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Etude Dune Methode Splitting Pour Des Lois De Conservation Scalaires Avec Terme De Source
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Book Synopsis Etude d'une méthode Splitting pour des lois de conservation scalaires avec terme de source by : Fabrice Peyroutet
Download or read book Etude d'une méthode Splitting pour des lois de conservation scalaires avec terme de source written by Fabrice Peyroutet and published by . This book was released on 1999 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce travail traite de l'étude théorique de l'approximation de lois de conservation scalaires avec terme de source au moyen d'une technique de Splitting. Cette méthode consiste à alterner la résolution d'une équation différentielle contenant le terme de source et la résolution de lois hyperboliques homogènes. Les solutions considérées vérifient, sur un ouvert borne, une formulation entropique avec prise en compte d'une condition de type Dirichlet sur la frontière. On démontre la convergence du schéma Splitting dans le cadre d'étude de fonctions à variation bornée puis on établit que l'erreur commise est d'ordre 1. Dans le cadre d'étude de solutions seulement bornées, la convergence de la technique est à nouveau prouvée. De plus, une estimation de l'erreur est obtenue dès que seule la donnée initiale du problème continu possède un degré de régularité intermédiaire. En outre, on montre que cette méthode s'adapte aussi au cas de problèmes unilatéraux. Dans ce cas, il suffit, dans le procédé de décomposition d'opérateurs, de prendre en compte la contrainte d'obstacle au niveau du traitement de l'équation différentielle. On prouve la convergence du schéma Splitting en proposant, dans le cas du problème de Cauchy, une estimation de l'erreur. Finalement, on donne une illustration numérique de ce résultat.
Book Synopsis Approximation numérique de lois de conservation hyperboliques stochastiques scalaires by : Sylvain Dotti
Download or read book Approximation numérique de lois de conservation hyperboliques stochastiques scalaires written by Sylvain Dotti and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nous étudions dans cette thèse, une loi de conservation scalaire hyperbolique d'ordre un avec terme source stochastique et flux non-linéaire. Le terme source stochastique peut être considéré comme la superposition d'une infinité de bruits Gaussiens dépendants de la quantité conservée. Nous donnons une définition de solution de cette équation aux dérivées partielles stochastiques (EDPS) d'un point de vue intermédiaire entre celui de l'analyste (solution non régulière en espace, introduction d'une variable supplémentaire dite cinétique) et celui du probabiliste (solution processus stochastique continu à droite limité à gauche en temps). L'unicité de la solution est prouvée grâce à un dédoublement des variables à la Kruzkov. Nous étudions la stabilité de la loi de conservation pour donner un théorème général donnant les conditions d'existence d'une solution et les conditions de convergence d'une suite de solutions approchées vers la solution de la loi de conservation. Cette étude se fait grâce à des outils probabilistes : représentation des martingales sous forme d'intégrales stochastiques, existence d'un espace probabilisé sur lequel la convergence de lois de probabilités est équivalente à la convergence presque sûre de variables aléatoires. Pour finir l'étude, nous prouvons l'existence d'une solution grâce aux propriétés de l'approximation de l'EDPS par un schéma numérique des Volumes Finis explicite en temps, puis la convergence de cette approximation vers la solution de l'EDPS. Les outils utilisés sont ceux de l'analyse, spécifiquement ceux de la méthode des Volumes Finis en déterministe, auxquels il faut ajouter ceux du calcul stochastique (outils probabilistes).
