This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.

INHALT LANG: Introduction: Introductory Survey; Vector Norm. Matrix Norm. Matrix Measure; Functional Analysis, Function Norms and Control Signals.- Differential Sensitivity. Small-Scale Perturbation: Kronecker Calculus in Control Theory; Analysis Using Matrices and Control Theory; Eigenvalue and Eigenvector Differential Sensitivity; Transition Matrix Differential Sensitivity; Characteristic Polynomial Differential Sensitivity; Optimal Control and Performance Sensitivity; Desensitizing Control.- Robustness in the Time Domain: General Stability Bounds in Perturbed Systems; Robust Dynamic Interval Systems; Lyapunov-Based Methods for Perturbed Continuous-Time Systems; Lyapunov-Based Methods for Perturbed Discrete-Time Systems; Robust Pole Assignment; Models for Optimal and Interconnected Systems; Robust State Feedback Using Ellipsoid Sets; Robustness of Observers and Kalman-Bucy Filters; Initial Condition Perturbation, Overshoot and Robustness; Lnp-Stability and Robust Nonlinear Control.- Robustness in the Frequency Domain: Uncertain Polynomials. Interval Polynomials; Eigenvalues and Singular Values of Complex Matrices; Resolvent Matrix and Stability Radius; Robustness Via Singular-Value Analysis; Generalized Nyquist Stability of Perturbed Systems; Block-Structured Uncertainty and Structured Singular Value; Performance Robustness; Robust Controllers Via Spectral Radius Technique.- Coprime Factorization and Minimax Frequency Optimization: Robustness Based on the Internal Model Principle; Parametrization and Factorization of Systems; Hardy Space Robust Design.- Robustness Via Approximative Models: Robust Hyperplane Design in Variable Structure Control; SIngular Perturbaitons. Unmodelled High-Frequendy Dynamics; Control Using Aggregation Models; Optimum Control of Approximate and Nonlinear Systems; System Analysis via Orthogonal Functions; System Analysis Via Pulse Functions and Piecewise Linear Functions; Orthogonal Decomposition Applications.

Geochemical modeling is an important tool in environmental studies, and in the areas of subsurface and surface hydrology, pedology, water resources management, mining geology, geothermal resources, hydrocarbon geology, and related areas dealing with the exploration and extraction of natural resources. The book fills a gap in the literature through its discussion of geochemical modeling, which simulates the chemical and physical processes affecting the distribution of chemical species in liquid, gas, and solid phases. Geochemical modeling applies to a diversity of subsurface environments, from the vadose zone close to the Earth's surface, down to deep-seated geothermal reservoirs. This book provides the fundamental thermodynamic concepts of liquid-gas-solid phase systems. It introduces the principal types of geochemical models, such as speciation, reaction-path or forward, inverse- and reactive-transport models, together with examples of the most common codes and the best-practices for constructing geochemical models. The physical laws describing homogeneous and heterogeneous chemical reactions, their kinetics, and the transport of reactive solutes are presented. The partial differential or algebraic equations representing these laws, and the principal numerical methods that allow approximate solutions of these equations that can provide useful solutions to model different geochemical processes, are discussed in detail. Case studies applying geochemical models in different scientific areas and environmental settings, conclude the book. The book is addressed to students, teachers, other professionals, and to the institutions involved in water, geothermal and hydrocarbon resources, mining, and environmental management. The book should prove useful to undergraduate and graduate students, postgraduates, professional geologists and geophysicists, engineers, environmental scientists, soil scientists, hydrochemists, and others interested in water and geochemistry.

Mathematics of Planet Earth (MPE) was started and continues to be consolidated as a collaboration of mathematical science organisations around the world. These organisations work together to tackle global environmental, social and economic problems using mathematics.This textbook introduces the fundamental topics of MPE to advanced undergraduate and graduate students in mathematics, physics and engineering while explaining their modern usages and operational connections. In particular, it discusses the links between partial differential equations, data assimilation, dynamical systems, mathematical modelling and numerical simulations and applies them to insightful examples.The text also complements advanced courses in geophysical fluid dynamics (GFD) for meteorology, atmospheric science and oceanography. It links the fundamental scientific topics of GFD with their potential usage in applications of climate change and weather variability. The immediacy of examples provides an excellent introduction for experienced researchers interested in learning the scope and primary concepts of MPE.

