The aim of this book is to introduce the simulation of various physical fields and their applications for biomedical engineering, which will provide a base for researchers in the biomedical field to conduct further investigation. The entire book is classified into three levels. It starts with the first level, which presents the single physical fields including structural analysis, fluid simulation, thermal analysis, and acoustic modeling. Then, the second level consists of various couplings between two physical fields covering structural thermal coupling, porous media, fluid structural interaction (FSI), and acoustic FSI. The third level focuses on multi-coupling that coupling with more than two physical fields in the model. Each part in all levels is organized as the physical feature, finite element implementation, modeling procedure in ANSYS, and the specific applications for biomedical engineering like the FSI study of Abdominal Aortic Aneurysm (AAA), acoustic wave transmission in the ear, and heat generation of the breast tumor. The book should help for the researchers and graduate students conduct numerical simulation of various biomedical coupling problems. It should also provide all readers with a better understanding of various couplings.

The book consists of 29 extended chapters which have been selected and invited from the submissions to the "1st International Conference on Computer Science, Applied Mathematics and Applications" (ICCSAMA 2013) held on 9-10 May, 2013 in Warsaw, Poland. The book is organized into five parts, which are: Advanced Optimization Methods and Their Applications, Queuing Theory and Applications, Computational Methods for Knowledge Engineering, Knowledge Engineering with Cloud and Grid Computing, and Logic Based Methods for Decision Making and Data Mining, respectively. All chapters in the book discuss theoretical and practical issues connected with computational methods and optimization methods for knowledge engineering.

Mathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined. Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.

In this book, origami is treated as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers. Focusing on how classical and modern geometrical problems are solved by means of origami, the book explains the methods not only with mathematical rigor but also by appealing to our scientific intuition, combining mathematical formulas and graphical images to do so. In turn, it discusses the verification of origami using computer software and symbolic computation tools. The binary code for the origami software, called Eos and created by the author, is also provided.

Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, numerical and analytical solutions are included. The necessary steps for building and applying numerical methods in hydraulics comprise the core of the book and this is followed by a report of different example applications of computational hydraulics: river training effects on flood propagation, water quality modelling of lakes and coastal applications. The theory and exercises included in the book promote learning of concepts within academic environments. Sample codes are made available online for purchasers of the book. Computational Hydraulics is intended for under-graduate and graduate students, researchers, members of governmental and non-governmental agencies and professionals involved in management of the water related problems. Author: Ioana Popescu, Hydroinformatics group, UNESCO-IHE Institute for Water Education, Delft , The Netherlands.

This book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students' skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such training The book draws on current research in developing students' mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton's laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.

This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. Rigorous proofs are often replaced with sketches of arguments -- with indications as to why a particular result holds, and also how it is connected with other results -- and illustrated by examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered.

This special issue of Mathematical Thinking and Learning describes models and modeling perspectives toward mathematics problem solving, learning, and teaching. The concern is not only the mature forms of models and modeling in communities of scientists and mathematicians, but also the need to initiate students in these forms of thought. The contributions of this issue suggest a variety of ways that students (children through adults) can be introduced to highly productive forms of modeling practices. Collectively, they illustrate how modeling activities often lead to remarkable mathematical achievements by students formerly judged to be too young or too lacking in ability for such sophisticated and powerful forms of mathematical thinking. The papers also illustrate how modeling activities often create productive interdisciplinary niches for mathematical thinking, learning, and problem solving that involve simulations of similar situations that occur when mathematics is useful beyond school.

The thirty papers published in this book represent the latest developments in Discontinuous Deformation Analysis (DDA). The Numerical Manifold Method (NMM) and other numerical methods and their applications are also covered, as are the theoretical contributions of 3D DDA, modelling and visualization of 3D joint systems, and high-order NMM. Applications of these advances include the stability of underground works, rock slopes and boreholes.

Designing small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model.

Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization of micro- and nanoscale devices. After some introductory material, a review of continuum mechanics, and a study of scaling, the book is organized around phenomena. Each chapter addresses a sequence of real devices that share a common feature. The authors abstract that feature from the devices and present the mathematical tools needed to model it. They construct, analyze, and interpret a series of models of increasing complexity, then at the end of the chapter, they return to one of the devices described, apply the model to it, and interpret the analysis.