Book Synopsis Couplage de méthodes numériques pour les lois de conservation by : Martial Mancip
Download or read book Couplage de méthodes numériques pour les lois de conservation written by Martial Mancip and published by . This book was released on 2001 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nous nous intéressons aux méthodes permettant d'approcher les solutions de systèmes d'équations aux dérivées partielles conservatives. Dans les cas où l'écoulement est très complexe - lorsqu'il y a plusieurs modèles physiques à calculer sur des zones difficiles à délimiter - on utilise des méthodes de couplage par recouvrement de domaines. Nous présentons ici un algorithme, nouveau et performant, calculé grâce à une superposition de deux maillages correspondant à deux schémas différents. On utilise des projections conservatives de la solution d'un maillage vers l'autre. Cette méthode de décomposition de domaine ne fait pas intervenir de conditions aux limites artificielles. Elle est basée sur une régularisation de la fonction de Heaviside sur la zone de couplage. Elle est parfaitement conservative et donc bien indiquée pour l'étude des lois de conservation. L'analyse mathématique est réalisée pour les problèmes hyperboliques, dans le cas scalaire multidimensionnel. Elle est basée sur le convergence des schémas volumes finis. Tout d'abord, on obtient la convergence de la solution mesure grâce aux travaux de Diperna, puis on estime l'erreur de convergence en hơ. Une nouvelle estimation de type H1 faible permet d'estimer les erreurs induites par le couplage. De nombreuses applications numériques en mécanique des fluides avec les tubes à chocs et de détente montrent que la méthode est très stable et conservative. Nous utilisons aussi la méthode sans grille appelée Smooth Particule Hydrodynamics - plus précisément sa nouvelle variante renormalisée - pour calculer la création d'un jet en couplant la méthode volumes finis à la méthode SPH. On montre ainsi la robustesse de l'algorithme de couplage et sa souplesse pour le calcul des écoulements complexes. Cette étude a fait l'objet d'une collaboration avec l'équipe du Pr. D. Kröner de l'Institut des Mathématiques Appliquées à l'Université de Frieburg (Allemagne)
Book Synopsis ESTIMATION D'ERREUR POUR LES LOIS DE CONSERVATION SCALAIRES A L'AIDE D'APPROCHES CINETIQUES, ET ETUDE DU CAS DE CONDITIONS AUX LIMITES by : ABDENNEBI.. OMRANE
Download or read book ESTIMATION D'ERREUR POUR LES LOIS DE CONSERVATION SCALAIRES A L'AIDE D'APPROCHES CINETIQUES, ET ETUDE DU CAS DE CONDITIONS AUX LIMITES written by ABDENNEBI.. OMRANE and published by . This book was released on 1998 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: CETTE THESE PORTE SUR LES APPROCHES CINETIQUES POUR LES LOIS DE CONSERVATION SCALAIRES MULTIDIMENSIONNELLES. ON APPLIQUE LA METHODE DE TRANSPORT-ECROULEMENT DE Y. BRENIER, (AUSSI T. MIYAKAWA ET Y. GIGA), ET D'UNE DEUXIEME METHODE CINETIQUE FORMULEE PAR LE MODELE DE B. PERTHAME ET E. TADMOR. DEJA DES RESULTATS DE CONVERGENCE ONT ETE OBTENUS PAR CES AUTEURS. ICI. ON CALCULE AVEC EXACTITUDE L'ERREUR DE CONVERGENCE ENTRE LA SOLUTION ENTROPIQUE DE LA LOI CONSERVATIVE ET LA SOLUTION APPROCHEE FOURNIE PAR CHAQUE MODELE CINETIQUE. POUR SE FAIRE, ON UTILISE LA METHODE ENTROPIQUE DE DE S. N. KRUZKOV ET N. N. KUZNETSOV. CETTE TECHNIQUE SE TROUVE AINSI GENERALISEE AUX DEUX METHODES CINETIQUES. L'ERREUR DE CONVERGENCE OBTENUE EST EN T POUR LA PREMIERE METHODE DE TRANSPORT-ECROULEMENT (OU T REPRESENTE LE PAS DE TEMPS LE LONG DE CHAQUE PHASE DE TRANSPORT), ET ELLE EST DE ( ETANT LA DISTANCE MOYENNE ENTRE DEUX COLLISIONS DE PARTICULES) POUR CE QUI EST DU MODELE DE PERTHAME-TADMOR. L'ESTIMATION D'ERREUR, GLOBALE EN TEMPS, EST OBTENUE DANS L'ESPACE L#1(R#N#X) ; CE QUI EST OPTIMAL, COMPTE TENU DE L'UTILISATION DE LA METHODE DE KUZNETSOV. LA DEUXIEME PARTIE DE CETTE THESE CONCERNE LES CONDITIONS AUX BORDS POUR LES LOIS DE CONSERVATION SCALAIRES MULTIDIMENSIONNELLES DANS LE DEMI-ESPACE, A PARTIR D'UN MODELE CINETIQUE DE PERTHAME-TADMOR. ON MONTRE D'ABORD QUE CE MODELE EST BIEN POSE DANS L'ESPACE L#(0,T ; L#1(R#+ X R#N#-#1 X R#V)), DES ESTIMATIONS BV, ET UNE INEGALITE D'ENTROPIE APPROCHEE. SOUS UNE HYPOTHESE SUPPLEMENTAIRE, ON OBTIENT DES CONDITIONS AUX BORDS POUR LA SOLUTION ENTROPIQUE. SOUS CETTE MEME HYPOTHESE ET DANS LE CAS D'UNE DONNEE MAXWELLIENNE, L'ENSEMBLE DES CONDITIONS AUX BORD ADMISSIBLES EST INCLU DANS L'ENSEMBLE DES CONDITIONS DE BORD DE C. BARDOS, A. Y. LEROUX, ET J. C. NEDELEC OBTENU A PARTIR DE PROFILS VISQUEX. POURTANT LES DEUX PROBLEMES DE CAUCHY AVEC CONDITIONS AU BORD SONT EQUIVALENTS.
