Modeling and Simulation in Science, Engineering and Technology – serie

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works. The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods.Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems. "Modeling and Computational Methods of Kinetic Equations" will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

This book is an introduction to the stability analysis of noncharacteristic boundary layers, emphasizing selected topics and developing mathematical tools relevant to the study of multidimensional problems. Boundary layers are present in problems from physics, engineering, mechanics, and fluid mechanics and typically appear for problems with small diffusion. Boundary layers also occur in free boundary value problems, particularly in the analysis of shock waves. The main goal of this presentation is to provide basic tools for the understanding of multidimensional boundary layers for systems. Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, WKB methods, construction of profiles, introduction to the theory of Evans? functions, and energy methods with Kreiss? symmetrizers.

A collection of seven interdisciplinary surveys on modelling tumour dynamics and interactions between tumours and immune systems. Modelling and simulation of general behaviours of immune systems is also discussed. Each survey covers a specialized field and provides a detailed description of the current state of research. the reader should be able to obtain essential information on the methodological approach used and on the models that are categorized and used. Topics covered include: general tumour biology modelling; growth kinetics; kinetic cellular theory; tumour-immune system interactions; and heterogeneity and growth control. There is also a glossary of scientific terms in immunology and biology to ensure a clear understanding of biological terms.

Providing an introduction to a branch of climate theory - the study of climate by means of the quality theory of partial differential equations, this text is oriented towards specialists and graduates in geophysical hydrodynamics and climate modelling. The first part of the book concentrates on current theory of infinite-dimensional and finite-dimensional nonlinear dissipative systems. Section two of the text contains the results of analysis of climate models of different complexity from barotropic models to models based on the full system of hydrothermodynamics equations.

A reference for the field of particle modelling - the study of dynamical behaviour of solids and fluids in response to external forces, with the solids and fluids modelled as systems of atoms and molecules.

This text develops a functional approach for boundary value problems and includes the following components; the introduction of special functional spaces; the definition of spaces for boundary values; the analysis of the problems of trace existence; and the extension of functions with preservation of classes of regularity. This approach proves the existence of generalized solutions to problems concerned on the basis of those functional spaces introduced and also proper variational formulations of problems. The book also presents various applications of the theory developed.

Fluid mechanics (FM) is a branch of science dealing with the investi­ gation of flows of continua under the action of external forces. The fundamentals of FM were laid in the works of the famous scientists, such as L. Euler, M. V. Lomonosov, D. Bernoulli, J. L. Lagrange, A. Cauchy, L. Navier, S. D. Poisson, and other classics of science. Fluid mechanics underwent a rapid development during the past two centuries, and it now includes, along with the above branches, aerodynamics, hydrodynamics, rarefied gas dynamics, mechanics of multi phase and reactive media, etc. The FM application domains were expanded, and new investigation methods were developed. Certain concepts introduced by the classics of science, however, are still of primary importance and will apparently be of importance in the future. The Lagrangian and Eulerian descriptions of a continuum, tensors of strains and stresses, conservation laws for mass, momentum, moment of momentum, and energy are the examples of such concepts and results. This list should be augmented by the first and second laws of thermodynamics, which determine the character and direction of processes at a given point of a continuum. The availability of the conservation laws is conditioned by the homogeneity and isotrop­ icity properties of the Euclidean space, and the form of these laws is related to the Newton's laws. The laws of thermodynamics have their foundation in the statistical physics.

Providing a unified treatment of the subject, this text addresses modelling, qualitative analysis and simulation of real physical systems using ordinary differential equations. The scientific computational aspects are presented using the computer program, Mathematica, both for plentiful exercises and examples. Special attention is given to classical mechanics in light of new computational methods and concept.

Micropolar fluids are fluids with microstructure. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the well-established Navier-Stokes model of classical fluids that we shall call ordinary fluids. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of fluid particles is ignored. The model of micropolar fluids introduced in [65] by C. A. Eringen is worth studying as a very well balanced one. First, it is a well-founded and significant generalization of the classical Navier-Stokes model, covering, both in theory and applications, many more phenomena than the classical one. Moreover, it is elegant and not too complicated, in other words, man­ ageable to both mathematicians who study its theory and physicists and engineers who apply it. The main aim of this book is to present the theory of micropolar fluids, in particular its mathematical theory, to a wide range of readers. The book also presents two applications of micropolar fluids, one in the theory of lubrication and the other in the theory of porous media, as well as several exact solutions of particular problems and a numerical method. We took pains to make the presentation both clear and uniform.

