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Author: Carlo Cercignani Publisher: Birkhäuser ISBN: 3034881657 Category : Science Languages : en Pages : 391
Book Description
The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.
Author: Carlo Cercignani Publisher: Birkhäuser ISBN: 3034881657 Category : Science Languages : en Pages : 391
Book Description
The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.
Author: Gregory V. Vereshchagin Publisher: Cambridge University Press ISBN: 1107048222 Category : Science Languages : en Pages : 343
Book Description
This book presents fundamentals, equations, and methods of solutions of relativistic kinetic theory, with applications in astrophysics and cosmology.
Author: Alexander I. Zhmakin Publisher: Springer Nature ISBN: 3031259734 Category : Science Languages : en Pages : 419
Book Description
This book presents a broad and well-structured overview of various non-Fourier heat conduction models. The classical Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation becomes dominant and memory or non-local spatial effects become significant; e.g., during ultrafast heating, heat transfer at the nanoscale, in granular and porous materials, at extremely high values of the heat flux, or in heat transfer in biological tissues. The book looks at numerous non-Fourier heat conduction models that incorporate time non-locality for materials with memory, such as hereditary materials, including fractional hereditary materials, and/or spatial non-locality, i.e. materials with a non-homogeneous inner structure. Beginning with an introduction to classical transport theory, including phase-lag, phonon, and thermomass models, the book then looks at various aspects of relativistic and quantum transport, including approaches based on the Landauer formalism as well as the Green-Kubo theory of linear response. Featuring an appendix that provides an introduction to methods in fractional calculus, this book is a valuable resource for any researcher interested in theoretical and numerical aspects of complex, non-trivial heat conduction problems.
Author: Sauro Succi Publisher: Oxford University Press ISBN: 0199592357 Category : Mathematics Languages : en Pages : 789
Book Description
An introductory textbook to Lattice Boltzmann methods in computational fluid dynamics, aimed at a broad audience of scientists working with flowing matter. LB has known a burgeoning growth of applications, especially in connection with the simulation of complex flows, and also on the methodological side.
Author: Gilberto M. Kremer Publisher: Springer Science & Business Media ISBN: 3642116965 Category : Technology & Engineering Languages : en Pages : 313
Book Description
This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.
Author: Henning Struchtrup Publisher: Springer Science & Business Media ISBN: 3540323864 Category : Science Languages : en Pages : 262
Book Description
The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description. This book discusses classical and modern methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equation, for small and moderate Knudsen numbers, i.e. at and above the Navier-Stokes-Fourier level. The main methods discussed are the classical Chapman-Enskog and Grad approaches, as well as the new order of magnitude method, which avoids the short-comings of the classical methods, but retains their benefits. The relations between the various methods are carefully examined, and the resulting equations are compared and tested for a variety of standard problems. The book develops the topic starting from the basic description of an ideal gas, over the derivation of the Boltzmann equation, towards the various methods for deriving macroscopic transport equations, and the test problems which include stability of the equations, shock waves, and Couette flow.
Author: Gabriel S. Denicol Publisher: Springer Nature ISBN: 3030820777 Category : Science Languages : en Pages : 306
Book Description
This book provides an introduction to relativistic dissipative fluid dynamics, with particular emphasis on its derivation from microscopic transport theory. After a phenomenological derivation of relativistic dissipative fluid dynamics from the second law of thermodynamics, the intrinsic instabilities of relativistic Navier-Stokes theory are discussed. In turn, analytical solutions of relativistic dissipative fluid dynamics are presented. Following, the authors discuss several theories and approaches to derive transport coefficients in dissipative fluid dynamics such as the Chapman-Enskog theory, the theory of Israel and Stewart, and a more recent derivation of relativistic dissipative fluid dynamics based on kinetic theory, which constitutes the main focus of the second part of this book. This book is intended for advanced graduate students and researchers in physics and requires basic knowledge of the theory of special and general relativity. It should be of particular interest to researchers that apply relativistic fluid dynamics in cosmology, astrophysics, and high-energy nuclear physics.
Author: Ilya L. Shapiro Publisher: Springer Nature ISBN: 3030268950 Category : Science Languages : en Pages : 331
Book Description
This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.
Author: Piotr T. Chruściel Publisher: Springer Science & Business Media ISBN: 9783764371302 Category : Science Languages : en Pages : 500
Book Description
Accompanying DVD-ROM contains the electronic proceedings of the summer school on mathematical general relativity and global properties of solutions of Einstein's equations held at Cargèse, Corsica, France, July 20-Aug. 10, 2002.
Author: Carlo Cercignani
Author: Carlo Cercignani
Author: Gregory V. Vereshchagin
Author: Alexander I. Zhmakin
Author: Sauro Succi
Author: Gilberto M. Kremer
Author: Henning Struchtrup
Author: Luca Lusanna
Author: Gabriel S. Denicol
Author: Ilya L. Shapiro
Author: Piotr T. Chruściel