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Author: Franck Boyer Publisher: Springer Science & Business Media ISBN: 1461459753 Category : Mathematics Languages : en Pages : 538
Book Description
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
Author: Franck Boyer Publisher: Springer Science & Business Media ISBN: 1461459753 Category : Mathematics Languages : en Pages : 538
Book Description
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
Author: Marc Savel Publisher: ISBN: Category : Languages : en Pages : 155
Book Description
In this work we study the well-posedness, the control and the stabilization of some fluid flow models. First, we focus on the 1D compressible Navier-Stokes equations. Under a geometric assumption on the flow of the target velocity corresponding to the possibility of emptying the domain under the action of the flow, we prove the local exact boundary controllability to trajectory. The main novelty of this work is that the target trajectory can now depend on time and space. In the second part, we study a model of an immersed boundary in an incompressible viscous fluid in 2D and 3D. Contrary to Peskin's Immersed Boundary Method where the boundary force depends on the elastic properties of the structure and its geometry, we consider that the boundary force is a given data. Two results are established: a local in time existence of strong solutions and an existence of strong solutions for all time with small data. This work is a first step on the mathematical analysis of Peskin's Immersed Boundary Method. Finally, we are interested in the stabilization of the interface between two fluid layers coupled through surface tension effect in 2D and 3D. We prove that the system is exponentially stabilizable at any rate around a flat configuration with fluids at rest using a control of finite dimension acting locally at one fluid boundary. This work is a first step in the study of the stabilization of Rayleigh-Taylor instabilities.
Author: Thierry Goudon Publisher: John Wiley & Sons ISBN: 111937118X Category : Mathematics Languages : en Pages : 478
Book Description
This book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail, through the mathematical perspective.
Author: Jacques Henry Publisher: Elsevier ISBN: 0081010907 Category : Mathematics Languages : en Pages : 258
Book Description
Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems. Develops the invariant embedding technique for boundary value problems Makes a link between control theory, boundary value problems and the Gauss factorization Presents a new theory for successively solving linear elliptic boundary value problems Includes a transformation in two initial value problems that are uncoupled
Book Description
LE SYSTEME D'EQUATIONS AUX DERIVEES PARTIELLES CONSIDERE EST CONSTITUE D'UNE EQUATION DE TYPE NAVIER-STOKES OU EULER COMPRESSIBLE OU INCOMPRESSIBLE COUPLEE AVEC UNE EQUATION DE TYPE TRANSPORT. CE SYSTEME EST D'UN TYPE COMPOSITE ET CHAQUE PROBLEME DOIT FAIRE L'OBJET D'UNE ETUDE PARTICULIERE. LA PREMIERE PARTIE (CHAPITRE 1 ET 2) EST CONSACREE A L'ETUDE D'ECOULEMENTS INCOMPRESSIBLES, UTILISANT UNE METHODE DE COMPACITE LOCALE ET LA METHODE DE POINT FIXE, NOUS AVONS MONTRE DES RESULTATS D'EXISTENCE ET D'UNICITE DE SOLUTIONS REGULIERES. NOUS AVONS D'ABORD CONSIDERE DES ECOULEMENTS DANS UN DOMAINE NON BORNE, L'ESPACE ENTIER OU UN DOMAINE EXTERIEUR REGULIER PAR EXEMPLE. NOUS AVONS AUSSI ETUDIE L'ECOULEMENT DANS UN CANAL BORNE AVEC CONDITIONS AUX LIMITES RENTRANTES A L'ENTREE, ET PERIODIQUES SUR LES PAROIS. LA DEUXIEME PARTIE (CHAPITRE 3 ET 4) EST CONSACREE A L'ETUDE D'ECOULEMENTS FAIBLEMENT COMPRESSIBLES. NOUS AVONS PROPOSE UNE MODELISATION POUR CHACUN DES CAS, INSTATIONNAIRE OU STATIONNAIRE. UTILISANT DES METHODES DE POINT FIXE, NOUS MONTRONS DES RESULTATS D'EXISTENCE DE SOLUTIONS REGULIERES: CAS DU MODELE DE JEFFREYS INSTATIONNAIRE (AVEC UNICITE), CAS DES MODELES DE MAXWELL ET JEFFREYS STATIONNAIRES, OU NOUS MONTRONS EN OUTRE LA CONVERGENCE DU CAS FAIBLEMENT COMPRESSIBLE VERS LE CAS INCOMPRESSIBLE. ENFIN NOUS PRESENTONS UNE ETUDE DE L'HYPERBOLICITE DU MODELE DE MAXWELL INSTATIONNAIRE
Author: Habib Ammari Publisher: Springer Science & Business Media ISBN: 3540795537 Category : Medical Languages : en Pages : 198
Book Description
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.
