This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme 'Optimization with PDEs' (OPTPDE).

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

ThisvolumecelebratestheeightiethbirthdayofJosephB. Keller. The authors who contributed to this volume belong to what can be called the "Keller school of applied mathematics. " They are former students, postdoctoral fellows and visiting scientists who have collaborated with Joe (some of them still do) during his long career. They all look at Joe as their ultimate (role) model. JoeKeller'sdistinguishedcareerhasbeendividedbetweentheCourant Institute of Mathematical Sciences at New York University, where he received all his degrees (his PhD adviser being the great R. Courant himself) and served as a professor for 30 years, and Stanford University, where he has been since 1978. The appended photos highlight some scenes from the old days. Those who know Joe Keller's work have been always amazed by its diversity and breadth. It is considered a well-known truth that there is not a single important area in applied mathematics or physics which Keller did not contribute to. This can be appreciated, for example, by glancing through his list of publication included in this volume. App- priately, the papers in this book, written with Joe's inspiration, cover a variety of application areas; together they span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to ?nance, waves, - croorganisms, shocks, DNA, ?ames, contact, optics, ?uids, bubbles and jets. Joe's activity includes many more areas, which unfortunately are not represented here.

This monograph concisely but thoroughly introduces the reader to the field of mathematical immunology. The book covers first basic principles of formulating a mathematical model, and an outline on data-driven parameter estimation and model selection. The authors then introduce the modeling of experimental and human infections and provide the reader with helpful exercises. The target audience primarily comprises researchers and graduate students in the field of mathematical biology who wish to be concisely introduced into mathematical immunology.

The goal of this textbook is to provide first-year engineering students with a firm grounding in the fundamentals of chemical and bioprocess engineering. However, instead of being a general overview of the two topics, Fundamentals of Chemical and Bioprocess Engineering will identify and focus on specific areas in which attaining a solid competency is desired. This strategy is the direct result of studies showing that broad-based courses at the freshman level often leave students grappling with a lot of material, which results in a low rate of retention. Specifically, strong emphasis will be placed on the topic of material balances, with the intent that students exiting a course based upon this textbook will be significantly higher on Bloom's Taxonomy (knowledge, comprehension, application, analysis and synthesis, evaluation, creation) relating to material balances. In addition, this book also provides students with a highly developed ability to analyze problems from the material balances perspective, which leaves them with important skills for the future. The textbook consists of numerous exercises and their solutions. Problems are classified by their level of difficulty. Each chapter has references and selected web pages to vividly illustrate each example. In addition, to engage students and increase their comprehension and rate of retention, many examples involve real-world situations.

Numerical methods and related computer based algorithms form the logical solution for many complex problems encountered in science and engineering. Although numerical techniques are now well established, they have continued to expand and diversify, particularly in the fields of engineering analysis and design. Various engineering departments in the University College of Swansea, in particular, Civil, Chemical, Electrical and Computer Science, have groups working in these areas. It is from this mutual interest that the NUMET A conference series was conceived with the main objective of providing a link between engineers developing new numerical techniques and those applying them in practice. Encouraged by the success of NUMETA '85, the second conference, NUMETA '87, was held at Swansea, 6-10 July 1987. Over two hundred and twenty abstracts were submitted for consideration together with a number of invited papers from experts in the field of numerical methods. The final selection of contributed and invited papers were of a high quality and have culminated in the two volumes which form these proceedings. This volume contains papers on the themes of 'Transient/Dynamic Analysis and Constitutive Laws for Engineering Materials'. Many new developments on a wide variety of topics have been reported and these proceedings contain a wealth of information and references which we believe will be of great interest to theoreticians and practising engineers alike.

Integrated assessment modelling is an active and rapidly developing field, triggered by the debate on climate change and the move towards the goal of sustainable development. This book provides an integrated approach to modelling, using a transdisciplinary approach. The author summarizes the main issues involved in the changing global system, and gives an overview of the emerging field of integrated assessment. He then presents a general discussion of the methodological principles of a multidisciplinary integrated modelling approach. Existing tools are examined and new methodological approaches are applied to various aspects of the problem of global change. The case studies focus on optimizing climate change mitigating policies, the allocation of emission rights and the the adaptive behaviour of social and biological agents. Special attention is given to the role of uncertainty, especially the subjective interpretation of uncertainties (world views), and the role of adaptive multi-agent modelling. The book concludes with a discussion on future uses of integrated assessment modelling in the global environment. Modelling Global Change will be vital to economists and scientists who have an interest in integrated assessment modelling, global modelling and decision support, environmental and ecological economists and those interested in sustainable development.

