This book is a guide to the use of Monte Carlo techniques in radiation transport. This topic is of great interest for medical physicists. Praised as a "gold standard" for accurate radiotherapy dose calculations, Monte Carlo has stimulated a high level of research activity that has produced thousands of papers within the past few years. The book is designed primarily to address the needs of an academically inclined medical physicist who wishes to learn the technique, as well as experienced users of standard Monte Carlo codes who wish to gain insight into the underlying mathematics of Monte Carlo algorithms. The book focuses on the fundamentals-giving full attention to and explaining the very basic concepts. It also includes advanced topics and covers recent advances such as transport of charged particles in magnetic fields and the grid-based solvers of the Boltzmann equation.

This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule's internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.

This accessible text presents a detailed introduction to the use of a wide range of software tools and modeling environments for use in the biosciences, as well as the fundamental mathematical background. The practical constraints presented by each modeling technique are described in detail, enabling the researcher to determine which software package would be most useful for a particular problem. Features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; discusses agent-based models, stochastic modeling techniques, differential equations, spatial simulations, and Gillespie's stochastic simulation algorithm; provides exercises; describes such useful tools as the Maxima algebra system, the PRISM model checker, and the modeling environments Repast Simphony and Smoldyn; contains appendices on rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; offers supplementary material at an associated website.

The purpose of this book is to examine the geospatial and temporal linkage between offshore supply vessels and oil and gas activity in the Outer Continental Shelf Gulf of Mexico, and to model OSV activity expected to result from future lease sales. Oil and gas operations occur throughout the world wherever commercial accumulations exist, but no quantitative assessment has ever been performed on the marine vessels that support offshore activity. The OCS Gulf of Mexico is the largest and most prolific offshore oil and gas basin in the world, and a large number of marine vessels are engaged in operations in the region, but tracking their activity is difficult and requires specialized data sources and the development of empirical models. The challenge of modeling arises from the complexity and size of the system, and the particular limitations governing stochastic difficult-to-observe networks. This book bridges the gap with the latest technological perspective and provides insight and computational methods to inform and better understand the offshore sector. Offshore Service Industry and Logistics Modeling in the Gulf of Mexico is presented in three parts.  In Part 1, background information on the life cycle stages of offshore development and activity is reviewed, along with a description of the service vessels and port infrastructure in the region.  In Part 2, OSV activity in the Gulf of Mexico is baselined using PortVision data to establish spatial and temporal characteristics of vessel activity. In Part 3, the analytic framework used to quantify the connection between OSVs, ports, and offshore activity is described, and activity expected to arise from the 2012-2017 OCS lease program is forecast. Providing an invaluable resource for academics and researchers, this book is also intended for government regulators, energy and environmental analysts, industry professionals, and others interested in this often-overlooked sector.

This thesis investigates the sound generated by solid bodies in steady subsonic flows with unsteady perturbations, as is typically used when determining the noise generated by turbulent interactions. The focus is predominantly on modelling the sound generated by blades within an aircraft engine, and the solutions are presented as asymptotic approximations. Key analytical techniques, such as the Wiener-Hopf method, and the matched asymptotic expansion method are clearly detailed. The results allow for the effect of variations in the steady flow or blade shape on the noise generated to be analysed much faster than when solving the problem numerically or considering it experimentally.

This volume presents the work of leading scientists from Russia, Georgia, Estonia, Lithuania, Israel and the USA, revealing major insights long unknown to the scientific community. Without any doubt their work will provide a springboard for further research in anticipation. Until recently, Robert Rosen (Anticipatory Systems) and Mihai Nadin (MIND - Anticipation and Chaos) were deemed forerunners in this still new knowledge domain. The distinguished neurobiologist, Steven Rose, pointed to the fact that Soviet neuropsychological theories have not on the whole been well received by Western science. These earlier insights as presented in this volume make an important contribution to the foundation of the science of anticipation. It is shown that the daring hypotheses and rich experimental evidence produced by Bernstein, Beritashvili, Ukhtomsky, Anokhin and Uznadze, among others-extend foundational work to aspects of neuroscience, physiology, motorics, education.

This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the "long-tail" power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier's, Fick's and Darcy's laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.

The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who like to enter this field.