Author: Sid M. Becker Publisher: Academic Press ISBN: 0128046198 Category : Medical Languages : en Pages : 396
Book Description
Modeling of Microscale Transport in Biological Processes provides a compendium of recent advances in theoretical and computational modeling of biotransport phenomena at the microscale. The simulation strategies presented range from molecular to continuum models and consider both numerical and exact solution method approaches to coupled systems of equations. The biological processes covered in this book include digestion, molecular transport, microbial swimming, cilia mediated flow, microscale heat transfer, micro-vascular flow, vesicle dynamics, transport through bio-films and bio-membranes, and microscale growth dynamics. The book is written for an advanced academic research audience in the fields of engineering (encompassing biomedical, chemical, biological, mechanical, and electrical), biology and mathematics. Although written for, and by, expert researchers, each chapter provides a strong introductory section to ensure accessibility to readers at all levels. Features recent developments in theoretical and computational modeling for clinical researchers and engineers Furthers researcher understanding of fluid flow in biological media and focuses on biofluidics at the microscale Includes chapters expertly authored by internationally recognized authorities in the fundamental and applied fields that are associated with microscale transport in living media
Book Description
Nous présentons un cadre abstrait qui généralise des techniques utilisées lors de l'étude des équations d'évolution de Navier-Stokes sur un ouvert borné de Rd (d = 2 ou 3). Nous montrons comment ce cadre permet d'étendre certains résultats établis, pour les équations de Navier-Stokes sur un ouvert de Rd avec conditions aux limites homogènes, à diverses équations de la mécanique des fluides visqueux et incompressibles. Nous traitons ici les conditions aux limites non homogènes, les équations de Navier-Stokes sur une variété riemannienne, les équations de la magnétohydrodynamique et enfin les équations de la thermohydraulique. Nous prouvons, en particulier, que les attracteurs associés à ces équations, bornés dans H1, sont de dimension fractale finie et sont portés par l'ensemble des fonctions C∞.
Author: Franck Assous Publisher: Springer ISBN: 3319708422 Category : Mathematics Languages : en Pages : 460
Book Description
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Author: Antoine Garapon (physicien).) Publisher: ISBN: Category : Languages : fr Pages : 167
Book Description
UNE METHODE EULERIENNE A MAILLAGE ADAPTATIF EST UTILISEE POUR MODELISER UN ECOULEMENT DE FLUIDE VISQUEUX, INCOMPRESSIBLE ET TURBULENT AUTOUR D'UN PROFIL BIDIMENSIONNEL PLACE SOUS LA SURFACE LIBRE. LA FERMETURE DES EQUATIONS EST ASSUREE PAR LE MODELE DE TURBULENCE DE -. LA DISCRETISATION DES EQUATIONS DE TRANSPORT EST EFFECTUEE PAR LE SCHEMA UNIEXPONENTIEL, L'EQUATION DE PRESSION EST OBTENUE PAR LA RECONSTRUCTION DE RHYE & CHOW, ENFIN, L'ALGORITHME PISO ASSURE LE COUPLAGE VITESSE-PRESSION. L'APPLICATION DE CETTE METHODE A L'ETUDE DE L'ECOULEMENT TRIDIMENSIONNEL AUTOUR D'UNE CARENE DE SERIES 60 CONDUISANT A L'ECHEC, UNE NOUVELLE METHODE DE PRISE EN COMPTE DE LA SURFACE LIBRE A ETE DEVELOPPEE. CETTE METHODE A ETE ENSUITE VALIDEE ET COMPAREE AUX RESULTATS EXPERIMENTAUX ET NUMERIQUES PROVENANT DE L'ATELIER DE TOKYO (1994)
Author: Franck Boyer
Author: Franck Boyer
Author: Marc Savel
Author: Thierry Goudon
Author: Jacques Henry
Author: RAAFAT.. TALHOUK
Author: Habib Ammari
Author: Sid M. Becker
Author: Jean-Michel Ghidaglia (mathématicien).)
Author: Franck Assous
Author: Antoine Garapon (physicien).)