Human decision-making often transcends our formal models of "rationality." Designing intelligent agents that interact proficiently with people necessitates the modeling of human behavior and the prediction of their decisions. In this book, we explore the task of automatically predicting human decision-making and its use in designing intelligent human-aware automated computer systems of varying natures-from purely conflicting interaction settings (e.g., security and games) to fully cooperative interaction settings (e.g., autonomous driving and personal robotic assistants). We explore the techniques, algorithms, and empirical methodologies for meeting the challenges that arise from the above tasks and illustrate major benefits from the use of these computational solutions in real-world application domains such as security, negotiations, argumentative interactions, voting systems, autonomous driving, and games. The book presents both the traditional and classical methods as well as the most recent and cutting edge advances, providing the reader with a panorama of the challenges and solutions in predicting human decision-making.

A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors' extensive work in this field, Dynamics of the Chemostat: A Bifurcation Theory Approach explores the use of bifurcation theory to analyze the static and dynamic behavior of the chemostat. IntroductionThe authors first survey the major work that has been carried out on the stability of continuous bioreactors. They next present the modeling approaches used for bioreactive systems, the different kinetic expressions for growth rates, and tools, such as multiplicity, bifurcation, and singularity theory, for analyzing nonlinear systems. ApplicationThe text moves on to the static and dynamic behavior of the basic unstructured model of the chemostat for constant and variable yield coefficients as well as in the presence of wall attachment. It then covers the dynamics of interacting species, including pure and simple microbial competition, biodegradation of mixed substrates, dynamics of plasmid-bearing and plasmid-free recombinant cultures, and dynamics of predator-prey interactions. The authors also examine dynamics of the chemostat with product formation for various growth models, provide examples of bifurcation theory for studying the operability and dynamics of continuous bioreactor models, and apply elementary concepts of bifurcation theory to analyze the dynamics of a periodically forced bioreactor. Using singularity theory and bifurcation techniques, this book presents a cohesive mathematical framework for analyzing and modeling the macro- and microscopic interactions occurring in chemostats. The text includes models that describe the intracellular and operating elements of the bioreactive system. It also explains the mathematical theory behind the models.

This second edition provides a broad range of methods and concepts required for the analysis and solution of equations which arise in the modeling of phenomena in the natural, engineering, and applied mathematical sciences. It may be used productively by both undergraduate and graduate students, as well as others who wish to learn, understand, and apply these techniques. Detailed discussions are also given for several topics that are not usually included in standard textbooks at this level of presentation: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations and several perturbation procedures. Further, this second edition includes several new topics covering functional equations, the Lambert-W function, nonstandard sets of periodic functions, and the method of dominant balance. Each chapter contains a large number of worked examples and provides references to the appropriate books and literature.

Carefully separating the essential from the ornamental, Essentials of Control Techniques and Theory presents the nuts and bolts for designing a successful controller. It discusses the theory required to support the art of designing a working controller as well as the various aspects to convince a client, employer, or examiner of your expertise. A Compelling Account of the Basics of Control Theory Control solutions for practicing engineers Using the author's own Javascript On-Line Learning Interactive Environment for Simulation (Jollies), the text relies on computer-based graphical analysis methods, such as Nyquist, Nichols, root locus, and phase-plane, to illustrate how useful computer simulation can be for analyzing both linear and nonlinear systems. It explains step-by-step the design and modeling of various control systems, including discrete time systems and an inverted pendulum. Along with offering many web-based simulations, the book shows how mathematics, such as vectors, matrices, and the differential equations that govern state variables, can help us understand the concepts that underpin the controller's effects. From frequency domain analysis to time-domain state-space representation, this book covers many aspects of classical and modern control theory. It presents important methods for designing and analyzing linear systems and controllers.

'Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory.'Quantitative Finance This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails - two particularly valuable tools of today's research in economics, finance, econometrics and other fields - in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions - all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.

