Download or read book M thodes math matiques en chimie quantique Une introduction written by Eric Cances and published by Springer Science & Business Media. This book was released on 2006-09-09 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce cours est une introduction à la modélisation mathématique et à l'analyse numérique pour la chimie moléculaire quantique, un champ peu connu des mathématiciens et pourtant riche en sujets d'investigation. Le point de vue choisi est celui du mathématicien appliqué. Le cours est construit de manière auto-consistante.
Download or read book An Introduction to Mathematics of Emerging Biomedical Imaging written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2008-05-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.
Download or read book Analysis written by Jean-Paul Penot and published by Springer. This book was released on 2016-12-18 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.
Download or read book Practical Augmented Lagrangian Methods for Constrained Optimization written by Ernesto G. Birgin and published by SIAM. This book was released on 2014-04-30 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.
Download or read book ANALYSE DE METHODES NUMERIQUES DE SIMULATION ET CONTROLE EN CHIMIE QUANTIQUE written by Gabriel Turinici and published by . This book was released on 2000 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: LA CHIMIE QUANTIQUE EST UN DOMAINE DE RECHERCHE DE PLUS EN PLUS PRESENT DANS LES PREOCCUPATIONS DES MATHEMATICIENS APPLIQUES. S'INSCRIVANT DANS CET MOUVEMENT, CETTE THESE PROPOSE QUELQUES ETUDES D'ANALYSE DE METHODES NUMERIQUES DE SIMULATION ET CONTROLE EN CHIMIE QUANTIQUE. LA PARTIE I EST DEDIEE A LA PRESENTATION DU CADRE GENERAL DE LA CHIMIE QUANTIQUE COMPUTATIONNELLE. LES TECHNIQUES D'ESTIMATION A POSTERIORI ET LEURS APPLICATIONS A LA CHIMIE QUANTIQUE SONT PRESENTEES DANS LA PARTIE II. APRES UNE INTRODUCTION AUX METHODES A POSTERIORI (CHAPITRE II-1) ON PRESENTE DANS LE CHAPITRE II-2 UNE ETUDE MATHEMATIQUE DE LA METHODE DES VARIABLES ADIABATIQUES ET ON PROPOSE EN PARTICULIER UN ESTIMATEUR A POSTERIORI. DES SIMULATIONS NUMERIQUES QUI ILLUSTRENT LES QUALITES DE CET ESTIMATEUR SONT AUSSI PRESENTEES. UNE ETUDE D'ANALYSE A POSTERIORI DE L'EQUATION DE HARTREE-FOCK EST PRESENTEE EN CHAPITRE II-3. OUTRE LA CONSTRUCTION D'UN INTERVALLE DE CONFIANCE POUR LOCALISER L'ENERGIE DE HARTREE-FOCK, LA MEME METHODE FOURNIT UN PROCEDE D'AMELIORATION DES SOLUTIONS NUMERIQUES. CES RESULTATS THEORIQUES ONT ETE TESTES ET IMPLEMENTES SUR UN CODE DE CHIMIE QUANTIQUE. UNE ETUDE CONCERNANT LE CONTROLE AU NIVEAU QUANTIQUE DES PHENOMENES CHIMIQUES EST PRESENTEE DANS LA PARTIE III. DES RESULTATS PERMETTANT DE DECIDER DE LA CONTROLABILITE D'UN SYSTEME DE DIMENSION FINIE SONT PRESENTES EN III-1-2. LES CRITERES SONT SIMPLES A VERIFIER ET DONNENT LIEU A DES INTERPRETATIONS INTUITIVES. DES RESULTATS THEORIQUES COMPLEMENTAIRES ET DES EXEMPLES NUMERIQUES SONT PROPOSES DANS III-1.3. FINALEMENT, UN CODE QUI IMPLEMENTE DES ALGORITHMES GENETIQUES POUR L'ETUDE DES MECANISMES DE CONTROLE EST DECRIT EN CHAPITRE III-2.
Download or read book Les Methodes Mathematiques en Chimie written by György Alexits and published by . This book was released on 1969 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Feedback Stabilization of the Linear Reaction Convection Diffusion Equation and the Wave Equation written by Weijiu Liu and published by Springer Science & Business Media. This book was released on 2009-12-01 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.
Download or read book Mathematical Models and Methods for Ab Initio Quantum Chemistry written by M. Defranceschi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.
