Innovative Computing Methods and Their Applications to Engineering Problems

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book, first published in 2005, lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. Th

This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.

What is the relationship between fear, danger, and the law? Cass Sunstein attacks the increasingly influential Precautionary Principle - the idea that regulators should take steps to protect against potential harms, even if causal chains are uncertain and even if we do not know that harms are likely to come to fruition. Focusing on such problems as global warming, terrorism, DDT, and genetic engineering, Professor Sunstein argues that the Precautionary Principle is incoherent. Risks exist on all sides of social situations, and precautionary steps create dangers of their own. Diverse cultures focus on very different risks, often because social influences and peer pressures accentuate some fears and reduce others. Instead of adopting the Precautionary Principle, Professor Sunstein argues for three steps: a narrow Anti-Catastrophe Principle, designed for the most serious risks; close attention to costs and benefits; and an approach called 'libertarian paternalism', designed to respect fre

Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of

The editors and contributors describe the most up-to-date methods in predicting turbulent heat transfer processes in fundamental and idealized flows and in engineering applications. After an introduct

In 1989, Michael Rabin proposed a fundamentally new approach to the problems of fault-tolerant routing and memory management in parallel computation, based on the idea of information dispersal. Yuh-Dauh Lyuu developed this idea in a number of new and exciting ways in his PhD thesis. Further work has led to extensions of these methods to other applications such as shared memory emulations. This volume presents an extended and updated printing of Lyuu's thesis. It gives a detailed treatment of the information dispersal approach to the problems of fault-tolerance and distributed representations of information which have resisted rigorous analysis by previous methods.

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and

Modern technology depends on materials with precisely controlled properties. Ion beams are a favoured method to achieve controlled modification of surface and near-surface regions. In every integrated circuit production line, for example, there are ion implantation systems. In addition to integrated circuit technology, ion beams are used to modify the mechanical, tribological and chemical properties of metal, intermetallic and ceramic materials without altering their bulk properties. Ion–solid interactions are the foundation that underlies the broad application of ion beams to the modification of materials. This text is designed to cover the fundamentals and applications of ion–solid interactions and is aimed at graduate students and researchers interested in electronic devices, surface engineering, reactor and nuclear engineering and material science issues associated with metastable phase synthesis.

Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they e

This book was first published in 2004. In many applications, images, such as ultrasonic or X-ray signals, are recorded and then analyzed with digital or optical processors in order to extract information. Such processing requires the development of algorithms of great precision and sophistication. This book presents a unified treatment of the mathematical methods that underpin the various algorithms used in remote image formation. The author begins with a review of transform and filter theory. He then discusses two- and three-dimensional Fourier transform theory, the ambiguity function, image construction and reconstruction, tomography, baseband surveillance systems, and passive systems (where the signal source might be an earthquake or a galaxy). Information-theoretic methods in image formation are also covered, as are phase errors and phase noise. Throughout the book, practical applications illustrate theoretical concepts, and there are many homework problems. The book is aimed at gr

The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

When stresses and hassles challenge our abilities to cope, we frequently turn to family, friends, and partners for help. Yet social support from close relational partners does not uniformly benefit recipients or their relationships. By probing the communication processes that link enactments of social support to participants' reactions, this book provides new explanations for when and how receiving social support will be evaluated as helpful and relationally satisfying. The author's research addresses a variety of types of relationships and stresses, including young adult friends and romantic partners coping with the stresses of university life; adult friends, family and spouses responding to everyday hassles' and married couples coping with chronic health conditions. This innovative program of research combines qualitative and quantitative methods to develop a distinctive communication-based framework for understanding why the content, form, style, and sequence of talk matter for our

This is a comprehensive account of RR Lyrae stars, and traces the story from their initial discovery a century ago, through to their present status. This book reviews our current understanding of RR Lyrae stars. It is a unique explanation of the multiple applications of these variable stars for a range of astrophysical problems. Horace A. Smith describes the use of RR Lyrae stars as probes of old stellar populations, both in the Milky Way and other galaxies, and as an outstanding testing ground for stellar evolution and pulsation theories. He stresses the significance of variable stars for our ultimate understanding of the history and scale of the Milky Way and nearer extragalactic systems. For advanced students and researchers of astronomy, this is a definitive account of the modern theories surrounding RR Lyrae stars.

This book sets out the basic principles of composite construction with reference to beams, slabs, columns and frames, and their applications to building structures. It deals with the problems likely t

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field* A cent

In common with republicanism or socialism in continental Europe, Liberalism in nineteenth-century Britain was a mass movement. By focussing on the period between the 1860s and the 1880s, this book sets out to explain why and how that happened, and to examine the people who supported it, their beliefs, and the way in which the latter related to one another and to reality. Popular suport for the Liberal party was not irrational in either its objectives or its motivations: on the contrary, its dissemination was due to the fact that the programme of reforms proposed by the party leaders offered convincing solutions to some of the problems perceived as being the most urgent at the time. This is a revealing, innovative synthesis of the history of popular support for the Liberal party, which emphasises the extent to which Liberalism stood in the common heritage of European and American democracy.

Information retrieval, IR, the science of extracting information from any potential source, can be viewed in a number of ways: logical, probabilistic and vector space models are some of the most important. In this book, the author, one of the leading researchers in the area, shows how these views can be reforged in the same framework used to formulate the general principles of quantum mechanics. All the usual quantum-mechanical notions have their IR-theoretic analogues, and the standard results can be applied to address problems in IR, such as pseudo-relevance feedback, relevance feedback and ostensive retrieval. The relation with quantum computing is also examined. To keep the book self-contained appendices with background material on physics and mathematics are included. Each chapter ends with bibliographic remarks that point to further reading. This is an important, ground-breaking book, with much new material, for all those working in IR, AI and natural language processing.

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents.

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields.

This tract presents an exposition of methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces. The first chapter contains the theoretical background to the subject, largely in a general Hilbert space setting, and theorems in which the structure of Hilbert space is revealed by properties of its bases are dealt with. Later parts of the book deal with methods: for example, the Vitali criterion, together with its generalisations and applications, is discussed in some detail, and there is an introduction to the theory of stability of bases. The last chapter deals with complete sets as eigenfunctions of differential and a table of a wide variety of bases and complete sets of special functions. Dr Higgins' account will be useful to graduate students of mathematics and professional mathematicians, especially Banach spaces. The emphasis on methods of testing and their applications will also interest scientists and engineers engaged in field

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

* This book deals with the fundamentals of genetic algorithms and their applications in a variety of different areas of engineering and science * Most significant update to the second edition is the M

Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.

Part two of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of integral analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.

Two volume set of the authors' comprehensive and innovative work on multidimensional real analysis. These books are based on extensive teaching experience at Utrecht University and give a thorough account of analysis in multidimensional Euclidean space. They are an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects these books present an original treatment of the subject and they contain many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make these books ideal as either the text for a course, a source of problems for a seminar or for self study.

The statistical bootstrap is one of the methods that can be used to calculate estimates of a certain number of unknown parameters of a random process or a signal observed in noise, based on a random sample. Such situations are common in signal processing and the bootstrap is especially useful when only a small sample is available or an analytical analysis is too cumbersome or even impossible. This book covers the foundations of the bootstrap, its properties, its strengths and its limitations. The authors focus on bootstrap signal detection in Gaussian and non-Gaussian interference as well as bootstrap model selection. The theory developed in the book is supported by a number of useful practical examples written in MATLAB. The book is aimed at graduate students and engineers, and includes applications to real-world problems in areas such as radar and sonar, biomedical engineering and automotive engineering.

The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

The stereographic projection is an essential tool in the fields of structural geology and geotechnics, which allows three-dimensional orientation data to be represented and manipulated. This book has been designed to make the subject as accessible as possible. It gives a straightforward and simple introduction to the subject and, by means of examples, illustrations and exercises, encourages the student to visualise the problems in three dimensions. Students of all levels will be able to work through the book and come away with a clear understanding of how to apply these vital techniques. This revised edition contains additional material on geotechnical applications, improved illustrations and links to useful web resources and software programs. It will provide students of geology, rock mechanics, geotechnical and civil engineering with an indispensable guide to the analysis and interpretation of field orientation data.

