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Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers
The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.
In the last 40 years geophysicists have found that it is possible to construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. To make these images and extract this information requires the application of an advanced understanding of the mathematical physics of wave propagation. The oil and gas industry labels a major collection of the necessary seismic data processing methods by the name seismic "migration". This text ist the first to treat many kinds of migration in a unified mahtematical way. The audience is mathematically oriented geophysicists or applied mathematicians working in the field of "inverse scattering imaging". The text can serve as a bridge between the applied math and geophysics community by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophistiated geophysicist.
This book explains the nature and computation of mathematical wavelets, which provide a framework and methods for the analysis and the synthesis of signals, images, and other arrays of data. The material presented here addresses the au dience of engineers, financiers, scientists, and students looking for explanations of wavelets at the undergraduate level. It requires only a working knowledge or memories of a first course in linear algebra and calculus. The first part of the book answers the following two questions: What are wavelets? Wavelets extend Fourier analysis. How are wavelets computed? Fast transforms compute them. To show the practical significance of wavelets, the book also provides transitions into several applications: analysis (detection of crashes, edges, or other events), compression (reduction of storage), smoothing (attenuation of noise), and syn thesis (reconstruction after compression or other modification). Such applications include one-dimensional signals (sounds or other time-series), two-dimensional arrays (pictures or maps), and three-dimensional data (spatial diffusion). The ap plications demonstrated here do not constitute recipes for real implementations, but aim only at clarifying and strengthening the understanding of the mathematics of wavelets."
The book presents new clustering schemes, dynamical systems and pattern recognition algorithms in geophysical, geodynamical and natural hazard applications. The original mathematical technique is based on both classical and fuzzy sets models. Geophysical and natural hazard applications are mostly original. However, the artificial intelligence technique described in the book can be applied far beyond the limits of Earth science applications. The book is intended for research scientists, tutors, graduate students, scientists in geophysics and engineers
Designing satellite structures poses an ongoing challenge as the interaction between analysis, experimental testing, and manufacturing phases is underdeveloped. "Finite Element Analysis for Satellite Structures: Applications to Their Design, Manufacture & Testing "explains the theoretical and practical knowledge needed to perform design of satellite structures. By layering detailed practical discussions with fully developed examples, "Finite Element Analysis for Satellite Structures: Applications to Their Design, Manufacture & Testing" provides the missing link between theory and implementation. Computational examples cover all the major aspects of advanced analysis; including modal analysis, harmonic analysis, mechanical and thermal fatigue analysis using finite element method. Test cases are included to support explanations an a range of different manufacturing simulation techniques are described from riveting to shot peening to material cutting. Mechanical design of a satellites structures are covered in three steps: analysis step under design loads, experimental testing to verify design, and manufacturing. Stress engineers, lecturers, researchers and students will find "Finite Element Analysis for Satellite Structures: Applications to Their Design, Manufacture & Testing "a key guide on with practical instruction on applying manufacturing simulations to improve their design and reduce project cost, how to prepare static and dynamic test specifications, and how to use finite element method to investigate in more details any component that may fail during testing. "
The increasing power of computer technologies, the evolution of software en- neering and the advent of the intelligent transport systems has prompted traf c simulation to become one of the most used approaches for traf c analysis in s- port of the design and evaluation of traf c systems. The ability of traf c simulation to emulate the time variability of traf c phenomena makes it a unique tool for capturing the complexity of traf c systems. In recent years, traf c simulation - and namely microscopic traf c simulation - has moved from the academic to the professional world. A wide variety of traf- c simulation software is currently available on the market and it is utilized by thousands of users, consultants, researchers and public agencies. Microscopic traf c simulation based on the emulation of traf c ows from the dynamics of individual vehicles is becoming one the most attractive approaches. However, traf c simulation still lacks a uni ed treatment. Dozens of papers on theory and applications are published in scienti c journals every year. A search of simulation-related papers and workshops through the proceedings of the last annual TRB meetings would support this assertion, as would a review of the minutes from speci cally dedicated meetings such as the International Symposiums on Traf c Simulation (Yokohama, 2002; Lausanne, 2006; Brisbane, 2008) or the International Workshops on Traf c Modeling and Simulation (Tucson, 2001; Barcelona, 2003; Sedona, 2005; Graz 2008). Yet, the only comprehensive treatment of the subject to be found so far is in the user's manuals of various software products.
