Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics or linearized Boltzmann models. “Caseology” is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models.
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
Ce livre est un des tout premiers « si non le premier » exclusivement dédié au domaine des bétons de végétaux. Nous nous employons au fur et à mesure des chapitres de décrire l’intérêt de l’usage de tels matériaux, de décliner les nombreuses propriétés multiphysiques et enfin d’illustrer les modes de fabrication et de mise en œuvre. Le livre se focalise principalement sur l’exemple du béton de chanvre. Ce matériau est aujourd’hui très largement utilisé dans l’industrie de la maison individuelle. Le confort thermique, hygrothermique et acoustique est induit par la structure exceptionnelle du matériau dans le sens où elle associe porosité, légèreté et inertie. Le comportement mécanique n’est pas en reste, une grande ductilité et des propriétés loin des standards habituels sont précisées dans cet ouvrage. Par ailleurs, l’Analyse de cycle de vie dont la plus grande partie du volume est d’origine végétale fait ressortir un bilan qui lui est très favorable.
The fascinating correspondence between Paul Lévy and Maurice Fréchet spans an extremely active period in French mathematics during the twentieth century. The letters of these two Frenchmen show their vicissitudes of research and passionate enthusiasm for the emerging field of modern probability theory. The letters cover various topics of mathematical importance including academic careers and professional travels, issues concerning students and committees, and the difficulties both mathematicians met to be elected to the Paris Academy of Sciences. The technical questions that occupied Lévy and Fréchet on almost a daily basis are the primary focus of these letters, which are charged with elation, frustration and humour. Their mathematical victories and setbacks unfolded against the dramatic backdrop of the two World Wars and the occupation of France, during which Lévy was obliged to go into hiding. The clear and persistent desire of these mathematicians to continue their work whatever the circumstance testifies to the enlightened spirit of their discipline which was persistent against all odds. The book contains a detailed and comprehensive introduction to the central topics of the correspondence. The original text of the letters is also annotated by numerous footnotes for helpful guidance. Paul Lévy and Maurice Fréchet will be useful to anybody interested in the history of mathematics in the twentieth century and, in particular, the birth of modern probab ility theory.
This book provides the tools to understand the issues related to bio-based concretes using lime as binder. Themes covered include specific properties of lignocellulosic aggregates (density, porosity, size distribution, water absorption, microstructure, soluble components under alkaline conditions), hardening of lime-based binders by carbonation and hydration (natural and curing processes) and microstructure of the binder in the vicinity of aggregates (dense or porous interphase). The mechanical (uniaxial and triaxial compression) and insulating properties of the relatively well-known hemp concretes and the novel rice husk concretes are also reviewed. Finally, a detailed and comprehensive description of the tools and methodologies that make it easier the design of such bio-based concretes is discussed. Written for students as well as researchers, this book is aimed at individuals working in both academic and industrial fields.
Les maladies systémiques regroupent un cadre hétérogène de maladies (connectivites, vascularites, granulomatoses…) dont la pathogénie est caractérisée par une atteinte de plusieurs organes. Bien qu’il s’agisse pour la plupart de maladies orphelines, ces pathologies sont susceptibles d’intéresser tous les médecins du fait de leur polymorphisme clinique. L’atteinte ophtalmologique est fréquente dans bon nombre de ces maladies, principalement en rapport avec une atteinte inflammatoire ou vasculaire. Elle constitue souvent une clé pour le diagnostic et peut mettre en jeu le pronostic fonctionnel en raison du risque de cécité. La sémiologie oculaire des maladies systémiques et les moyens d’explorations ophtalmologiques sont souvent mal connus des internistes ou des spécialistes d’organes. Inversement, les maladies systémiques sont l’objet de nombreuses interrogations de la part des ophtalmologistes. De ce constat est né Œil et Maladies systémiques qui présente, en 50 chapitres : • les principaux syndromes ophtalmologiques et les moyens d’explorations, destinés principalement aux non-ophtalmologistes • l’expression ophtalmologique des maladies systémiques (connectivites et vascularites, certaines maladies infectieuses et autres affections multiviscérales) ainsi que les aspects diagnostiques, pronostiques et thérapeutiques. Le professeur Pascal Sève, interniste, et le professeur Laurent Kodjikian, ophtalmologiste, tous deux rattachés à hôpital de la Croix-Rousse à Lyon, ont coordonné l’ouvrage dont les rédacteurs sont issus des diverses spécialités concernées : ophtalmologistes et internistes bien sûr, mais également spécialistes d’organes tels que dermatologues, néphrologues, neurologues, etc., tous référents reconnus dans leur domaine d’expertise. Ce livre apporte des réponses utiles et précises aux praticiens confrontés aux atteintes ophtalmologiques des maladies systémiques. Il intéressera donc les ophtalmologistes, internistes, rhumatologues, neurologues, pneumologues et autres spécialistes d’organes.
This book book explores the ways that elaborate flux functions can be constructed, mainly in a one-dimensional context for hyperbolic systems admitting shock-type solutions and also for kinetic equations in the discrete-ordinate approximation.
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
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