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."

This book addresses the issue of Machine Learning (ML) attacks on Integrated Circuits through Physical Unclonable Functions (PUFs). It provides the mathematical proofs of the vulnerability of various PUF families, including Arbiter, XOR Arbiter, ring-oscillator, and bistable ring PUFs, to ML attacks. To achieve this goal, it develops a generic framework for the assessment of these PUFs based on two main approaches. First, with regard to the inherent physical characteristics, it establishes fit-for-purpose mathematical representations of the PUFs mentioned above, which adequately reflect the physical behavior of these primitives. To this end, notions and formalizations that are already familiar to the ML theory world are reintroduced in order to give a better understanding of why, how, and to what extent ML attacks against PUFs can be feasible in practice. Second, the book explores polynomial time ML algorithms, which can learn the PUFs under the appropriate representation. More importantly, in contrast to previous ML approaches, the framework presented here ensures not only the accuracy of the model mimicking the behavior of the PUF, but also the delivery of such a model. Besides off-the-shelf ML algorithms, the book applies a set of algorithms hailing from the field of property testing, which can help to evaluate the security of PUFs. They serve as a "toolbox", from which PUF designers and manufacturers can choose the indicators most relevant for their requirements. Last but not least, on the basis of learning theory concepts, the book explicitly states that the PUF families cannot be considered as an ultimate solution to the problem of insecure ICs. As such, it provides essential insights into both academic research on and the design and manufacturing of PUFs.

This book presents the main tools for aggregation of information given by several members of a group or expressed in multiple criteria, and for fusion of data provided by several sources. It focuses on the case where the availability knowledge is imperfect, which means that uncertainty and/or imprecision must be taken into account. The book contains both theoretical and applied studies of aggregation and fusion methods in the main frameworks: probability theory, evidence theory, fuzzy set and possibility theory. The latter is more developed because it allows to manage both imprecise and uncertain knowledge. Applications to decision-making, image processing, control and classification are described.

Efficient and equitable policies for managing disaster risks and adapting to global environmental change are critically dependent on development of robust options supported by integrated modeling.

The book is based on research and state-of-the art models developed at IIASA (International Institute for Applied Systems Analysis) and within its cooperation network. It addresses the methodological complexities of assessing disaster risks, which call for stochastic simulation, optimization methods and economic modeling. Furthermore, it describes policy frameworks for integrated disaster risk management, including stakeholder participation facilitated by user-interactive decision-support tools.

Applications and results are presented for a number of case studies at different problem scales and in different socio-economic contexts, and their implications for loss sharing policies and economic development are discussed. Among others, the book presents studies for insurance policies for earthquakes in the Tuscany region in Italy and flood risk in the Tisza river basin in Hungary. Further, it investigates the economic impact of natural disasters on development and possible financial coping strategies; and applications are shown for selected South Asian countries.

The book is addressed both to researchers and to organizations involvedwith catastrophe risk management and risk mitigation policies.

The book presents the latest findings in experimental plasticity, crystal plasticity, phase transitions, advanced mathematical modeling of finite plasticity and multi-scale modeling. The associated algorithmic treatment is mainly based on finite element formulations for standard (local approach) as well as for non-standard (non-local approach) continua and for pure macroscopic as well as for directly coupled two-scale boundary value problems. Applications in the area of material design/processing are covered, ranging from grain boundary effects in polycrystals and phase transitions to deep-drawing of multiphase steels by directly taking into account random microstructures.

One service mathematics has rendered the 'Et moi, .... si favait su comment en revenir, je n'y seTais point alle.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded n- sense', The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One scrvice logic has rendered com puter science .. .'; 'One service category theory has rendcred mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e"tre of this scries."

This volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling in Solid Mechanics', held in Cardiff from 25th to 29th June 2007. The Symposium was convened to address and place on record topical issues in theoretical, experimental and computational aspects of scaling approaches to solid mechanics and related fields. Scaling is a rapidly expanding area of research having multidisciplinaryapplications. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated.