This volume contains the proceedings of the Second International Workshop on Optimal Design and Control, held in Arlington, Virginia, 30 September-3 Octo ber, 1997. The First Workshop was held in Blacksburg, Virginia in 1994. The proceedings of that meeting also appeared in the Birkhauser series on Progress in Systems and Control Theory and may be obtained through Birkhauser. These workshops were sponsored by the Air Force Office of Scientific Re search through the Center for Optimal Design and Control (CODAC) at Vrrginia Tech. The meetings provided a forum for the exchange of new ideas and were designed to bring together diverse viewpoints and to highlight new applications. The primary goal of the workshops was to assess the current status of research and to analyze future directions in optimization based design and control. The present volume contains the technical papers presented at the Second Workshop. More than 65 participants from 6 countries attended the meeting and contributed to its success. It has long been recognized that many modern optimal design problems are best viewed as variational and optimal control problems. Indeed, the famous problem of determining the body of revolution that produces a minimum drag nose shape in hypersonic How was first proposed by Newton in 1686. Optimal control approaches to design can provide theoretical and computational insight into these problems. This volume contains a number of papers which deal with computational aspects of optimal control."
The current volume "New Advances in Intelligent Signal Processing" contains extended works based on a careful selection of papers presented originally at the jubilee sixth IEEE International Symposium on Intelligent Signal Processing (WISP'2009), held in Budapest Hungary, August 26-28, 2009 - celebrating the 10 years anniversary of the WISP event series. The present book does not intent to be an overall survey on the fields of interest of the area, but tries to find topics which represent new, hot, and challenging problems. The book begins with papers investigating selected problems of Modeling, Identification, and Clustering such as fuzzy random variables, evolutionary multi-objective neural network models, a structural learning model of neural networks within a Boltzmann machine, a robust DNA-based clustering techniques, and the advances of combining multi-criteria analysis of signals and pattern recognition using machine learning principles. In the second part of the book Image Processing is treated. The carefully edited chapters deal with fuzzy relation based image enhancement, image contrast control technique based on the application of ukasiewicz algebra operators, low complexity situational models of image quality improvement, flexible representation of map images to quantum computers, and object recognition in images. The last chapter presents an image processing application for elderly care, performing real-time 3D tracking based on a new evaluative multi-modal algorithm."
A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.
Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.
The present book fmds its roots in the International Conference on Methods and Applications of Multiple Criteria Decision Making held in Mons in May 1997. A small number of contributions to that conference were selected via a refereeing procedure and retained authors were requested to include in their final version their more recent results. This explains why some papers differ significantly from the original presentation. The introductory paper of Raynaud addresses the long range forecasts in Multiple Criteria Decision Making on the basis of a Delphi process that was run before and during the congress. In a second part, the French author explains how he and some of his partners could find the proof of an important conjecture : the iteration of a strongly monotonic choice function is not a strongly monotonic ranking function. The second part of the book covers methodological aspects of decision theory. The contribution of Bouyssou and Pirlot concerns the reformulation of classical conjoint measurement models that induce a complete and transitive preference binary relation on the set of alternatives which seem to be unrealistic when decision makers are asked to compare objects evaluated on several attributes. The authors propose to consider non transitive, non complete and non additive decomposable conjoint models. They define properties that characterize such models.
Nevanlinna-Pick interpolation for time-varying input-output maps: The discrete case.- 0. Introduction.- 1. Preliminaries.- 2. J-Unitary operators on ?2.- 3. Time-varying Nevanlinna-Pick interpolation.- 4. Solution of the time-varying tangential Nevanlinna-Pick interpolation problem.- 5. An illustrative example.- References.- Nevanlinna-Pick interpolation for time-varying input-output maps: The continuous time case.- 0. Introduction.- 1. Generalized point evaluation.- 2. Bounded input-output maps.- 3. Residue calculus and diagonal expansion.- 4. J-unitary and J-inner operators.- 5. Time-varying Nevanlinna-Pick interpolation.- 6. An example.- References.- Dichotomy of systems and invertibility of linear ordinary differential operators.- 1. Introduction.- 2. Preliminaries.- 3. Invertibility of differential operators on the real line.- 4. Relations between operators on the full line and half line.- 5. Fredholm properties of differential operators on a half line.- 6. Fredholm properties of differential operators on a full line.- 7. Exponentially dichotomous operators.- 8. References.- Inertia theorems for block weighted shifts and applications.- 1. Introduction.- 2. One sided block weighted shifts.- 3. Dichotomies for left systems and two sided systems.- 4. Two sided block weighted shifts.- 5. Asymptotic inertia.- 6. References.- Interpolation for upper triangular operators.- 1. Introduction.- 2. Preliminaries.- 3. Colligations & characteristic functions.- 4. Towards interpolation.- 5. Explicit formulas for ?.- 6. Admissibility and more on general interpolation.- 7. Nevanlinna-Pick Interpolation.- 8. Caratheodory-Fejer interpolation.- 9. Mixed interpolation problems.- 10. Examples.- 11. Block Toeplitz & some implications.- 12. Varying coordinate spaces.- 13. References.- Minimality and realization of discrete time-varying systems.- 1. Preliminaries.- 2. Observability and reachability.- 3. Minimality for time-varying systems.- 4. Proofs of the minimality theorems.- 5. Realizations of infinite lower triangular matrices.- 6. The class of systems with constant state space dimension.- 7. Minimality and realization for periodical systems.- References.
This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods. Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes or classification of system states. The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.
Covering CUSUMs from an application-oriented viewpoint, while also providing the essential theoretical underpinning, this is an accessible guide for anyone with a basic statistical training. The text is aimed at quality practitioners, teachers and students of quality methodologies, and people interested in analysis of time-ordered data. Further support is available from a Web site containing CUSUM software and data sets.
This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc .."
The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X. Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y.
Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model is crucial and difficult in engineering. As a hands-on approach to learn how to pose a differential
mathematical model the authors have selected 9 examples with
important practical application and treat them as following: Each step of the development of a differential model is enriched by respective Mathcad 11 commands, todays necessary linkage of engineering significance and high computing complexity. To support readers of the book with respect to changes that might occur in future versions of Mathcad (Mathcad 12 for example), updates of examples, codes etc. can be downloaded from the following web page www.thermal.ru. Readers can work with Mathcad-sheets of the book without any Mathcad by help Mathcad Application Server Technology.
This book contains the proceedings of the IUTAM Symposium on Multiscale Modeling and Uncertainty Quantification of Materials and Structures that was held at Santorini, Greece, September 9 11, 2013. It consists of 20 chapters which are divided in five thematic topics: Damage and fracture, homogenization, inverse problems identification, multiscale stochastic mechanics and stochastic dynamics. Over the last few years, the intense research activity at micro scale and nano scale reflected the need to account for disparate levels of uncertainty from various sources and across scales. As even over-refined deterministic approaches are not able to account for this issue, an efficient blending of stochastic and multiscale methodologies is required to provide a rational framework for the analysis and design of materials and structures. The purpose of this IUTAM Symposium was to promote achievements in uncertainty quantification combined with multiscale modeling and to encourage research and development in this growing field with the aim of improving the safety and reliability of engineered materials and structures. Special emphasis was placed on multiscale material modeling and simulation as well as on the multiscale analysis and uncertainty quantification of fracture mechanics of heterogeneous media. The homogenization of two-phase random media was also thoroughly examined in several presentations. Various topics of multiscale stochastic mechanics, such as identification of material models, scale coupling, modeling of random microstructures, analysis of CNT-reinforced composites and stochastic finite elements, have been analyzed and discussed. A large number of papers were finally devoted to innovative methods in stochastic dynamics."
These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland. With 172 participants from over 24 countries, this conference continued a long-standing tradition of internationally oriented meetings on Domain Decomposition Methods. The book features a well-balanced mix of established and new topics, such as the manifold theory of Schwarz Methods, Isogeometric Analysis, Discontinuous Galerkin Methods, exploitation of modern HPC architectures and industrial applications. As the conference program reflects, the growing capabilities in terms of theory and available hardware allow increasingly complex non-linear and multi-physics simulations, confirming the tremendous potential and flexibility of the domain decomposition concept.