The book shows how eastern and western perspectives and conceptions can be used to addresses recent topics laying at the crossroad between philosophy and cognitive science. It reports on new points of view and conceptions discussed during the International Conference on Philosophy and Cognitive Science (PCS2013), held at the Sun Yat-sen University, in Guangzhou, China, and the 2013 Workshop on Abductive Visual Cognition, which took place at KAIST, in Deajeon, South Korea. The book emphasizes an ever-growing cultural exchange between academics and intellectuals coming from different fields. It juxtaposes research works investigating new facets on key issues between philosophy and cognitive science, such as the role of models and causal representations in science; the status of theoretical concepts and quantum principles; abductive cognition, vision, and visualization in science from an eco-cognitive perspective. Further topics are: ignorance immunization in reasoning; moral cognition, violence, and epistemology; and models and biomorphism. The book, which presents a unique and timely account of the current state-of-the art on various aspects in philosophy and cognitive science, is expected to inspire philosophers, cognitive scientists and social scientists, and to generate fruitful exchanges and collaboration among them.

This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities. New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study.   Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8.  As in previous editions, end-of-chapter exercises appear for all chapters. From the reviews of the Third Edition: “… this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn.� (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)

The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject. This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB (R) supplement that gives basic codes and commands for solving differential equations. MATLAB (R) is not required; students are encouraged to utilize available software to plot many of their solutions. Solutions to even-numbered problems are available on springer.com.

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.

As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine “Kyiv Polytechnic Institute�. The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

This primer develops Conformal Field Theory (CFT) from scratch, whereby CFT is viewed as any conformally-invariant theory that describes a fixed point of a renormalization group flow in quantum field theory. The book is divided into four lectures: Lecture 1 addresses the physical foundations of conformal invariance, while Lecture 2 examines the constraints imposed by conformal symmetry on the correlation functions of local operators, presented using the so-called projective null cone - a procedure also known as the embedding formalism. In turn, Lecture 3 focuses on the radial quantization and the operator product expansion, while Lecture 4 offers a very brief introduction to the conformal bootstrap. Derived from course-based notes, these lectures are intended as a first point of entry to this topic for Master and PhD students alike.

This book focuses on recent research in modern optimization and its implications in control and data analysis. This book is a collection of papers from the conference "Optimization and Its Applications in Control and Data Science" dedicated to Professor Boris T. Polyak, which was held in Moscow, Russia on May 13-15, 2015. This book reflects developments in theory and applications rooted by Professor Polyak's fundamental contributions to constrained and unconstrained optimization, differentiable and nonsmooth functions, control theory and approximation. Each paper focuses on techniques for solving complex optimization problems in different application areas and recent developments in optimization theory and methods. Open problems in optimization, game theory and control theory are included in this collection which will interest engineers and researchers working with efficient algorithms and software for solving optimization problems in market and data analysis. Theoreticians in operations research, applied mathematics, algorithm design, artificial intelligence, machine learning, and software engineering will find this book useful and graduate students will find the state-of-the-art research valuable.

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

The book discusses modern channel coding techniques for wireless communications such as turbo codes, low parity check codes (LDPC), space-time coding, Reed Solomon (RS) codes and convolutional codes. Many illustrative examples are included in each chapter for easy understanding of the coding techniques. The text is integrated with MATLAB-based programs to enhance the understanding of the subject's underlying theories. It includes current topics of increasing importance such as turbo codes, LDPC codes, LT codes, Raptor codes and space-time coding in detail, in addition to the traditional codes such as cyclic codes, BCH and RS codes and convolutional codes. MIMO communications is a multiple antenna technology, which is an effective method for high-speed or high-reliability wireless communications. PC-based MATLAB m-files for the illustrative examples are included and also provided on the accompanying CD, which will help students and researchers involved in advanced and current concepts in coding theory. Channel coding, the core of digital communication and data storage, has undergone a major revolution as a result of the rapid growth of mobile and wireless communications. The book is divided into 11 chapters. Assuming no prior knowledge in the field of channel coding, the opening chapters (1 - 2) begin with basic theory and discuss how to improve the performance of wireless communication channels using channel coding. Chapters 3 and 4 introduce Galois fields and present detailed coverage of BCH codes and Reed-Solomon codes. Chapters 5-7 introduce the family of convolutional codes, hard and soft-decision Viterbi algorithms, turbo codes, BCJR algorithm for turbo decoding and studies trellis coded modulation (TCM), turbo trellis coded modulation (TTCM), bit-interleaved coded modulation (BICM) as well as iterative BICM (BICM-ID) and compares them under various channel conditions. Chapters 8 and 9 focus on low-density parity-check (LDPC) codes, LT codes and Raptor codes. Chapters 10 and 11 discuss MIMO systems and space-time (ST) coding.