“The authors have backgrounds which are ideally suited for writing this book. ...They have produced a compact, moderately general book which encompasses many fluid models of current interest…The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments. This is an excellent book which is highly recommended to students and researchers in fluid mechanics.” (Mathematical Reviews)“The writing style is quintessential Truesdellania: purely mathematical, breathtaking, irrepressible, irreverent, uncompromising, taking no prisoners...The book is filled with historical nuggets…Its pure, exact mathematics will baptize, enlighten and exhilarate.” (Applied Mechanics Review)“The most positive aspect of this book is its brevity; a large number of topics are covered within the space of a little more than 250 pages.” (Current Science)“This advanced monograph presents one of the best new views on the subject for those who like relative simplicity and certain abstractness combined with mathematical rigor and elegance…The book should be useful for graduates and researchers not only in applied mathematics and mechanical engineering but also in advanced materials science and technology…Each public scientific library as well as hydrodynamics hand libraries should own this timeless book…Everyone who decides to buy this book can be sure to have bought a classic of science and the heritage of an outstanding scientist.” (Silikáty)“All applied mathematicians, mechanical engineers, aerospace engineers, and engineering mechanics graduates and researchers will find the book an essential reading resource for fluids.” (Simulation News Europe)

The subject of mathematical modeling has expanded considerably in the past twenty years. This is in part due to the appearance of the text by Kemeny and Snell, "Mathematical Models in the Social Sciences," as well as the one by Maki and Thompson, "Mathematical Models and Applica­ tions. " Courses in the subject became a widespread if not standard part of the undergraduate mathematics curriculum. These courses included var­ ious mathematical topics such as Markov chains, differential equations, linear programming, optimization, and probability. However, if our own experience is any guide, they failed to teach mathematical modeling; that is, few students who completed the course were able to carry out the mod­ eling paradigm in all but the simplest cases. They could be taught to solve differential equations or find the equilibrium distribution of a regular Markov chain, but could not, in general, make the transition from "real world" statements to their mathematical formulation. The reason is that this process is very difficult, much more difficult than doing the mathemat­ ical analysis. After all, that is exactly what engineers spend a great deal of time learning to do. But they concentrate on very specific problems and rely on previous formulations of similar problems. It is unreasonable to expect students to learn to convert a large variety of real-world problems to mathematical statements, but this is what these courses require.

The goal of this is book to give a detailed presentation of multicomponent flow models and to investigate the mathematical structure and properties of the resulting system of partial differential equations. These developments are also illustrated by simulating numerically a typical laminar flame. Our aim in the chapters is to treat the general situation of multicomponent flows, taking into account complex chemistry and detailed transport phe­ nomena. In this book, we have adopted an interdisciplinary approach that en­ compasses a physical, mathematical, and numerical point of view. In par­ ticular, the links between molecular models, macroscopic models, mathe­ matical structure, and mathematical properties are emphasized. We also often mention flame models since combustion is an excellent prototype of multicomponent flow. This book still does not pretend to be a complete survey of existing models and related mathematical results. In particular, many subjects like multi phase-flows , turbulence modeling, specific applications, porous me­ dia, biological models, or magneto-hydrodynamics are not covered. We rather emphasize the fundamental modeling of multicomponent gaseous flows and the qualitative properties of the resulting systems of partial dif­ ferential equations. Part of this book was taught at the post-graduate level at the Uni­ versity of Paris, the University of Versailles, and at Ecole Poly technique in 1998-1999 to students of applied mathematics.