Download or read book ALGEBRE FERMIONIQUE ET CHIMIE QUANTIQUE written by PATRICK.. CASSAM-CHENAI and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: L'OBJET DE CETTE THESE EST D'INTRODUIRE LE FORMALISME DE L'ALGEBRE EXTERIEURE POUR DECRIRE UN ENSEMBLE DE FERMIONS IDENTIQUES, ET D'UTILISER SES OUTILS MATHEMATIQUES POUR APPROFONDIR NOTRE COMPREHENSION DES PROPRIETES DES SYSTEMES ELECTRONIQUES DE LA CHIMIE QUANTIQUE. DANS UN PREMIER TEMPS L'ALGEBRE EXTERIEURE EST PRESENTEE ET COMPAREE AUX AUTRES FORMALISMES EN VOGUE EN CHIMIE QUANTIQUE, PUIS EMPLOYEE POUR DERIVER LES EQUATIONS, JUSQU'ALORS INCONNUES, DES SOUS-ESPACES VARIATIONNELS DES METHODES DE CHAMP SELF-CONSISTANT DANS L'ESPACE DES CONFIGURATIONS A N ELECTRONS. CES METHODES N'ETAIENT CONNUES QUE PAR DES EQUATIONS METTANT EN JEU LES ORBITALES MONOELECTRONIQUES. EN SECOND LIEU, ON S'ATTACHE A CLARIFIER LES RAPPORTS QU'ENTRETIENNENT LES METHODES SANS CONTRAINTE AVEC LES METHODES CONTRAINTES DE SPIN. L'INTRODUCTION DES ANGLES D'ARAKI CONDUIT A UNE INTERPRETATION GEOMETRIQUE DE LA CONTAMINATION DE SPIN DANS UNE FONCTION DE HARTREE-FOCK SANS CONTRAINTE. L'ORIGINE DE LA POLARISATION DE SPIN DANS UNE TELLE FONCTION EST ALORS DISCUTEE EN DETAIL SUR L'ION MOLECULAIRE HE#2#+. ENFIN, NOUS ETUDIONS LES PROPRIETES DE LA TRANSFORMATION INDUITE DANS L'ESPACE DES CONFIGURATIONS A N ELECTRONS PAR UNE TRANSFORMATION DES ORBITALES MONOELECTRONIQUES. CETTE ETUDE DEBOUCHE SUR UNE NOUVELLE METHODE POUR SELECTIONNER UN ESPACE ACTIF ET UN NOMBRE LIMITE DE CONFIGURATIONS A PARTIR DESQUELLES ON PEUT CONSTRUIRE UN ESPACE DE REFERENCE POUR UN CALCUL D'INTERACTION DE CONFIGURATIONS, PAR EXEMPLE. EN DEFINITIVE, L'ALGEBRE EXTERIEURE S'AVERE SPECIFIQUEMENT ADAPTE DANS LEQUEL PEUT ETRE SITUE TOUT PROBLEME THEORIQUE CONCERNANT UN ENSEMBLE DE FERMIONS. ON PEUT DONC LUI DONNER LE NOM EN PHYSIQUE D'ALGEBRE FERMIONIQUE. SON EMPLOI EN CHIMIE QUANTIQUE PERMET DE VOIR SOUS UN JOUR NOUVEAU LES METHODES TRADITIONNELLES DE CALCUL ELECTRONIQUE, ET DE RESOUDRE DES PROBLEMES FONDAMENTAUX QUI AVAIENT ETE ELUDES JUSQU'ICI
Download or read book Introduction la chimie quantique written by Philippe Hiberty and published by Editions Ecole Polytechnique. This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Présentation de la théorie des orbites moléculaires et des modèles simples qui lui sont associés : théorie de Hückel, modèle des orbitales frontières, diagrammes de corrélation, méthode des orbitales de fragments, etc. Montre les liens entre la théorie des orbitales moléculaires et la théorie de liaison de valence.--[Memento].
Download or read book Quelques Mod les Math matiques en Chimie Quantique Et Propagation D incertitudes written by Virginie Ehrlacher and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions of this thesis work are two fold. The first part deals with the study of local defects in crystalline materials. Chapter 1 gives a brief overview of the main models used in quantum chemistry for electronic structure calculations. In Chapter 2, an exact variational model for the description of local defects in a periodic crystal in the framework of the Thomas-Fermi-von Weisz"acker theory is presented. It is justified by means of thermodynamic limit arguments. In particular, it is proved that the defects modeled within this theory are necessarily neutrally charged. Chapters 3 and 4 are concerned with the so-called spectral pollution phenomenon. Indeed, when an operator is discretized, spurious eigenvalues which do not belong to the spectrum of the initial operator may appear. In Chapter 3, we prove that standard Galerkin methods with finite elements discretization for the approximation of perturbed periodic Schrödinger operators are prone to spectral pollution. Besides, the eigenvectors associated with spurious eigenvalues can be characterized as surface states. It is possible to circumvent this problem by using augmented finite element spaces, constructed with the Wannier functions of the periodic unperturbed Schr"odinger operator. We also prove that the supercell method, which consists in imposing periodic boundary conditions on a large simulation domain containing the defect, does not produce spectral pollution. In Chapter 4, we give a priori error estimates for the supercell method. It is proved in particular that the rate of convergence of the method scales exponentiall with respect to the size of the supercell. The second part of this thesis is devoted to the study of greedy algorithms for the resolution of high-dimensional uncertainty quantification problems. Chapter 5 presents the most classical numerical methods used in the field of uncertainty quantification and an introduction to greedy algorithms. In Chapter 6, we prove that these algorithms can be applied to the minimization of strongly convex nonlinear energy functionals and that their convergence rate is exponential in the finite-dimensional case. We illustrate these results on obstacle problems with uncertainty via penalized formulations.
Download or read book Les m thodes math matiques de la th matiques de la th orie quantique des champs written by Colloque International sur les Méthodes Mathématiques de la Théorie Quantique des Champs and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction la chimie quantique et la spectroscopie written by Gilles Durocher and published by Presses de l'Université de Montréal. This book was released on 1971 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Les M thodes math matiques en chimie written by Georges Alexits and published by . This book was released on 1969 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methodes de la Chimie Quantique written by and published by Ed. Techniques Ingénieur. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book M thodes math matiques de la m canique quantique written by Austin Blaquière and published by . This book was released on 1958 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantique mol culaire written by Bernard Vidal and published by . This book was released on 1997 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce manuel s'adresse à tous les chimistes et étudiants en chimie (à partir du 2e cycle). Il leur permet d'améliorer leur compréhension des concepts de quantique moléculaire dans une optique résolument pratique. Il ne s'agit donc pas d'un exposé théorique ni mathématique mais bien d'une présentation de méthodes destinées à être mises en pratique au quotidien. S'appuyant sur des notions simples, Quantique moléculaire ne nécessite pas une maîtrise des mathématiques particulièrement élevée. Pour bien comprendre les concepts développés. Il suffit de suivre pas à pas le raisonnement à partir des premiers chapitres.