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information systems, web services, and web interoperability; obtaining a common understanding of verification needs in web applications; achieving a common understanding of the available rigorous approaches to system development, and the cases in which they have succeeded; identifying how rigorous software engineering methods can be exploited to develop suitable web applications; and at developing a European-scale research agenda combining theory, methods and tools that would lead to suitable web applications with the potential to implement systems for computation in the public domain.

This book investigates the latest modeling and control technologies in the context of air-conditioning systems. Firstly, it introduces the state-space method for developing dynamic models of all components in a central air-conditioning system. The models are primarily nonlinear and based on the fundamental principle of energy and mass conservation, and are transformed into state-space form through linearization. The book goes on to describe and discuss the state-space models with the help of graph theory and the structure-matrix theory. Subsequently, virtual sensor calibration and virtual sensing methods (which are very useful for real system control) are illustrated together with a case study. Model-based predictive control and state-space feedback control are applied to air-conditioning systems to yield better local control, while the air-side synergic control scheme and a global optimization strategy based on the decomposition-coordination method are developed so as to achieve energy conservation in the central air-conditioning system. Lastly, control strategies for VAV systems including total air volume control and trim & response static pressure control are investigated in practice.

This book presents several intelligent approaches for tackling and solving challenging practical problems facing those in the petroleum geosciences and petroleum industry. Written by experienced academics, this book offers state-of-the-art working examples and provides the reader with exposure to the latest developments in the field of intelligent methods applied to oil and gas research, exploration and production. It also analyzes the strengths and weaknesses of each method presented using benchmarking, whilst also emphasizing essential parameters such as robustness, accuracy, speed of convergence, computer time, overlearning and the role of normalization. The intelligent approaches presented include artificial neural networks, fuzzy logic, active learning method, genetic algorithms and support vector machines, amongst others. Integration, handling data of immense size and uncertainty, and dealing with risk management are among crucial issues in petroleum geosciences. The problems we have to solve in this domain are becoming too complex to rely on a single discipline for effective solutions and the costs associated with poor predictions (e.g. dry holes) increase. Therefore, there is a need to establish a new approach aimed at proper integration of disciplines (such as petroleum engineering, geology, geophysics and geochemistry), data fusion, risk reduction and uncertainty management. These intelligent techniques can be used for uncertainty analysis, risk assessment, data fusion and mining, data analysis and interpretation, and knowledge discovery, from diverse data such as 3-D seismic, geological data, well logging, and production data. This book is intended for petroleum scientists, data miners, data scientists and professionals and post-graduate students involved in petroleum industry.

This monograph presents the state of the art in aeroservoelastic (ASE) modeling and analysis and develops a systematic theoretical and computational framework for use by researchers and practicing engineers. It is the first book to focus on the mathematical modeling of structural dynamics, unsteady aerodynamics, and control systems to evolve a generic procedure to be applied for ASE synthesis. Existing robust, nonlinear, and adaptive control methodology is applied and extended to some interesting ASE problems, such as transonic flutter and buffet, post-stall buffet and maneuvers, and flapping flexible wing. The author derives a general aeroservoelastic plant via the finite-element structural dynamic model, unsteady aerodynamic models for various regimes in the frequency domain, and the associated state-space model by rational function approximations. For more advanced models, the full-potential, Euler, and Navier-Stokes methods for treating transonic and separated flows are also briefly addressed. Essential ASE controller design and analysis techniques are introduced to the reader, and an introduction to robust control-law design methods of LQG/LTR and H2/H synthesis is followed by a brief coverage of nonlinear control techniques of describing functions and Lyapunov functions. Practical and realistic aeroservoelastic application examples derived from actual experiments are included throughout. Aeroservoelasiticity fills an important gap in the aerospace engineering literature and will be a valuable guide for graduate students and advanced researchers in aerospace engineering, as well as professional engineers, technicians, and test pilots in the aircraft industry and laboratories.

Providing a comprehensive overview of various methods and applications in decision engineering, this book presents chapters written by a range experts in the field. It presents conceptual aspects of decision support applications in various areas including finance, vendor selection, construction, process management, water management and energy, agribusiness , production scheduling and control, and waste management. In addition to this, a special focus is given to methods of multi-criteria decision analysis. Decision making in organizations is a recurrent theme and is essential for business continuity.  Managers from various fields including public, private, industrial, trading or service sectors are required to make decisions. Consequently managers need the support of these structured methods in order to engage in effective decision making. This book provides a valuable resource for graduate students, professors and researchers of decision analysis, multi-criteria decision analysis and group decision analysis. It is also intended for production engineers, civil engineers and engineering consultants.

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics-one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.