Most materials used in contemporary life and industry are heterogeneous (composites) and multicomponent, possessing a rich and complex internal structure. This internal structure, or microstructure, plays a key role in understanding and controlling the continuum behavior, or macroscopic, of a wide variety of materials. The modeling process is a critical tool for scientists and engineers studying the analysis and experimentation for the micromechanics and behavior of these materials. "Heterogeneous Media" is a critical, in-depth edited survey of the major topics surrounding the modeling and analysis of problems in micromechanics of multicomponent systems, including conceptual and practical aspects. The goal of this extensive and comprehensive survey is to provide both specialists and nonspecialists with an authoritative and interdisciplinary perspective of current ideas and methods used for modeling heterogeneous materials behavior and their applications. Topics and Features: * all chapters use interdisciplinary modeling perspective for investigating heterogeneous media*Five chapters provide self-contained discussions, with background provided*Focuses only upon most important techniques and models, fully exploring micro-macro interconnections*extensive introductory survey chapter on micromechanics of heterogeneous media*microstructure characterization via statistical correlation functions*micro-scale deformation of pore space*wave fields and effective dynamical properties*modeling of the complex production technologies for composite materials The book is ideal for a general scientific and engineering audience needing an in-depth view and guide to current ideas, methods and

Despite the fact that fluid dynamics and filtration through porous media and mathematics, there are classical research areas in engineering, physics, are still many industrial processes that require the study of new mathemat­ ical models for flows of particular complexity, due to the peculiar properties of the systems involved. The aim of this book is to provide a number of examples showing how frequently such situations arise in various branches of industrial technology. The selection of the subjects was motivated not only by their industrial rel­ evance and mathematical interest. What I had in mind was a collection of problems having a really distinctive character, thus bringing some fresh air into one of the oldest and most revered domains of applied mathematics. The incredible richness of nonstandard flow problems in industrial appli­ cations has always been, and still is, a constant surprise to me. Therefore I tried to offer a very large spectrum of subjects, with special attention devoted to those problems in which the modeling phase is far from being obvious, and the mathematical content is absolutely nontrivial. With such a view to diversity, topics have been selected from a variety of sources (such as glass industry, polymers science, coffee brewing, fuels pipelining), and contributors from different backgrounds (mathematics, physics, chemical engineering) have been included. Consequently, the mathematical nature of the problems formulated spans over a large range, so that their theoret­ ical investigation and numerical computation require a variety of different techniques.

Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis. Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations. An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications. This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process. Topics and Features: * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinetic traffic-flow models * Models of granular media * Large communication networks * Thorough discussion of numerical simulations of Boltzmann equation This new book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers, and postgraduates will find the book a modern and authoritative guide to the topic.

Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica for Ordinary Differential Equations provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use ODEs and Mathematica in the Dynamics of rigid bodies. Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ordinary differential equations such as, phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica.

This book presents the language of random field theory and the principles of stochastic geometry in order to give the systematic and concise knowledge necessary for modeling real random heterogeneous media. This book is ideal for a general scientific audience needing an in-depth guide to current ideas, methods and models for the stochastic modeling of microstructures. It is an essential reference for practitioners, researchers and professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.

Modelling of granular and porous materials in science and engineering touches all kinds of problems arising from the necessity to successfully describe the behaviour of materials naturally existing in our surroundings. The book brings together scientists in engineering and mathematicians interested in solid behaviour and experts in particulate material modelling. The modelling process is a critical tool for studying the analysis and experimentation of micromechanics and behavior of granular and porous material. The text focuses upon the most important techniques and models currently in use, looking at: mechanics of porous media; modelling of soil behaviour; flow and transport phenomena in particulate materials; numerical simulation methods; and numerical model for finite elastoplastic deformations. The text should appeal to research workers, graduate students, and scientists in applied mathematics, continuum mechanics, finite element methods, solid mechanics and hydraulics engineering.

This book provides a thoroughly assessible and lucid overview of the different aspects, models and methodology of the kinetic theory modeling process. The study of fluid dynamics is a central theme in modern applied mathematics. It is used to model a vast range of physical phenomena and plays a central role in science and engineering. This book provides a comprehensive description of the relationship between kinetic theory and fluid dynamics. Equations used in fluid dynamics and their associated boundary conditions that consider the weak effect of gas rarefaction are derived from the Boltzmann system by systematic asymptotic analysis. Problems are presented so that they can easily be applied to other practical problems. The systems are applied to various interesting physical problems such as flows induced by temperature fields as well as evaporation and condensation problems.