In the beginning, the world of microdevices was dominated by experimental work and the development of fabrication techniques. As it matures, optimization and innovative designs are moving to the forefront. Modeling MEMS and NEMS not only provides the practical background and tools needed to design and optimize microdevices but it also helps develop the intuitive understanding that can lead to developing new and better designs and devices.

This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

Modeling hydrologic changes and predicting their impact on watersheds is a dominant concern for hydrologists and other water resource professionals, civil and environmental engineers, and urban and regional planners. As such changes continue, it becomes more essential to have the most up-to-date tools with which to perform the proper analyses and modeling of the complex ecology, morphology, and physical processes that occur within watersheds. An application-oriented text, Modeling Hydrologic Change: Statistical Methods provides a step-by-step presentation of modeling procedures to help you properly analyze and model real-world data.

The text addresses modeling systems where change has affected data that will be used to calibrate and test models of the system. The use of actual hydrologic data will help you learn how to handle the vagaries of real-world hydrologic-change data. All four elements of the modeling process are discussed: conceptualization, formulation, calibration, and verification. Although the book is oriented towards the statistical aspects of modeling, a strong background in statistics is not required. The statistical and modeling methods discussed here will be of value to all disciplines involved in modeling change. With approximately 100 illustrations, Modeling Hydrologic Change will equip you with an understanding with which to perform the proper analyses and modeling of the complex processes that occur across various disciplines.

The 20th century saw tremendous achievements and progress in science and
technology. Undoubtedly, computers and computer-related technologies acted as
one of vital catalysts for accelerating this progress in the latter half of
the century. The contributions of mathematical sciences have been equally
profound, and the synergy between mathematics and computer science has played a
key role in accelerating the progress of both fields as well as science
and engineering.

Mathematical sciences will undoubtedly continue to play this vital role in this
new century. In particular, mathematical modeling and numerical simulation will
continue to be among the essential methodologies for solving massive and
complex problems that arise in science, engineering and manufacturing. Underpinning this all from a sound, theoretical perspective will be numerical algorithms. In recognition of this observation, this volume focuses on the
following specific topics.

(1) Fundamental numerical algorithms
(2) Applications of numerical algorithms
(3) Emerging technologies.

The articles included in this issue by experts on advanced scientific and
engineering computations from numerous countries elucidate state-of-the-art achievements in these three topics from various angles and suggest the future directions. Although we cannot hope to cover all the aspects in scientific and engineering computations, we hope that the articles will interest, inform and inspire members of the science and engineering community.

This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

This edited volume features cutting-edge topics from the leading researchers in the areas of latent variable modeling. Content highlights include coverage of approaches dealing with missing values, semi-parametric estimation, robust analysis, hierarchical data, factor scores, multi-group analysis, and model testing. New methodological topics are illustrated with real applications. The material presented brings together two traditions: psychometrics and structural equation modeling. "Latent Variable and Latent Structure Models'" thought-provoking chapters from the leading researchers in the area will help to stimulate ideas for further research for many years to come.
This volume will be of interest to researchers and practitioners from a wide variety of disciplines, including biology, business, economics, education, medicine, psychology, sociology, and other social and behavioral sciences. A working knowledge of basic multivariate statistics and measurement theory is assumed.

This book presents a selection of Prof. Matteo Campanella's writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule - one of the key principles of the probabilistic interpretation of quantum mechanics - that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category.

There has been an explosive growth of methods in recent years for learning (or estimating dependency) from data, where data refers to known samples that are combinations of inputs and corresponding outputs of a given physical system. The main subject addressed in this thesis is model induction from data for the simulation of hydrodynamic processes in the aquatic environment. Firstly, some currently popular artificial neural network architectures are introduced, and it is then argued that these devices can be regarded as domain knowledge incapsulators by applying the method to the generation of wave equations from hydraulic data and showing how the equations of numerical-hydraulic models can, in their turn, be recaptured using artificial neural networks.
The book also demonstrates how artificial neural networks can be used to generate numerical operators on non-structured grids for the simulation of hydrodynamic processes in two-dimensional flow systems and a methodology has been derived for developing generic hydrodynamic models using artificial neural network. The book also highlights one other model induction technique, namely that of support vector machine, as an emerging new method with a potential to provide more robust models.