Measurement Data Modeling and Parameter Estimation integrates mathematical theory with engineering practice in the field of measurement data processing. Presenting the first-hand insights and experiences of the authors and their research group, it summarizes cutting-edge research to facilitate the application of mathematical theory in measurement and control engineering, particularly for those interested in aeronautics, astronautics, instrumentation, and economics. Requiring a basic knowledge of linear algebra, computing, and probability and statistics, the book illustrates key lessons with tables, examples, and exercises. It emphasizes the mathematical processing methods of measurement data and avoids the derivation procedures of specific formulas to help readers grasp key points quickly and easily. Employing the theories and methods of parameter estimation as the fundamental analysis tool, this reference: Introduces the basic concepts of measurements and errors Applies ideas from mathematical branches, such as numerical analysis and statistics, to the modeling and processing of measurement data Examines methods of regression analysis that are closely related to the mathematical processing of dynamic measurement data Covers Kalman filtering with colored noises and its applications Converting time series models into problems of parameter estimation, the authors discuss modeling methods for the true signals to be estimated as well as systematic errors. They provide comprehensive coverage that includes model establishment, parameter estimation, abnormal data detection, hypothesis tests, systematic errors, trajectory parameters, and modeling of radar measurement data. Although the book is based on the authors' research and teaching experience in aeronautics and astronautics data processing, the theories and methods introduced are applicable to processing dynamic measurement data across a wide range of fields.

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice.The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.

This volume contains a selection of papers presented at the conference on Modelling and Optimization of Distributed Parameter Systems with Applications to Engineering, held in Warsaw on July 17-21, 1995. This conference was a consecutive one in the series of conferences sponsored by the IFIP Working Group WG 7.2 "Computational Techniques in Distributed Systems," chaired by Irena Lasiecka. It was organized by the Systems Research Institute of the Polish Academy of Sciences and supported financially by the following institutions: -European Community on Computational Methods in Applied Sciences, -Fundacja Stefana Batorego, -International Mathematical Union, - Telekomunikacja Polska S.A. The following scientists took an active part in preparation of the scientific program of the conference, organizing or helping to organize special sessions: - E. Casas and I.Lasiecka (Optimization and Optimal ControQ, Z.Mr6z (Mechanical Applications), - M.Niezg6dka (Properties of Solutions to P.D.E.s), - L.Pandolfi (Hamilton and Riccati Equation Approaches to Optimization), - K.Sobczyk and J.Zabczyk (Stochastic Systems), - J.Sokolowski and J.-P.Zolesio (Shape Optimization), - J.Wa8niewski (Scientific Computation). In the conference participated 133 scientists from 22 countries. Ten invited plenary lectures and 103 contributed papers have been presented. This volume contains a part of the presented material. The core of it is constituted by papers devoted to control and optimization of distributed parameter systems. Other selection will be included in a special issue of the quarterly Control & Cybernetics to be published in 1996.

The modeling of item response data is governed by item response theory, also referred to as modern test theory. The eld of inquiry of item response theory has become very large and shows the enormous progress that has been made. The mainstream literature is focused on frequentist statistical methods for - timating model parameters and evaluating model t. However, the Bayesian methodology has shown great potential, particularly for making further - provements in the statistical modeling process. The Bayesian approach has two important features that make it attractive for modeling item response data. First, it enables the possibility of incorpor- ing nondata information beyond the observed responses into the analysis. The Bayesian methodology is also very clear about how additional information can be used. Second, the Bayesian approach comes with powerful simulation-based estimation methods. These methods make it possible to handle all kinds of priors and data-generating models. One of my motives for writing this book is to give an introduction to the Bayesian methodology for modeling and analyzing item response data. A Bayesian counterpart is presented to the many popular item response theory books (e.g., Baker and Kim 2004; De Boeck and Wilson, 2004; Hambleton and Swaminathan, 1985; van der Linden and Hambleton, 1997) that are mainly or completely focused on frequentist methods. The usefulness of the Bayesian methodology is illustrated by discussing and applying a range of Bayesian item response models.