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book/interactive CD-ROM presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers.Key features of this original, progressive, and comprehensive approach: - description of mathematical background and underlying tools - up-to-date review of grid construction and control, optimization algorithms, software differentiation and gradient calculations - practical solutions for implementation in many real- life problems - solution of illustrative examples and exercises - basic mathematical programming techniques used to solve constrained minimization problems are presented; these fairly self-contained chapters can serve as an introduction to the numerical solution of generic constrained optimization problems - companion CD-ROM contains source files and data; readers can test different solution strategies to determine their relevance and efficiency - CD-ROM also offers software building, updating computational grids, performing automatic code differentiation, and computing basic aeroelastic solutions "Numerical Methods in Sensitivity Analysis and Shape Optimization" will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.The

The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics, and the macroscopic behavior of such materials often depends critically on their substructures. This work, written by leading mathematicians and engineers, features a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories within the context of modeling material substructures. Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from the work and may find suggestions for further research in its rich collection of open problems.

This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The progress in the field over the last thirty years has greatly enhanced the original theory and has stimulated interesting and critical gas dynamic phenomena and problems. 'Molecular Gas Dynamics,' unique in the literature, presents working knowledge, theory, techniques, and typical phenomena in rarefied gases for theoretical development and application.Basic theory is developed in a systematic way and presented in a form easily applied for practical use. After presenting various simple flows, such as unidirectional or quasi-unidirectional flows, and flows around a sphere, the author discusses additional topics, including: * flows induced by temperature fields, which are typical in rarefied gases * flows with evaporation and condensation * bifurcation of flows in rarefied gases * the ghost effect in gases in the continuum limitDiscovery of the ghost effect has made molecular gas dynamics indispensable to the study of a gas in the continuum limit, which is traditionally treated by classical fluid dynamics.In this work, the ghost effect and non-Navier-Stokes effects are demonstrated for typical examples. Benard and Taylor-Couette problems in the context of a new framework. A new type of ghost effect is also discussed, and a long-standing problem bifurcation of the plane Couette flow in classical fluid dynamics is resolved. The book is useful for those working in different communities where kinetic theory or fluid dynamics is important: graduate students, researchers, and practitioners in theoretical physics, applied mathematics, and various branches of engineering. The work may be used as a self-study reference or as a textbook in graduate-level courses in fluid dynamics, gas dynamics, molecular gas dynamics, kinetic theory, and applied mathematics.

This self-contained book is devoted to the application of neural networks to the concrete problem of handling the time series of sea data, i.e., significant wave heights and sea levels. Beginning with an explanation of neural networks fundamentals for beginners, the authors follow with a review of general statements and rigorous facts, and conclude with applications and algorithms for particular data sets having well-defined parameters.Specifically analyzed are the time series of measures observed from a system of sea buoys, as well as the reconstruction of missing values that are largely present in these time series. Neural networks are used to solve this problem, and the reconstructed time series are modeled to estimate the probability of large events using extreme value theory. This ability to model and estimate is important for the construction of sea structures, ports, and marine experiments."Neural Networks and Sea Time Series" is a unique monograph on the topic and may stimulate new research and results in the field.The book will be a useful resource for a diverse audience of graduate students, researchers and practitioners in applied mathematics, data analysis, meteorology, hydraulic, civil and marine engineering.

Modern aerospace vehicles, such as the space shuttle, other launch vehicles, and long-range ballistic missiles, do not discriminate between atmospheric and space flight. Most texts on flight dynamics, however, make this artificial distinction and therefore do not simultaneously cover aircraft and spacecraft. Bridging this gap in the literature, "Atmospheric and Space Flight Dynamics" is a unified presentation, demonstrating that the two disciplines have actually evolved from the same set of physical principles. Introduced is a broad range of modern topics in an accessible, yet mathematically rigorous presentation. A key feature of the text is the integration of many MATLAB- and Simulink-based numerical examples and real-world simulations throughout for the design of aircraft, missiles, launch vehicles, re-entry vehicles, and spacecraft. The author uses the software as an instructional, hands-on tool, moving away from the "cook book" approach found in other works. Replete with illustrations, end-of-chapter exercises, and selected solutions, the work is primarily useful as a textbook for advanced undergraduate and beginning graduate-level students.The book is also suitable as a reference or self-study guide for researchers and practitioners in aerospace engineering, aviation, mechanical engineering, dynamics, astrodynamics, aeronautics, and astronautics.