Book Synopsis Boundary-Layer Theory by : Hermann Schlichting (Deceased)
Download or read book Boundary-Layer Theory written by Hermann Schlichting (Deceased) and published by Springer. This book was released on 2016-10-04 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
Book Synopsis Quantum Mechanics, Volume 3 by : Claude Cohen-Tannoudji
Download or read book Quantum Mechanics, Volume 3 written by Claude Cohen-Tannoudji and published by John Wiley & Sons. This book was released on 2019-12-16 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly * Comprehensive: in addition to the fundamentals themselves, the books comes with a wealth of elaborately explained examples and applications Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the Collège des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloë was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.
Download or read book Mean Field Games written by Yves Achdou and published by Springer Nature. This book was released on 2021-01-19 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.
Book Synopsis The General Theory of Homogenization by : Luc Tartar
Download or read book The General Theory of Homogenization written by Luc Tartar and published by Springer Science & Business Media. This book was released on 2009-12-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
Book Synopsis Clifford Algebras and Their Applications in Mathematical Physics by : J.S.R. Chisholm
Download or read book Clifford Algebras and Their Applications in Mathematical Physics written by J.S.R. Chisholm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann's algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley's book, 'The Algebraic Theory of Spinors' in 1954, and of Marcel Riesz' Maryland Lectures in 1959. Some of the contributors to this volume, Georges Deschamps, Erik Folke Bolinder, Albert Crumeyrolle and David Hestenes were working in this field around that time, and in their turn have persuaded others of the importance of the subject.
Download or read book Physics on Manifolds written by M. Flato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one considers the global behaviour of solutions of differential systems on manifolds. In this sense, General Relativity is an exceptional theory in which the solutions of a highly non-linear system of partial differential equations define by themselves the very manifold on which they are supposed to exist. This is why a solution of Einstein's equations cannot be physically interpreted before its global behaviour is known, taking into account the entire hypothetical underlying manifold. In her youth, Yvonne Choquet-Bruhat contributed in a spectacular way to this domain stretching between physics and mathematics, when she gave the proof of the existence of solutions to Einstein's equations on differential manifolds of a quite general type. The methods she created have been worked out by the French school of mathematics, principally by Jean Leray. Her first proof of the local existence and uniqueness of solutions of Einstein's equations inspired Jean Leray's theory of general hyperbolic systems.
Book Synopsis Bogoliubov-de Gennes Method and Its Applications by : Jian-Xin Zhu
Download or read book Bogoliubov-de Gennes Method and Its Applications written by Jian-Xin Zhu and published by Springer. This book was released on 2016-06-21 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an elementary yet systematic description of the Bogoliubov-de Gennes (BdG) equations, their unique symmetry properties and their relation to Green’s function theory. Specifically, it introduces readers to the supercell technique for the solutions of the BdG equations, as well as other related techniques for more rapidly solving the equations in practical applications. The BdG equations are derived from a microscopic model Hamiltonian with an effective pairing interaction and fully capture the local electronic structure through self-consistent solutions via exact diagonalization. This approach has been successfully generalized to study many aspects of conventional and unconventional superconductors with inhomogeneities – including defects, disorder or the presence of a magnetic field – and becomes an even more attractive choice when the first-principles information of a typical superconductor is incorporated via the construction of a low-energy tight-binding model. Further, the lattice BdG approach is essential when theoretical results for local electronic states around such defects are compared with the scanning tunneling microscopy measurements. Altogether, these lectures provide a timely primer for graduate students and non-specialist researchers, while also offering a useful reference guide for experts in the field.