This volume gathers together key new contributions on the subject of the relationship, both empirical and theoretical, between economic oscillations, growth and structural change. Employing a sophisticated level of mathematical modelling, the collection contains articles from, amongst others, William Baumol, Katsuhito Iwai and William Brock.

eBook available with sample pages: 0203164830

This title was first published in 2003. India's tax revenues depend on manufacturing while agriculture and services generate employment. WTO's Uruguay and Doha rounds imply large tariff cuts. This affects the competitiveness of the Indian manufacturing sector and has implications for government deficits. Excessive dependence on indirect taxes and subsidies to regulate markets introduces distortions and is incompatible with free market principles. The book analyses welfare implications of fiscal and trade policies for India. To put the results in perspective, developments in trade theory, public finance and Computable General Equilibrium (CGE) modelling are covered. Theoretical results are juxtaposed with empirical findings from these models. Methodology to construct CGE models is also covered. The trade model covers tariff cuts under various assumptions besides incorporating "new trade theory". As tax reforms and tariff cuts are independent, past tax reforms like MODVAT (MODified VAT) and proposed reforms like VAT, elimination/reduction of subsidies are covered using a separate tax model.

This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient 'toolkit' for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) - only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the 'Geometric Algebra', can be applied in many areas of engineering, robotics and computer science, with no changes necessary - it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible. There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout 'Space-Time Algebra', despite its short length, and some of them are effectively still research topics for the future. From the Foreward by Anthony Lasenby

Fuel cells are widely regarded as the future of the power and transportation industries. Intensive research in this area now requires new methods of fuel cell operation modeling and cell design. Typical mathematical models are based on the physical process description of fuel cells and require a detailed knowledge of the microscopic properties that govern both chemical and electrochemical reactions. Advanced Methods of Solid Oxide Fuel Cell Modeling proposes the alternative methodology of generalized artificial neural networks (ANN) solid oxide fuel cell (SOFC) modeling. Advanced Methods of Solid Oxide Fuel Cell Modeling provides a comprehensive description of modern fuel cell theory and a guide to the mathematical modeling of SOFCs, with particular emphasis on the use of ANNs. Up to now, most of the equations involved in SOFC models have required the addition of numerous factors that are difficult to determine. The artificial neural network (ANN) can be applied to simulate an object's behavior without an algorithmic solution, merely by utilizing available experimental data. The ANN methodology discussed in Advanced Methods of Solid Oxide Fuel Cell Modeling can be used by both researchers and professionals to optimize SOFC design. Readers will have access to detailed material on universal fuel cell modeling and design process optimization, and will also be able to discover comprehensive information on fuel cells and artificial intelligence theory.

Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension.

Mathematical Analysis for Modeling is intended for those who want to understand the substance of mathematics, rather than just having familiarity with its techniques. It provides a thorough understanding of how mathematics is developed for and applies to solving scientific and engineering problems. The authors stress the construction of mathematical descriptions of scientific and engineering situations, rather than rote memorizations of proofs and formulas. Emphasis is placed on algorithms as solutions to problems and on insight rather than formal derivations.

This contributed volume brings together research papers presented at the 4th International Conference on Dynamics in Logistics, held in Bremen, Germany in February 2014. The conference focused on the identification, analysis and description of the dynamics of logistics processes and networks. Topics covered range from the modeling and planning of processes, to innovative methods like autonomous control and knowledge management, to the latest technologies provided by radio frequency identification, mobile communication, and networking. The growing dynamic poses wholly new challenges: logistics processes and networks must be(come) able to rapidly and flexibly adapt to constantly changing conditions. The book primarily addresses the needs of researchers and practitioners from the field of logistics, but will also be beneficial for graduate students.

The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics. This book will be an invaluable reference source for those whose work is in the area of discrete dynamical systems, difference equations, and control theory or applied areas that use discrete time models.