Many ecological phenomena involve space as well as time and arise from a combination of random and deterministic processes. Such phenomena include the effects of habitat fragmentation, which is a common result of human activity and a major problem in biological conservation. Reaction-diffusion models provide one approach to describing how random movements and deterministic interactions between individuals combine to influence the dynamics of populations and the structure of ecological communities. Spatial Ecology via Reaction-Diffusion Equations addresses the problem of modeling spatial effects in ecology and population dynamics using reaction-diffusion models.

• Provides broad coverage of a rapidly expanding area of research for ecologists and applied mathematicians.
• Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models.
• Provides the reader with the tools needed to construct and interpret models.
• Includes specific applications of both the models and the methods described.

Spatial Ecology via Reaction-Diffusion Equations provides a practical introduction to the subject for graduate students and researchers working in spatial modeling from mathematics, statistics, ecology, geography and biology.

This book is designed primarily for upper level undergraduate and graduate level students taking a course in multilevel modelling and/or statistical modelling with a large multilevel modelling component. The focus is on presenting the theory and practice of major multilevel modelling techniques in a variety of contexts, using Mplus as the software tool, and demonstrating the various functions available for these analyses in Mplus, which is widely used by researchers in various fields, including most of the social sciences. In particular, Mplus offers users a wide array of tools for latent variable modelling, including for multilevel data.

Molecular biologists are performing increasingly large and complicated experiments, but often have little background in data analysis. The book is devoted to teaching the statistical and computational techniques molecular biologists need to analyze their data. It explains the big-picture concepts in data analysis using a wide variety of real-world molecular biological examples such as eQTLs, ortholog identification, motif finding, inference of population structure, protein fold prediction and many more. The book takes a pragmatic approach, focusing on techniques that are based on elegant mathematics yet are the simplest to explain to scientists with little background in computers and statistics.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

One of the most challenging topics in applied mathematics over the past decades has been the developent of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc lead to such equations when formulated in mathematical terms. However, despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogenous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion contiatns many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems. Volume 2 will be devoted to essentially new results for compressible models. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena. Pierre-Louis Lions is Professor of Mathematics at the University of Paris-Dauphine and of Applied Mathematics at the Ecole Polytechnique.

Mathemusical Conversations celebrates the understanding of music through mathematics, and the appreciation of mathematics through music. This volume is a compilation of the invited talks given at the Mathemusical Conversations workshop that took place in Singapore from 13-15 February 2015, organized by Elaine Chew in partnership with Gerard Assayag for the scientific program and with Bernard Lanskey for the artistic program. The contributors are world experts and leading scholars, writing on the intersection of music and mathematics. They also focus on performance and composition, two topics which are foundational both to the understanding of human creativity and to the creation of tomorrow's music technologies. This book is essential reading for researchers in both music and mathematics. It will also appeal more broadly to scholars, students, musicians, and anyone interested in new perspectives on the intimate relationship between these two universal human activities.

Advanced modeling techniques are a necessary tool in order to design and manage manufacturing systems effectively. This book contains a set of tutorial chapters on topics ranging from aggregate production planning to real time control, including predictive and reactive scheduling, flow management in assembly systems, simulation of robotic cells, design of manufacturing systems under uncertainty and a historical perspective on production management philosophies. The book will be of interest both to researchers and practitioners, including graduate students in Manufacturing Engineering and Operations Research.

This is a book of an international series on interdisciplinary topics of the Mathematical and Biological Sciences. The chapters are related to selected papers on the research themes presented at BIOMAT 2015 International Symposium on Mathematical and Computational Biology which was held in the Roorkee Institute of Technology, in Roorkee, Uttarakhand, India, on November 02-06, 2015. The treatment is both pedagogical and advanced in order to motivate research students to fulfill the requirements of professional practitioners. As in other volumes of this series, there are new important results on the interdisciplinary fields of mathematical and biological sciences and comprehensive reviews written by prominent scientific leaders of famous research groups.There are new results based on the state of art research in Population Dynamics, on Pattern Recognition of Biological Phenomena, the Mathematical Modelling of Infectious Diseases, Computational Biology, the Dynamic and Geometric Modelling of Biological Phenomena, the Modelling of Physiological Disorders, the Optimal Control Techniques in Mathematical Modelling of Biological Phenomena, the Hydrodynamics and Elasticity of Cell Tissues and Bacterial Growth and the Mathematical Morphology of Biological Structures. All these contributions are also strongly recommended to professionals from other scientific areas aiming to work on these interdisciplinary fields.

