Topic
Boltzmann constant
About: Boltzmann constant is a research topic. Over the lifetime, 4508 publications have been published within this topic receiving 90601 citations. The topic is also known as: k & k_B.
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Book•
01 Jan 1994
TL;DR: In this article, the authors present rigorous mathematical results in the kinetic theory of a gas of hard spheres, including the Boltzmann equations, global existence theory, and the fluid-dynamical limits.
Abstract: This book is devoted to the presentation of rigorous mathematical results in the kinetic theory of a gas of hard spheres. Recent developments as well as classical results are presented in a unified way, such that the book should become the standard reference on the subject. There is no such book available at present. The reader will find a systematic treatment of the main mathematical results, a discussion of open problems, and a guide to the existing literature. There is a rigorous and comprehensive presentation of strict validation of the Boltzmann equations, global existence theory, and the fluid-dynamical limits. The authors also review and discuss classical derivation and properties of the Boltzmann equation, particle simulation methods, and boundary conditions.
1,450 citations
Book•
01 Jan 1970
TL;DR: In this article, the authors compare Boltzmann's H-theorem and the Maxwellian velocity-distribution function for simple and dense gases and show that the third approximation to the velocity distribution function is the best known.
Abstract: Foreword Introduction 1. Vectors and tensors 2. Properties of a gas: definitions and theorems 3. The equations of Boltzmann and Maxwell 4. Boltzmann's H-theorem and the Maxwellian velocity-distribution 5. The free path, the collision-frequency and persistence of velocities 6. Elementary theories of the transport phenomena 7. The non-uniform state for a simple gas 8. The non-uniform state for a binary gas-mixture 9. Viscosity, thermal conduction, and diffusion: general expressions 10. Viscosity, thermal conduction, and diffusion: theoretical formulae for special molecular models 11. Molecules with internal energy 12 Viscosity: comparison of theory with experiment 13. Thermal conductivity: comparison of theory with experiment 14. Diffusion: comparison of theory with experiment 15. The third approximation to the velocity-distribution function 16. Dense gases 17. Quantum theory and the transport phenomena 18. Multiple gas mixtures 19. Electromagnetic phenomena in ionized gases Historical summary Name index Subject index References to numerical data for particular gases (simple and mixed).
1,431 citations
TL;DR: This paper shows that both of these effects of a non-Galilean invariance caused by a density-dependent coefficient in the convection term can be eliminated exactly in a lattice Boltzmann-equation model.
Abstract: It is known that the Frisch-Hasslacher-Pomeau lattice-gas automaton model and related models possess some rather unphysical effects. These are (1) a non-Galilean invariance caused by a density-dependent coefficient in the convection term, and (2) a velocity-dependent equation of state. In this paper, we show that both of these effects can be eliminated exactly in a lattice Boltzmann-equation model.
1,394 citations
Book•
01 Jan 1989TL;DR: Combinatorial Optimization and Boltzmann Machines, Parallel Simulated Annealing Algorithms, and Neural Computing.
Abstract: SIMULATED ANNEALING. Combinatorial Optimization. Simulated Annealing. Asymptotic Convergence. Finite-Time Approximation. Simulated Annealing in Practice. Parallel Simulated Annealing Algorithms. BOLTZMANN MACHINES. Neural Computing. Boltzmann Machines. Combinatorial Optimization and Boltzmann Machines. Classification and Boltzmann Machines. Learning and Boltzmann Machines. Appendix. Bibliography. Indices.
1,294 citations
TL;DR: In this article, the authors studied the large-data Cauchy problem for Boltzmann equations with general collision kernels and proved that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution.
Abstract: We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution. From this stability result we deduce global existence of a solution to the Cauchy problem. Our method relies upon recent compactness results for velocity averages, a new formulation of the Boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions. It allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations.
1,155 citations