and their rigorous justification. Several contributions are devoted to collisionless magnetized plasmas. Rigorous results concerning the well-posedness of the Vlasov-Maxwell system are presented.

Kinetic Equations

Kinetic Equations
  • Author : Alexander V. Bobylev
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 12 October 2020
GET THIS BOOKKinetic Equations

This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.

Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences
  • Author : Giovanni Naldi,Lorenzo Pareschi,Giuseppe Toscani
  • Publisher : Springer Science & Business Media
  • Release : 12 August 2010
GET THIS BOOKMathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.

Plasma Kinetic Theory

Plasma Kinetic Theory
  • Author : Donald Gary Swanson
  • Publisher : CRC Press
  • Release : 13 May 2008
GET THIS BOOKPlasma Kinetic Theory

Developed from the lectures of a leading expert in plasma wave research, Plasma Kinetic Theory provides the essential material for an introductory course on plasma physics as well as the basis for a more advanced course on kinetic theory. Exploring various wave phenomena in plasmas, it offers wide-ranging coverage of the field. After introducing basic kinetic equations and the Lenard–Balescu equation, the book covers the important Vlasov–Maxwell equations. The solutions of these equations in linear and quasilinear approximations

Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

Advanced Numerical Approximation of Nonlinear Hyperbolic Equations
  • Author : B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
  • Publisher : Springer
  • Release : 14 November 2006
GET THIS BOOKAdvanced Numerical Approximation of Nonlinear Hyperbolic Equations

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are

Transport Phenomena and Kinetic Theory

Transport Phenomena and Kinetic Theory
  • Author : Carlo Cercignani,Ester Gabetta
  • Publisher : Springer Science & Business Media
  • Release : 03 December 2007
GET THIS BOOKTransport Phenomena and Kinetic Theory

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning.