الصفحة 1
الصفحة 1
Numerical Treatment of Partial Differential Equations
In 1988 we started work on the frst German edition of our book, which appeared in 1992. Our aim was to give students a textbook that contained the basic concepts and ideas behind most numerical methods for partial di?er- tial equations. The success of this frst edition and the second edition in 1994 encouraged us, ten years later, to write an almost completely new version, taking into account comments from colleagues and students and drawing on the enormous progress made in the numerical analysis of partial di?erential equations in recent times. The present English version slightly improves the third German edition of 2005: we have corrected some minor errors and added additional material and references.
Numerical Continuation Methods for Dynamical Systems : Path following and boundary value problems
The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Numerical Approximation Methods for Elliptic Boundary Value Problems : Finite and Boundary Elements
Although the aim of this book is to give a unified introduction into finite and boundary element methods, the main focus is on the numerical analysis of boundary integral and boundary element methods. Starting from the variational formulation of elliptic boundary value problems boundary integral operators and associated boundary integral equations are introduced and analyzed. By using finite and boundary elements corresponding numerical approximation schemes are considered.
Nonsmooth Variational Problems and their Inequalities : Comparison Principles and Applications
The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained.
Nonlinear Elliptic and Parabolic Problems : A Special Tribute to the Work of Herbert Amann
The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.
Nonlinear Dynamics of Structures Under Extreme Transient Loads
Covers model building for different engineering structures and provides detailed presentations of extreme loading conditions. A number of illustrations are given quantifying; a plane crash or explosion induced impact loading, the effects of strong earthquake motion, and the impact and long-duration effects of strong stormy winds—along with a relevant framework for using modern computational tools. The book considers the levels of reserve in existing structures, and ways of reducing the negative impact of high-risk situations by employing sounder design procedures.
Multiphase Flow Dynamics 3 : Turbulence, Gas Absorption and Release, Diesel Fuel Properties
Volume 3 is devoted to selected Chapters of the multiphase fluid dynamics that are important for practical applications. The state of the art of the turbulence modeling in multiphase flows is presented. As introduction, some basics of the single-phase boundary layer theory including some important scales and flow oscillation characteristics in pipes and rod bundles are presented. Then the scales characterizing the dispersed flow systems are presented. The description of the turbulence is provided at different level of complexity: simple algebraic models for eddy viscosity, algebraic models based on the Boussinesq hypothesis, modification of the boundary layer share due to modification of the bulk turbulence, modification of the boundary layer share due to nucleate boiling. Then the role of the following forces on the matematical description of turbulent flows is discussed: the lift force, the lubrication force in the wall boundary layer, and the dispersion force.
Multifield Problems in Solid and Fluid Mechanics
This book summarizes the main scientific results of the Collaborative Research Center on Multifield Problems in Continuum Mechanics. The book is divided into three main sections: A: Volume-Coupled Problems, devoted to fields which are coupled inside the processing domain or volume, B: Boundary-Coupled Problems, here physical fields and processes are coupled via domain boundaries, C: Fundamental Methods, search into the mathematical concepts and backgrounds of multifield and multiscale modeling.
Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology
It covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian difieomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere
Modern Ferrite Technology
odern Ferrite Technology ; 2nd ed. offers the readers an expert overview of the latest ferrite advances as well as their applications in electronic components. This volume develops the interplay among material properties, component specification and device requirements using ferrites. Throughout, emphasis is placed on practical technological concerns as opposed to mathematical and physical aspects of the subject. The book traces the origin of the magnetic effect in ferrites from the level of the simplest particle and then increases the scope to include larger hierarchies. From the desired magnetic properties, the author deduces the physical and chemical material parameters, taking into consideration major chemistry, impurity levels, ceramic microstructures and grain boundary effects. He then discusses the processing conditions and associated conditions required for implementation. In addition to conventional ceramic techniques, he describes non-conventional methods such as co-precipitation, co-spray roasting and single crystal growth.
Modeling of Creep for Structural Analysis
"Creep Modeling for Structural Analysis" develops methods to simulate and analyze the time-dependent changes of stress and strain states in engineering structures up to the critical stage of creep rupture. The principal subjects of creep mechanics are the formulation of constitutive equations for creep in structural materials under multi-axial stress states; the application of structural mechanics models of beams, plates, shells and three-dimensional solids and the utilization of procedures for the solution of non-linear initial-boundary value problems. The objective of this book is to review some of the classical and recently proposed approaches to the modeling of creep for structural analysis applications as well as to extend the collection of available solutions of creep problems by new, more sophisticated examples.
