Calculations Of Collision Integrals In The Moment Equations
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Calculations Of Collision Integrals In The Moment Equations
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Author : Kurt Suchy
language : en
Publisher:
Release Date : 1961
Calculations Of Collision Integrals In The Moment Equations written by Kurt Suchy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
For the calculation of the collision integrals in the moment equations Weitzsch's ansatz is made for the velocity distribution functions being represented as integral superposition of Gaussian distributions. Its weighting function must contain a finite number of velocity independent parameters for the treatment of problems with strong deviations from equilibrium. For weak deviations a series expansion yields Grad's expansion of the distribution function in tensorial Hermite polynomials. The moment equations with their collision integrals are established up to the third order and the transport cross sections occurring therein are calculated for inverse power interaction potentials. (Author).
Calculation Of Collision Integrals In The Moment Equations
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Author : Kurt Suchy
language : en
Publisher:
Release Date : 1963
Calculation Of Collision Integrals In The Moment Equations written by Kurt Suchy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Calculation Of Standard Integrals In Moment Kinetic Equations Vychislenie Standartnykh Integralov V Momentnykh Kineticheskikh Uravneniyakh
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Author : E. V. Alekseeva
language : en
Publisher:
Release Date : 1967
Calculation Of Standard Integrals In Moment Kinetic Equations Vychislenie Standartnykh Integralov V Momentnykh Kineticheskikh Uravneniyakh written by E. V. Alekseeva and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
The method of kinetic moment equations permits the evaluation of a significant number of quadratures using an analytic form which is identical for the entire class of problems covered by the integral kinetic operator of the aerodynamics of rarified gases. Such quadratures represent a contribution to the solution of all kinetic problems since they refer to that part of the development which can be covered using general procedures. The physical content and universal character of such quadratures makes the study of their internal structure worthwhile. The paper presents the evaluation of these integrals appearing during Hermite polynomial expansions of the collision and generating functions within a monatomic gas. (Author).
Collision Integrals For A Modified Stockmayer Potential
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Author : Eugene C. Itean
language : en
Publisher:
Release Date : 1961
Collision Integrals For A Modified Stockmayer Potential written by Eugene C. Itean and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Collision integrals categories.
Collision integrals were calculated for the modified Stockmayer potential E(r) = 4 epsilon [(sigma/r)(exp 12) - (sigma/r)(exp 6) - delta(sigma/r)(exp 3)], which may be applied to polar molecules. It was assumed that the colliding molecules maintain their same relative orientation during the encounter. Calculations of the integrals were made for a large reduced temperature range and for a range of delta from 0 to 10. The results agree with other work on non-polar interactions (delta = 0). However for polar interactions the only previously published calculations have been found to be in error and do not agree with this work. Assuming that the molecules interact as alined dipoles of maximum attraction, values for sigma, epsilon, and delta were determined for various polar molecules by a least squares fit of experimental viscosity data. Satisfactory results were obtained for slightly polar molecules, but not for more highly polar molecules such as NH3 or H2O. Therefore, it appears that the assumed model of molecules interacting at all times as alined dipoles of maximum attraction is not satisfactory for estimating trans- port properties of polar molecules.
An Introduction To The Theory Of The Boltzmann Equation
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Author : Stewart Harris
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
An Introduction To The Theory Of The Boltzmann Equation written by Stewart Harris and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Science categories.
This introductory graduate-level course for students of physics and engineering features detailed presentations of Boltzmann's equation, including applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes physical aspects of the theory and offers a practical resource for researchers and other professionals. 1971 edition.
Direct Methods For Solving The Boltzmann Equation And Study Of Nonequilibrium Flows
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Author : V.V. Aristov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-31
Direct Methods For Solving The Boltzmann Equation And Study Of Nonequilibrium Flows written by V.V. Aristov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-31 with Science categories.
This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.
Transport Theory
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Author : Paul Nelson
language : en
Publisher: CRC Press
Release Date : 2023-05-31
Transport Theory written by Paul Nelson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.
This book includes seminal papers on technical subjects - transport theory, invariant imbedding, and integral equations - presented as contributions to honour George Milt Wing in celebration of his 65th birth anniversary in 1988.
Collision Integrals And The Generalized Kinetic Equation For Charged Particle Beams
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Author :
language : en
Publisher:
Release Date : 1998
Collision Integrals And The Generalized Kinetic Equation For Charged Particle Beams written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
In the present paper we study the role of particle interactions on the evolution of a high energy beam. The interparticle forces taken into account are due to space charge alone. We derive the collision integral for a charged particle beam in the form of Balescu-Lenard and Landau and consider its further simplifications. Finally, the transition to the generalized kinetic equation has been accomplished by using the method of adiabatic elimination of fast variables.
Addition Of Inelastic Scattering To The Univac Moment Calculations
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Author : J. Certaine
language : en
Publisher:
Release Date : 1960
Addition Of Inelastic Scattering To The Univac Moment Calculations written by J. Certaine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Neutrons categories.
Hydrodynamic Limits Of The Boltzmann Equation
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Author : Laure Saint-Raymond
language : en
Publisher: Springer
Release Date : 2009-04-20
Hydrodynamic Limits Of The Boltzmann Equation written by Laure Saint-Raymond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Science categories.
The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.