Modelling is now an accepted part in the understanding, prediction and planning of environmental strategies. Perfect for undergraduate students and non-specialist readers, Modelling Coastal and Marine Processes (2nd Edition) offers an introduction into how coastal and marine models are constructed and used.The mathematics, statistics and numerical techniques used are explained in the first few chapters, making this book accessible to those without a high-level maths background. Later chapters cover modelling sea bed friction, tides, shallow sea dynamics, and ecosystem dynamics. Importantly, there is also a chapter on modelling the impact of climate change on coastal and near shore processes.New to this revised edition is a chapter on tides, tsunamis and the prediction of sea level, and additional material on the new application of the numerical techniques: flux corrected transport, finite volumes and adaptive grids to coastal and marine modelling.

Modelling is now an accepted part in the understanding, prediction and planning of environmental strategies. Perfect for undergraduate students and non-specialist readers, Modelling Coastal and Marine Processes (2nd Edition) offers an introduction into how coastal and marine models are constructed and used.The mathematics, statistics and numerical techniques used are explained in the first few chapters, making this book accessible to those without a high-level maths background. Later chapters cover modelling sea bed friction, tides, shallow sea dynamics, and ecosystem dynamics. Importantly, there is also a chapter on modelling the impact of climate change on coastal and near shore processes.New to this revised edition is a chapter on tides, tsunamis and the prediction of sea level, and additional material on the new application of the numerical techniques: flux corrected transport, finite volumes and adaptive grids to coastal and marine modelling.

This bestselling text provides a practical guide to structural equation modeling (SEM) using the Amos Graphical approach. Using clear, everyday language, the text is ideal for those with little to no exposure to either SEM or Amos. The author reviews SEM applications based on actual data taken from her own research. Each chapter "walks" readers through the steps involved (specification, estimation, evaluation, and post hoc modification) in testing a variety of SEM models. Accompanying each application is: an explanation of the issues addressed and a schematic presentation of hypothesized model structure; Amos input and output with interpretations; use of the Amos toolbar icons and pull-down menus; and data upon which the model application was based, together with updated references pertinent to the SEM model tested. Thoroughly updated throughout, the new edition features: All new screen shots featuring Amos Version 23. Descriptions and illustrations of Amos' new Tables View format which enables the specification of a structural model in spreadsheet form. Key concepts and/or techniques that introduce each chapter. Alternative approaches to model analyses when enabled by Amos thereby allowing users to determine the method best suited to their data. Provides analysis of the same model based on continuous and categorical data (Ch. 5) thereby enabling readers to observe two ways of specifying and testing the same model as well as compare results. All applications based on the Amos graphical mode interface accompanied by more "how to" coverage of graphical techniques unique to Amos. More explanation of key procedures and analyses that address questions posed by readers All application data files are available at www.routledge.com/9781138797031. The two introductory chapters in Section 1 review the fundamental concepts of SEM methodology and a general overview of the Amos program. Section 2 provides single-group analyses applications including two first-order confirmatory factor analytic (CFA) models, one second-order CFA model, and one full latent variable model. Section 3 presents multiple-group analyses applications with two rooted in the analysis of covariance structures and one in the analysis of mean and covariance structures. Two models that are increasingly popular with SEM practitioners, construct validity and testing change over time using the latent growth curve, are presented in Section 4. The book concludes with a review of the use of bootstrapping to address non-normal data and a review of missing (or incomplete) data in Section 5. An ideal supplement for graduate level courses in psychology, education, business, and social and health sciences that cover the fundamentals of SEM with a focus on Amos, this practical text continues to be a favorite of both researchers and practitioners. A prerequisite of basic statistics through regression analysis is recommended but no exposure to either SEM or Amos is required.

Multi-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH).This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences.