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Relativistic fluid dynamics. --- Relativistic fluid dynamics --- Mathematical models. --- Fluid dynamics --- Relativistic mechanics --- Relativity (Physics)
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This title provides an up-to-date, lively and approachable introduction to the mathematical formalism, numerical techniques and applications of relativistic hydrodynamics. The topic is presented here in a form which will be appreciated both by students and researchers in the field. The book is especially recommended to astrophysicists, particle physicists and applied mathematicians.
Relativistic fluid dynamics. --- Hydrodynamics. --- Fluid dynamics --- Relativistic mechanics --- Relativity (Physics) --- Relativistic fluid dynamics --- Hydrodynamics --- Hidrodinàmica --- Dinàmica de fluids --- Mecànica de fluids --- Aerodinàmica --- Capa límit --- Equacions de Navier-Stokes --- Fluídica --- Fluïdització --- Magnetohidrodinàmica --- Ones de xoc --- Turbulència --- Vòrtexs --- Tixotropia --- Enginyeria hidràulica --- Mecànica --- Mecànica analítica --- Cavitació --- Ones --- Ones de gravetat --- Urodinàmica --- Viscositat
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This book takes a fresh, systematic approach to determining the equation of motion for the classical model of the electron introduced by Lorentz 130 years ago. The original derivations of Lorentz, Abraham, Poincaré, and Schott are modified and generalized for the charged insulator model of the electron to obtain an equation of motion consistent with causal solutions to the Maxwell-Lorentz equations and the equations of special relativity. The solutions to the resulting equation of motion are free of pre-acceleration and pre-deceleration. The generalized method is applied to obtain the causal solution to the equation of motion of a charge accelerating in a uniform electric field for a finite time interval. Alternative derivations of the Landau-Lifshitz approximation are given as well as necessary and sufficient conditions for the Landau-Lifshitz approximation to be an accurate solution to the exact Lorentz-Abraham-Dirac equation of motion. Binding forces and a total stress-momentum-energy tensor are derived for the charged insulator model. Appendices provide simplified derivations of the self-force and power at arbitrary velocity. In this third edition, some of the history has been made more accurate and some of the derivations have been simplified and clarified. A detailed three-vector exact solution to the Landau-Lifshitz approximate equation of motion is given for the problem of an electron traveling in a counterpropagating plane-wave laser-beam pulse. Semi-classical analyses are used to derive the conditions that determine the significance of quantum effects not included in the classical equation of motion. The book is a valuable resource for students and researchers in physics, engineering, and the history of science.
Differential equations --- Mathematical physics --- Classical mechanics. Field theory --- Electromagnetism. Ferromagnetism --- Experimental nuclear and elementary particle physics --- differentiaalvergelijkingen --- deeltjesfysica --- elektrodynamica --- wiskunde --- fysica --- mechanica --- Lorentz transformations. --- Relativistic fluid dynamics. --- Electromagnetic theory.
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"This is a remarkable book. […] A fresh and novel approach to old problems and to their solution." –Fritz Rohrlich, Professor Emeritus of Physics, Syracuse University This book takes a fresh, systematic approach to determining the equation of motion for the classical model of the electron introduced by Lorentz more than 100 years ago. The original derivations of Lorentz, Abraham, Poincaré and Schott are modified and generalized for the charged insulator model of the electron to obtain an equation of motion consistent with causal solutions to the Maxwell-Lorentz equations and the equations of special relativity. The solutions to the resulting equation of motion are free of pre-acceleration and runaway behavior. Binding forces and a total stress–momentum–energy tensor are derived for the charged insulator model. Appendices provide simplified derivations of the self-force and power at arbitrary velocity. In this Second Edition, the method used for eliminating the noncausal pre-acceleration from the equation of motion has been generalized to eliminate pre-deceleration as well. The generalized method is applied to obtain the causal solution to the equation of motion of a charge accelerating in a uniform electric field for a finite time interval. Alternative derivations of the Landau-Lifshitz approximation are given as well as necessary and sufficient conditions for the Landau-Lifshitz approximation to be an accurate solution to the exact Lorentz-Abraham-Dirac equation of motion. The book is a valuable resource for students and researchers in physics, engineering, and the history of science.