Modeling of Adhesively Bonded Joints
A lot of recent developments have been made about adhesively bonded joints modeling using various methods of analysis. The increasing application of adhesives in industry is partly due to the increased sophistication and reliability of adhesive joints modeling. The book proposed intends to provide the designer with the most advanced stress analyses techniques in adhesive joints to reinforce the use of this promising bonding technique.
Modeling and computations in electromagnetics ; A volume dedicated to Jean-Claude Nédélec
Modeling and computations in electromagnetics is a quite novel and growing discipline, expanding as a result of the steadily increasing demand for designing electrical devices, modeling electromagnetic materials, and simulating electromagnetic fields in nanoscale structures. The aim of this volume is to bring together prominent worldwide experts to review state-of-the-art developments and future trends of modeling and computations in electromagnetics. This volume is devoted to merging the expertise of scientists working in this dynamic discipline, and to raising interest for challenging issues. The most significant advances in computational techniques have been made only in the last few years, and several challenging technological applications are presented in this volume.
Modeling and computation of boundary-layer flows : Laminar, turbulent and transitional boundary layers in incompressible and compressible flows
This second edition of our book extends the modeling and calculation of boundary-layer flows to include compressible flows. The subjects cover laminar, transitional and turbulent boundary layers for two- and three-dimensional incompressible and compressible flows. The viscous-inviscid coupling between the boundary layer and the inviscid flow is also addressed. The book has a large number of homework problems.
Micromechanics of Contact and Interphase Layers
Micromechanics provides a link between the structure and the properties at different scales of observation. This book deals with micromechanical analysis of interfaces and interface layers and presents several modelling tools, ranging from the rigorous method of asymptotic expansions to practical finite element simulations, suitable for this class of problems. Two application areas are discussed. Boundary layers associated with contact of rough bodies are modelled by applying a scale transition approach in which a macroscopic interface of zero thickness is seen at the micro-scale as a layer with some finite thickness. Secondly, evolution of laminated microstructures accompanying stress-induced martensitic transformations in shape memory alloys (SMA) is analyzed as an illustration of the case when the local interfacial phenomena – here the propagation of phase transformation fronts – govern the macroscopic behaviour of a heterogeneous material.
Methods of nonlinear analysis : Applications to differential equations
In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Every method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. Applications and generalizations are shown. In particular, a large number of methods is applied to boundary value problems for partial differential equations.
Methods and Applications of Singular Perturbations : Boundary Layers and Multiple Timescale Dynamics
Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences.In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems.
Mediterranean Land-surface Processes Assessed from Space
1. 1 Space View and Ground Observations 1 1. 2 Mediterranean Climatic Environment 2 1. 3 Processes at Surfaces 10 1. 3. 1 Deforestation and Land-use Changes 10 1. 3. 2 Water Related Problems 16 1. 3. 3 Fire, Grazing, and Land Degradation 19 1. 3. 4 Drought, Floods, Frost, and Desertification 21 1. 3. 5 Coupling Between Surface and Atmosphere: The Role of the Atmospheric Boundary Layer 25 1. 4 Role and Capabilities of Measurements Made From Space 30 1. 4. 1 Research Programmes 30 1. 4. 2 Expected Information 32 1. 4. 3 Research Strategy 33 1. 4. 4 Observation of Changes in Heterogeneous Landscapes: Spatial and Temporal Scales 35 1. 4. 5 Land-surface Change Indicators Observable from Space 36 Spectral Characteristics of Vegetation and Soils (36); Responses of Remote Sensing Signals to Changes of Land-surface Properties (40) 1. 5 About this Book 48 Chapter 2 Processing and Archiving of Satellite and Ancillary Data 51 2. 1 Introduction 51 2. 2 The Remote Sensing Data Base 55 2. 2. 1 Satellite Instruments 55 The NOAA Observing System (55); Meteosat (57); Nimbus-7 (59); Landsat (59); SPOT (61); DMSP (62); ERS-1 and ERS-2 (62); TRMM (63); Terra (64); Envisat (65); Aqua (66) 2. 2. 2 Aircraft Instruments 66 The Use of Aircraft for Land-surface Process Studies (66); AVIRIS (67); TMS (68); AIRSAR (68); DIAL (69) 2. 3 Reception, Acquisition and Availability of Satellite Data 70 2. 3.
Introduction to Partial Differential Equations: A Computational Approach
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses.
Introduction to Numerical Methods in Differential Equations
This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets.