Pattern analysis and recognition pervade many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis---a fundamental building block in many approaches to these applications---is also used in statistics, biomedical applications (Magnetic Resonnance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, algorithms, and programs available in a single resource. The book gives an overview of planar and three-dimensional shape analysis and reviews developments from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine."Statistics and Analysis of Shapes" will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field.The book may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. Experienced researchers and practitioners in academia and industry needing a single and concise source of state-of-the-art techniques will also find this a useful book.

This book develops methods using mathematical kinetic theory to describe the evolution of several socio-biological systems. Specifically, it deals with modeling and simulations of biological systems constituted by large populations of interacting cells, whose dynamics follow both the rules of mechanics as well as their own ability to organize movement and biological functions. Proposed is a new biological model focused on the analysis of competition between cells of an aggressive host and cells of the immune system. Modeling in kinetic theory may represent a way to understand phenomena of nonequilibrium statistical mechanics that is not described by the traditional macroscopic approach. The authors of this work focus on models that refer to the Boltzmann equation (generalized Boltzmann models) with the dynamics of populations of several interacting individuals (kinetic population models). The book follows the classical research line applied to modeling real systems, linking the phenomenological observation of systems to modeling and simulations. Computational algorithms are applied and qualitative analysis techniques are used to identify the prediction ability of specific models.The book will be a valuable resource for applied mathematicians as well as researchers in the field of biological sciences. It may also be used for advanced graduate courses in biological systems modeling with applications to collective social behavior, immunology, and epidemiology.

One of the primary purposes and obligations of science, in addition to - derstandingnatureingeneralandlifeinparticular, istoassistinenhancing the quality and longevity of life, indeed a most daunting challenge. To be able to meaningfully meet the last of the above expectations, it is nec- sary to provide the practitioner of medicine with diagnostic and predictive capabilities that science will accord when its seemingly disparate parts are melded together and brought to bear on the problems that they face. The development of interdisciplinary activities involving the various basic sciences—biology, physics, chemistry, and mathematics, and their applied counterparts, engineering and technology—is a necessary key to unlocking the mysteries of medicine, which at the moment is a curious admixture of art, craft, and science. Signi?cant strides have been taken during the past decades for putting intoplaceamethodologythattakesintoaccounttheinterplayofthevarious basic sciences. Considerable progress has been made in understanding the role that mechanics has to play in the development of medical procedures. Thiscollectionofsurveyarticlesaddressestheroleofmechanicswithregard to advances in the medical sciences. In particular, these survey articles bring to one’s attention the central role played by mathematical modeling in general and the modeling of mechanical issues in particular that have a bearing on the biology, chemistry, and physics of living matter.

Modern aerospace vehicles, such as the space shuttle, other launch vehicles, and long-range ballistic missiles, do not discriminate between atmospheric and space flight.

This volume aims to provide an overview of some recent developments of mathematical kinetic theory focused on its application in modelling complex systems in various ?elds of applied sciences. Mathematical kinetic theory is essentially based on the Boltzmann eq- tion, which describes the evolution, possibly far from equilibrium, of a class of particles modelled as point masses. The equation de?nes the evolution in time and space of the distribution function over the possible microscopic states of the test particle, classically position and velocity. The test particle is subject to pair collisions with the ?eld particles. The interested reader can ?nd in the book, Theory and Application of the Boltzmann Equation, by C. Cercignani, R. Illner, and M. Pulvirenti, Springer, Heidelberg, 1993, all necessary knowledge of the physics and mathematical topics related to this celebrated model of non-equilibrium statistical mech- ics. Another important model of mathematical kinetic theory is the Vlasov equation, where interactions between particles are not speci?cally collisions, but mean ?eld actions of the ?eld particles over the test particle. The model de?nes again an evolution equation for the one-particle distribution function over the microscopic state of the test particle. The two models brie?y mentioned above can be regarded as the fun- mental models of mathematical kinetic theory and the essential background o?ered from the kinetic theory for classical particles towards the modelling of large systems of several particles undergoing non classical interactions.