Scaling methods apply wherever there is similarity across many scales or a need to bridge different scales, e.g. the nanoscale and macroscale. The emphasis in the Symposium was upon fundamental issues such as: mathematical foundations of scaling methods based on transformations and connections between multi-scale approaches and transformations. The Symposium remained focussed on fundamental research issues of practical significance. The topics considered included damage accumulation, growth of fatigue cracks, development of patterns of flaws in the earth's core and in ice, abrasiveness of rough surfaces, and so on. The Symposium showed that scaling methods cannot be reduced solely to dimensional analysis and fractal approaches. Modern scaling approaches consist of a great diversity of techniques.

These proceedings contain lectures on state-of-the-art developments in self-similar solutions, fractal models, models involving interplay between different scales, size effects in fracture of solids and bundles of fibres, scaling in problems of fracture mechanics, nanomechanics, contact mechanics and testing of materials byindentation, scaling issues in mechanics of agglomeration of adhesive particles, and in biomimetic of adhesive contact.

Introduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. This book includes techniques that are not covered in those texts. Through their experience involving undergraduate and graduate students in a research topic related to traveling waves, the authors found that the main difficulty is to provide reading materials that contain the background information sufficient to start a research project without an expectation of an extensive list of prerequisites beyond regular undergraduate coursework. This book meets that need and serves as an entry point into research topics about the existence and stability of traveling waves. Features Self-contained, step-by-step introduction to nonlinear waves written assuming minimal prerequisites, such as an undergraduate course on linear algebra and differential equations. Suitable as a textbook for a special topics course, or as supplementary reading for courses on modeling. Contains numerous examples to support the theoretical material. Supplementary MATLAB codes available via GitHub.

This book covers several bases at once. It is useful as a textbook for a second course in experimental optimization techniques for industrial production processes. In addition, it is a superb reference volume for use by professors and graduate students in Industrial Engineering and Statistics departments. It will also be of huge interest to applied statisticians, process engineers, and quality engineers working in the electronics and biotech manufacturing industries. In all, it provides an in-depth presentation of the statistical issues that arise in optimization problems, including confidence regions on the optimal settings of a process, stopping rules in experimental optimization, and more.

This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be.

Die Autoren fuhren auf anschauliche und systematische Weise in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik ein. Es geht um Klassen von Modellen und um die Vielfalt an Beschreibungsarten. Aber es geht immer auch darum, wie aus Modellen konkrete Simulationsergebnisse gewonnen werden konnen. Nach einem kompakten Repetitorium zum benotigten mathematischen Apparat wird das Konzept anhand von Szenarien u. a. aus den Bereichen Spielen entscheiden planen" und Physik im Rechner" umgesetzt."

Mathematical Modelling in Medicine is divided into four distinct parts which cover mathematical models of heart, arterial tree, baroreceptor control and applications for simulators. The mathematical models covering these four topics are contained in a number of articles in each part. In addition, historical reviews on the heart, arterial tree and baroreceptors are also included in the articles offering a broader view and understanding of the current physiological models. The models presented are all based on fundamental physiological principles. This common guideline may result in more solid models from which we can obtain new physiological insights. Mathematical Modelling in Medicine demonstrates that the increase in popularity and success of mathematical models, is not solely a consequence of the development and spread of fast computers, making easier access to simulations of complex systems. An important element for this success is the precise continuous samplings of new clinical data have generated experiments, from which one can gain new insights into the dynamics of physiological systems and not only into their steady state behaviour patterns. Another important element is the attempts to focus on precise definitions of physiological concepts in order to avoid confusion, misunderstandings and waste of efforts. Furthermore, it is shown, that mathematics may also provide a tool to structure thoughts, an area which have gained an increasing attention lately. This book will be of interest to graduate students as well as researchers in the interdisciplinary fields of bioengeneering, biophysics and mathematical physiology.