Electromagnetic theory. --- Lorentz transformations. --- Relativistic fluid dynamics. --- Théorie électromagnétique --- Lorentz, Transformations de --- Electromagnetic theory --- Lorentz transformations --- Relativistic fluid dynamics --- Electricity & Magnetism --- Physics --- Physical Sciences & Mathematics --- Light, Electromagnetic theory of --- Physics. --- Gravitation. --- Mechanics. --- Optics. --- Electrodynamics. --- Optics and Electrodynamics. --- Theoretical, Mathematical and Computational Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Classical Electrodynamics. --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Mathematical physics. --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Physical mathematics --- Light --- Properties --- Mathematics
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Pham Mau Quam: Problèmes mathématiques en hydrodynamique relativiste.- A. Lichnerowicz: Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes.- A.H. Taub: Variational principles in general relativity.- J. Ehlers: General relativistic kinetic theory of gases.- K. Marathe: Abstract Minkowski spaces as fibre bundles.- G. Boillat: Sur la propagation de la chaleur en relativité.
Fluid dynamics -- Computer simulation. --- Fluid dynamics -- Mathematical models. --- Relativistic fluid dynamics. --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Relativistic fluid dynamics --- Hydrodynamics --- Mathematics. --- Partial differential equations. --- Gravitation. --- Continuum mechanics. --- Partial Differential Equations. --- Continuum Mechanics and Mechanics of Materials. --- Classical and Quantum Gravitation, Relativity Theory. --- Fluid dynamics --- Relativistic mechanics --- Relativity (Physics) --- Differential equations, partial. --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Partial differential equations --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties
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Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.
Relativistic fluid dynamics. --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Nuclear Physics --- Dirac equation. --- Quantum chromodynamics. --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Physics. --- Energy. --- Mathematical physics. --- Quantum field theory. --- String theory. --- Elementary particles (Physics). --- Quantum Field Theories, String Theory. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Energy, general. --- Particles (Nuclear physics) --- Quantum electrodynamics --- Differential equations, Partial --- Quantum field theory --- Wave equation --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Mathematics
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The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev’s approach, which generalizes the notion of Gibbs’ ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev’s method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly
relativistic fluid dynamics --- statistical operator --- non-equilibrium states --- transport coefficients --- correlation functions --- open quantum system --- master equation --- non-equilibrium statistical operator --- relevant statistical operator --- quasi-temperature --- dynamic correlations --- QCD matter --- phase transition --- critical point --- nonequilibrium thermo-field dynamics --- kinetics --- hydrodynamics --- kinetic equations --- bound states --- quark-gluon plasma --- out-of-equilibrium quantum field theory --- dimensional renormalization --- finite-time-path formalism --- Boltzmann equation --- gluon saturation --- pion enhancement --- ALICE --- LHC --- thermalization --- hadronization --- Gibbs equilibrium statistical mechanics --- Bogoliubov’s quasi-averages --- pressure fluctuations --- relativistic ideal gas --- kinetic theory --- particle production --- Schwinger effect --- Zitterbewegung --- low density approximation --- quantum statistical mechanics --- relativistic hydrodynamics --- Kubo formulae --- graphene --- dynamic critical phenomena --- high-field and nonlinear effects --- QCD --- gluons --- Bose-Einstein condensate --- Fokker-Planck equation --- relaxation time approximation --- linear response theory --- permittivity, dynamical conductivity, absorption coefficient, dynamical collision frequency --- ordered lattice, disordered lattice --- Umklapp process --- interband transitions --- finite temperature field theory --- path integrals --- quantum fields in curved spacetime --- symmetries --- quantum anomalies --- irreversibility --- entropy --- electrical conductivity --- Zubarev operator --- Unruh effect --- acceleration --- Zubarev formalism --- pion chemical potential
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