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Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms : offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development ; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws ; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods ; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods ; includes MATLAB software with which all main methods and computational results in the book can be reproduced ; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication. This book is intended for graduate students in computational mathematics and researchers seeking a comprehensive introduction to modern methods for solving conservation laws. Students and researchers in applied sciences and engineering will benefit from the book's emphasis on algorithmic aspects of complex algorithms. The text also includes extensive references which allows researchers to pursue advanced research and results.
Conservation laws (Physics) --- Lois de conservation (physique) --- MATLAB (logiciel)
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Cet ouvrage s'adresse aux ingénieurs numériciens et aux chercheurs en mathématiques appliquées et en mécanique des fluides numérique.L'étude de la dynamique des gaz demande de maîtriser les modèles physiques comme la thermodynamique et la mécanique des milieux continus, les mathématiques appliquées et enfin l'art de l'ingénieur pour concevoir et mettre en œuvre les méthodes d'approximation numérique. Ce mémoire permet d'aborder les modèles physiques de la dynamique des gaz et les éléments fondamentaux en vue de leur mise en application pratique au sein de logiciels, en s'appuyant avant tout sur les éléments mathématiques rigoureux : solution faible d'une loi de conservation pour formuler correctement la présence de discontinuités, notion d'entropie mathématique, problème de Riemann, discrétisation via l'approche des volumes finis, convergence des schémas numériques. Ouvrage d'introduction, des connaissances de mathématiques générales sont suffisantes pour en aborder la lecture. Des exercices corrigés permettent également au lecteur de mesurer l'acquisition de ses connaissances tout en lui proposant de découvrir un point de vue complémentaire. [Éditeur]
Conservation laws (Physics) --- Gas dynamics --- Lois de conservation (physique) --- Gaz, Dynamique des.
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Shock waves --- Conservation laws (Physics) --- Differential equations, Hyperbolic --- Ondes de choc --- Lois de conservation (Physique) --- Numerical solutions
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Mechanica. --- Mécanique analytique. --- Mécanique. --- Physique mathématique. --- Équations du mouvement. --- Lois de conservation (physique). --- Mechanics, Analytic. --- Mécanique analytique --- Mechanics, Analytic
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Au cours des trente dernières années, les progrès de la physique théorique ont été étroitement corrélés à ceux des mathématiques, en particulier dans le domaine de la théorie des cordes. Ce livre porte à la fois sur les développements de la physique et des mathématiques contemporaines. La conception de l'ouvrage est extrêmement originale : l'auteur ne se contente pas d'exposer sa vision des théories scientifiques, mais il appuie son argumentation en lui donnant un aspect ludique grâce à des énigmes intrigantes de mathématiques et de physique qui défient parfois l'intuition. Par exemple, si l'on rallonge d'un mètre une ceinture entourant la Terre à l'Equateur, quelle est la taille de l'objet qu'on peut glisser sous cette ceinture ? Après une revue des progrès récents dans notre compréhension de l'Univers (symétries et modèle standard des particules, trous noirs et cosmologie, etc.), l'auteur développe dans l'avant dernier chapitre le lien intime entre physique et mathématiques, en introduisant en particulier les notions de dualité et de symétrie miroir en théorie des cordes. Cet ouvrage s'adresse aux étudiants de physique et de mathématiques et à toute personne curieuse des développements récents de la science. Edward Witten, lauréat de la médaille Fields de mathématiques, écrit à propos de cet ouvrage : "Ce livre est un voyage fascinant et original dans les idées les plus avancées en physique et en mathématiques. Il est illustré par des énigmes élémentaires et amusantes. Le lecteur y trouvera de quoi apprendre et de quoi s'amuser"
Physics --- Mathematics --- Symmetry (Physics) --- Conservation laws (Physics) --- Conservation laws (Mathematics) --- Univers --- Mathématiques --- Physique --- Symétrie (physique) --- Lois de conservation (physique) --- Lois de conservation (mathématiques) --- Universe
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Mécanique. --- Mecanique --- Physique. --- Lois de conservation (Physique) --- Probleme des N corps --- Probleme a deux corps --- Mechanics --- Mécanique --- Study and teaching (Higher) --- Etude et enseignement (supérieur) --- Mécanique --- Mecanique - Problemes et exercices --- Étude et enseignement (supérieur) --- Étude et enseignement (supérieur)
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Symmetry (Physics) --- Conservation laws (Physics) --- Differential invariants --- Physics --- Mathematics --- Symétrie (Physique) --- Lois de conservation (Physique) --- Invariants différentiels --- Physique --- Mathématiques --- History --- Histoire --- Noether, Emmy, --- Influence. --- Noether's theorem. --- Mathématiques --- Symétrie (physique) --- Calcul des variations. --- History. --- Histoire. --- Noether, Emmy --- Symétrie (physique)
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"Material and energy (M&E) balances are fundamental to biological, chemical, electrochemical, photochemical and environmental engineering disciplines and important in many fields related to sustainable development. This comprehensive compendium presents the basic M&E balance concepts and calculations in a format easily digested by students, engineering professionals and those concerned with related environmental issues. The useful reference text includes worked examples for each chapter and demonstrates process balances in the framework of M&E concerns of the 21st century. The additional problems and solutions in the Appendix embrace a wide range of subjects, from fossil fuels to fuel cells, solar energy, space stations, carbon dioxide capture and sodium-ion batteries.
Chemical processes --- Chemical engineering --- Mathematical optimization --- Nonlinear programming --- Conservation laws (Physics) --- Chemical processes. --- Mathematical optimization. --- Nonlinear programming. --- Procédés chimiques. --- Génie chimique --- Optimisation mathématique. --- Programmation non linéaire. --- Lois de conservation (physique) --- Mathematics. --- Mathématiques. --- Procédés chimiques. --- Génie chimique --- Optimisation mathématique. --- Programmation non linéaire. --- Mathématiques.
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The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this envi ronment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conserva tion laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyper bolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are realized as continuous media, and so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The reader may flesh it out with the help of a specialized text on the subject.
Champs [Théorie des ] (Physique) --- Conservatiewetten (Fysica) --- Conservation [Lois de ] --- Conservation laws (Physics) --- Differentiaalvergelijkingen [Hyperbolische ] --- Differential equations [Hyperbolic] --- Equations différentielles hyperboliques --- Field theory (Physics) --- Lois de conservation (Physique) --- Veldtheorie (Fysica) --- Differential equations, Hyperbolic. --- Conservation laws (Physics). --- Field theory (Physics). --- Partial differential equations. --- Thermodynamics. --- Mechanics. --- Partial Differential Equations. --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Chemistry, Physical and theoretical --- Mechanics --- Heat --- Heat-engines --- Partial differential equations
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Partial differential equations --- 514.8 --- Geometric study of objects of mechanics and physics --- 514.8 Geometric study of objects of mechanics and physics --- Conservation laws (Physics) --- Einstein field equations. --- Shock waves. --- Singularities (Mathematics) --- General relativity (Physics) --- Lois de conservation (physique) --- Einstein, Équations du champ d' --- Ondes de choc --- Singularités (mathématiques) --- Relativité générale (physique) --- Einstein field equations --- Shock waves --- Geometry, Algebraic --- Shock (Mechanics) --- Waves --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- Gravitational fields --- Physical laws --- Einstein, Équations du champ d'. --- Ondes de choc.
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