Risk models are models of uncertainty, engineered for some purposes. They are "educated guesses and hypotheses" assessed and valued in terms of well-defined future states and their consequences. They are engineered to predict, to manage countable and accountable futures and to provide a frame of reference within which we may believe that "uncertainty is tamed". Quantitative-statistical tools are used to reconcile our information, experience and other knowledge with hypotheses that both serve as the foundation of risk models and also value and price risk. Risk models are therefore common to most professions, each with its own methods and techniques based on their needs, experience and a wisdom accrued over long periods of time. This book provides a broad and interdisciplinary foundation to engineering risks and to their financial valuation and pricing. Risk models applied in industry and business, heath care, safety, the environment and regulation are used to highlight their variety while financial valuation techniques are used to assess their financial consequences. This book is technically accessible to all readers and students with a basic background in probability and statistics (with 3 chapters devoted to introduce their elements). Principles of risk measurement, valuation and financial pricing as well as the economics of uncertainty are outlined in 5 chapters with numerous examples and applications. New results, extending classical models such as the CCAPM are presented providing insights to assess the risks and their price in an interconnected, dependent and strategic economic environment. In an environment departing from the fundamental assumptions we make regarding financial markets, the book provides a strategic/game-like approach to assess the risk and the opportunities that such an environment implies. To control these risks, a strategic-control approach is developed that recognizes that many risks resulting by "what we do" as well as "what others do". In particular we address the strategic and statistical control of compliance in large financial institutions confronted increasingly with a complex and far more extensive regulation.
This book presents a modular and expandable technique in the rapidly emerging research area of automatic configuration and selection of the best algorithm for the instance at hand. The author presents the basic model behind ISAC and then details a number of modifications and practical applications. In particular, he addresses automated feature generation, offline algorithm configuration for portfolio generation, algorithm selection, adaptive solvers, online tuning, and parallelization. The author's related thesis was honorably mentioned (runner-up) for the ACP Dissertation Award in 2014, and this book includes some expanded sections and notes on recent developments. Additionally, the techniques described in this book have been successfully applied to a number of solvers competing in the SAT and MaxSAT International Competitions, winning a total of 18 gold medals between 2011 and 2014. The book will be of interest to researchers and practitioners in artificial intelligence, in particular in the area of machine learning and constraint programming.
Geometrical Dimensioning and Tolerancing for Design, Manufacturing and Inspection: A Handbook for Geometrical Product Specification Using ISO and ASME Standards, Third Edition presents the state-of-the art in geometrical dimensioning and tolerancing. The book describes the international standardization in this field while also indicating how it differs from the American Standard ASME Y14.5M. The general principles of geometric dimensioning and tolerancing are described, helping users define precision-related specifications unambiguously and consistently with the constraints of the manufacturing and inspection processes. Principles for the inspection of geometrical deviations are given, along with a basis for tolerancing suitable for inspection. Since publication of the second edition of this book in 2006 more than ten ISO GPS standards have been revised, involving the introduction of new symbols and concepts, and in many cases default interpretation of the tolerance indicators have changed, in addition two new versions of American standard ASME Y14.5 (2009 and 2018) have appeared. This book is an ideal introduction to geometrical dimensioning and tolerancing for students, and an essential reference for researchers and practitioners in the fields of design, manufacturing and inspection.
This book features original research papers presented at the International Conference on Computational and Applied Mathematics, held at the Indian Institute of Technology Kharagpur, India during November 23-25, 2018. This book covers various topics under applied mathematics, ranging from modeling of fluid flow, numerical techniques to physical problems, electrokinetic transport phenomenon, graph theory and optimization, stochastic modelling and machine learning. It introduces the mathematical modeling of complicated scientific problems, discusses micro- and nanoscale transport phenomena, recent development in sophisticated numerical algorithms with applications, and gives an in-depth analysis of complicated real-world problems. With contributions from internationally acclaimed academic researchers and experienced practitioners and covering interdisciplinary applications, this book is a valuable resource for researchers and students in fields of mathematics, statistics, engineering, and health care.
The aim of this book is to present a rigorous phenomenological and mathematical formulation of sedimentation processes and to show how this theory can be applied to the design and control of continuous thickeners. The book is directed to stu dents and researchers in applied mathematics and engineering sciences, especially in metallurgical, chemical, mechanical and civil engineering, and to practicing en gineers in the process industries. Such a vast and diverse audience should read this book differently. For this reason we have organized the chapters in such a way that the book can be read in two ways. Engineers and engineering students will find a rigorous formulation of the mathematical model of sedimentation and the exact and approximate solutions for the most important problems encountered in the laboratory and in industry in Chapters 1 to 3, 7 and 8, and 10 to 12, which form a self-contained subject. They can skip Chapters 4 to 6 and 9, which are most important to applied mathematicians, without losing the main features of sedimentation processes. On the other hand, applied mathematicians will find special interest in Chapters 4 to 6 and 9 which show some known but many recent results in the field of conservation laws of quasilinear hyperbolic and degenerate parabolic equations of great interest today. These two approaches to the theory keep their own styles: the mathematical approach with theorems and proofs, and the phenomenological approach with its deductive technique."
In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results. |
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