The need for a comprehensive survey-type exposition on formal languages and related mainstream areas of computer science has been evident for some years. In the early 1970s, when the book Formal Languages by the second mentioned editor appeared, it was still quite feasible to write a comprehensive book with that title and include also topics of current research interest. This would not be possible anymore. A standard-sized book on formal languages would either have to stay on a fairly low level or else be specialized and restricted to some narrow sector of the field. The setup becomes drastically different in a collection of contributions, where the best authorities in the world join forces, each of them concentrat ing on their own areas of specialization. The present three-volume Handbook constitutes such a unique collection. In these three volumes we present the current state of the art in formallanguage theory. We were most satisfied with the enthusiastic response given to our request for contributions by specialists representing various subfields. The need for a Handbook of Formal Languages was in many answers expressed in different ways: as an easily accessible his torical reference, a general source of information, an overall course-aid, and a compact collection of material for self-study. We are convinced that the final result will satisfy such various needs."

In this text, we introduce the basic concepts for the numerical modeling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Because of its versatility in analyzing a broad range of applications, multibody dynamics has grown in the past two decades to be an important tool for designing, prototyping, and simulating complex articulated mechanical systems. This textbooka "a result of the authora (TM)s many years of research and teachinga "brings together diverse concepts of dynamics, combining the efforts of many researchers in the field of mechanics. Bridging the gap between dynamics and engineering applications such as microrobotics, virtual reality simulation of interactive mechanical systems, nanomechanics, flexible biosystems, crash simulation, and biomechanics, the book puts into perspective the importance of modeling in the dynamic simulation and solution of problems in these fields.

To help engineering students and practicing engineers understand the rigid-body dynamics concepts needed for the book, the author presents a compiled overview of particle dynamics and Newtona (TM)s second law of motion in the first chapter. A particular strength of the work is its use of matrices to generate kinematic coefficients associated with the formulation of the governing equations of motion. Additional features of the book include:

* numerous worked examples at the end of each section

* introduction of boundary-element methods (BEM) in the description of flexible systems

* up-to-date solution techniques for rigid and flexible multibody dynamics using finite- element methods (FEM)

* inclusion of MATLAB-based simulations and graphical solutions

* in-depth presentation of constrained systems

* presentation of the general form of equations of motion ready for computerimplementation

* two unique chapters on stability and linearization of the equations of motion

Junior/senior undergraduates and first-year graduate engineering students taking a course in dynamics, physics, control, robotics, or biomechanics will find this a useful book with a strong computer orientation towards the subject. The work may also be used as a self-study resource or research reference for practitioners in the above-mentioned fields.

In the quest to understand and model the healthy or sick human body, re searchers and medical doctors are utilizing more and more quantitative tools and techniques. This trend is pushing the envelope of a new field we call Biomedical Computing, as an exciting frontier among signal processing, pattern recognition, optimization, nonlinear dynamics, computer science and biology, chemistry and medicine. A conference on Biocomputing was held during February 25-27, 2001 at the University of Florida. The conference was sponsored by the Center for Applied Optimization, the Computational Neuroengineering Center, the Biomedical En gineering Program (through a Whitaker Foundation grant), the Brain Institute, the School of Engineering, and the University of Florida Research & Graduate Programs. The conference provided a forum for researchers to discuss and present new directions in Biocomputing. The well-attended three days event was highlighted by the presence of top researchers in the field who presented their work in Biocomputing. This volume contains a selective collection of ref ereed papers based on talks presented at this conference. You will find seminal contributions in genomics, global optimization, computational neuroscience, FMRI, brain dynamics, epileptic seizure prediction and cancer diagnostics. We would like to take the opportunity to thank the sponsors, the authors of the papers, the anonymous referees, and Kluwer Academic Publishers for making the conference successful and the publication of this volume possible. Panos M. Pardalos and Jose C."

This book offers a valuable methodological approach to the state-of-the-art of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling non-linear phenomena governed by PDEs.

This introductory textbook is designed for a one-semester course on queueing theory that does not require a course on stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. This edition includes additional topics in methodology and applications. Key features: * An introductory chapter including a historical account of the growth of queueing theory in more than 100 years. * A modeling-based approach with emphasis on identification of models * Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics. * A chapter on matrix-analytic method as an alternative to the traditional methods of analysis of queueing systems. * A comprehensive treatment of statistical inference for queueing systems. * Modeling exercises and review exercises when appropriate. The second edition of An Introduction of Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research. "...This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books." - Assam Statistical Review of the first edition