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

This book presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. The relationship between domain decomposition and multigrid methods is carefully explained at an elementary level, and discussions of the implementation of domain decomposition methods on massively parallel super computers are also included. All algorithms are fully described and explained, and a mathematical framework for the analysis and complete understanding of the methods is also carefully developed. In addition, numerous numerical examples are included to demonstrate the behaviour of this important class of numerical methods. This book is ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

As ravagers of crops and carriers of diseases affecting plants, humans and animals, insects present a challenge to a growing human population. In Pest and Vector Control, first published in 2004, Professors van Emden and Service describe the available options for meeting this challenge, discussing their relative advantages, disadvantages and future potential. Methods such as chemical and biological control, host tolerance and resistance are discussed integrating (often for the first time) information and experience from the agricultural and medical/veterinary fields. Chemical control is seen as a major component of insect control, both now and in the future, but this is balanced with an extensive account of associated problems, especially the development of pesticide-tolerant populations.

As ravagers of crops and carriers of diseases affecting plants, humans and animals, insects present a challenge to a growing human population. In Pest and Vector Control, first published in 2004, Professors van Emden and Service describe the available options for meeting this challenge, discussing their relative advantages, disadvantages and future potential. Methods such as chemical and biological control, host tolerance and resistance are discussed integrating (often for the first time) information and experience from the agricultural and medical/veterinary fields. Chemical control is seen as a major component of insect control, both now and in the future, but this is balanced with an extensive account of associated problems, especially the development of pesticide-tolerant populations.

Over the past fifty years plant breeders have achieved impressive improvements in yield, quality and disease resistance. These gains suggest that many more modifications might be introduced if appropriate genes can be identified. Current DNA techniques allow the construction of transgenic plants and this important new book reviews the current state of knowledge. A team of leading researchers provide in-depth reviews at the cutting edge of technology for laboratory techniques for the transformation of important soil microorganisms and recalcitrant plants of economic value. The book is divided into three sections: soil microorganisms; cereal crops; and industrially important plants. The most effective methods used to date are compared, and their merits and limitations discussed. Some chapters emphasise case studies and applications. In cases where obstacles remain to be overcome, an overview of progress to date is given. The book will serve as a general guide and reference tool for those

This book presents an overview of the computational framework in which calculations of relativistic hydrodynamics have been developed. It summarizes the jargon and methods used in the field, and provides illustrative applications to real physical systems. The authors explain how to break down the complexities of Einstein's equations and fluid dynamics, stressing the viability of the Euler–Lagrange approach to astrophysical problems. The book contains techniques and algorithms enabling one to build computer simulations of relativistic fluid problems for various astrophysical systems in one, two and three dimensions. It also shows the reader how to test relativistic hydrodynamics codes. Suitable for graduate courses on astrophysical hydrodynamics and relativistic astrophysics, this book also provides a valuable reference for researchers already working in the field.

The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more tradi

The authors illustrate the basic physics and materials science of conjugated polymers and their interfaces, particularly, but not exclusively, as they are applied to polymer-based light emitting diodes. The approach is to describe the basic physical and associated chemical principles that apply to these materials, which in many instances are different from those that apply to their inorganic counterparts. The main aim of the authors is to highlight specific issues and properties of polymer surfaces and interfaces that are relevant in the context of the emerging field of polymer-based electronics in general, and polymer-based light emitting diodes in particular. Both theoretical and experimental methods used in the study of these systems are discussed. This book will be of interest to graduate students and research workers in departments of physics, chemistry, electrical engineering and materials sciences studying polymer surfaces and interfaces and their application in polymer-based el

This book presents an approach to introductory graduate courses on atomic structure. The author's approach utilizes conceptually powerful semiclassical modeling methods, and demonstrates the degree to which the Maslov-indexed EBK quantization elucidates the quantum mechanical formulation of level energies and lifetimes. It merges this with an update and extension of semiempirical data systematizations developed by Bengt Edlén to describe complex atoms, and adapts them to include the specification of lifetimes. The text emphasizes the historical basis of the nomenclature and methodologies of spectroscopy. However, interaction mechanisms are presented deductively, based on quantum mechanical and field theoretical models, rather than tracing their indirect paths of discovery. Many worked examples provide applications to areas such as astrophysics, hyperfine structure, and coherent anisotropic excitation. The book presents a firm foundation for specialists in atomic physics, as well as a c