Book Synopsis Mechanics of Ballasted Rail Tracks by : Buddhima Indraratna
Download or read book Mechanics of Ballasted Rail Tracks written by Buddhima Indraratna and published by CRC Press. This book was released on 2005-08-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors discuss testing of ballast, including the strength, deformation and degradation aspects of fresh and recycled ballast under monotonic and cyclic loading. The effectiveness of geosynthetics in stabilising recycled ballast has also been examined. A new stress-strain constitutive model for ballast incorporating particle breakage is presented. Finally, a new range of particle gradations, balancing the strength and permeability requirements, has been proposed for future rail tracks. This book is intended as a reference text for final year civil engineering students and postgraduates, and for practicing railway engineers with the task of modernizing existing designs.
Book Synopsis Exact Finite-Difference Schemes by : Sergey Lemeshevsky
Download or read book Exact Finite-Difference Schemes written by Sergey Lemeshevsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-09-26 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Author :International Livestock Research Institute Publisher :ILRI (aka ILCA and ILRAD) ISBN 13 :9789291460038 Total Pages :268 pages Book Rating :4.4/5 (6 download)
Book Synopsis Livestock Policy Analysis by : International Livestock Research Institute
Download or read book Livestock Policy Analysis written by International Livestock Research Institute and published by ILRI (aka ILCA and ILRAD). This book was released on 1995-01-01 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Policy concepts; Identification of policy issues; Production systems, supply and demand; Market, price and trade policies; Marketing and distribution systems; Budget and manpower planning; Land tenure police for the livestock sector; Policy analysis report writing and communication; Livestock production and marketing in alphabeta - a case study.
Book Synopsis Physical Reality and Mathematical Description by : C.P. Enz
Download or read book Physical Reality and Mathematical Description written by C.P. Enz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays is intended as a tribute to Josef Maria Jauch on his sixtieth birthd~. Through his scientific work Jauch has justly earned an honored name in the community of theo retical physicists. Through his teaching and a long line of dis tinguished collaborators he has put an imprint on modern mathema tical physics. A number of Jauch's scientific collaborators, friends and admirers have contributed to this collection, and these essays reflect to some extent Jauch's own wide interests in the vast do main of theoretical physics. Josef Maria Jauch was born on 20 September 1914, the son of Josef Alois and Emma (nee Conti) Jauch, in Lucerne, Switzerland. Love of science was aroused in him early in his youth. At the age of twelve he came upon a popular book on astronomy, and an exam ple treated in this book mystified him. It was stated that if a planet travels around a centre of Newtonian attraction with a pe riod T, and if that planet were stopped and left to fall into the centre from any point of the circular orbit, it would arrive at the centre in the time T/I32. Young Josef puzzled about this for several months until he made his first scientific discovery : that this result could be derived from Kepler's third law in a quite elementary way.
Book Synopsis Parallel Solution of Partial Differential Equations by : Petter Bjorstad
Download or read book Parallel Solution of Partial Differential Equations written by Petter Bjorstad and published by Springer. This book was released on 2012-10-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computers offer the promise of greatly increased perfor mance and the routine calculation of previously intractable problems. The papers in this volume were presented at the IMA workshop on the Paral lel Solution of PDE held during June 9-13, 1997. The workshop brought together leading numerical analysts, computer scientists, and engineers to assess the state-of-the-art and to consider future directions.
Book Synopsis The Structure of Atmospheric Turbulence by : John Leask Lumley
Download or read book The Structure of Atmospheric Turbulence written by John Leask Lumley and published by . This book was released on 1964 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
