The Monte Carlo Ray-Trace Method in Radiation Heat Transfer and Applied Optics

This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo Variance reduction techniques such as the transform likelihood ratio method and the screening method The score function method for sensitivity analysis The stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization The cross-entropy method to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.

This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.

Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition is a comprehensively updated new edition and is a unique book on the application of the finite element method to heat and mass transfer. • Addresses fundamentals, applications and computer implementation • Educational computer codes are freely available to download, modify and use • Includes a large number of worked examples and exercises • Fills the gap between learning and research

An authoritative guide to theory and applications of heat transfer in humans Theory and Applications of Heat Transfer in Humans 2V Set offers a reference to the field of heating and cooling of tissue, and associated damage. The author—a noted expert in the field—presents, in this book, the fundamental physics and physiology related to the field, along with some of the recent applications, all in one place, in such a way as to enable and enrich both beginner and advanced readers. The book provides a basic framework that can be used to obtain ‘decent’ estimates of tissue temperatures for various applications involving tissue heating and/or cooling, and also presents ways to further develop more complex methods, if needed, to obtain more accurate results. The book is arranged in three sections: The first section, named ‘Physics’, presents fundamental mathematical frameworks that can be used as is or combined together forming more complex tools to determine tissue temperatures; the second section, named ‘Physiology’, presents ideas and data that provide the basis for the physiological assumptions needed to develop successful mathematical tools; and finally, the third section, named ‘Applications’, presents examples of how the marriage of the first two sections are used to solve problems of today and tomorrow. This important text is the vital resource that: Offers a reference book in the field of heating and cooling of tissue, and associated damage. Provides a comprehensive theoretical and experimental basis with biomedical applications Shows how to develop and implement both, simple and complex mathematical models to predict tissue temperatures Includes simple examples and results so readers can use those results directly or adapt them for their applications Designed for students, engineers, and other professionals, a comprehensive text to the field of heating and cooling of tissue that includes proven theories with applications. The author reveals how to develop simple and complex mathematical models, to predict tissue heating and/or cooling, and associated damage.

Simulation and Monte Carlo is aimed at students studying for degrees in Mathematics, Statistics, Financial Mathematics, Operational Research, Computer Science, and allied subjects, who wish an up-to-date account of the theory and practice of Simulation. Its distinguishing features are in-depth accounts of the theory of Simulation, including the important topic of variance reduction techniques, together with illustrative applications in Financial Mathematics, Markov chain Monte Carlo, and Discrete Event Simulation. Each chapter contains a good selection of exercises and solutions with an accompanying appendix comprising a Maple worksheet containing simulation procedures. The worksheets can also be downloaded from the web site supporting the book. This encourages readers to adopt a hands-on approach in the effective design of simulation experiments. Arising from a course taught at Edinburgh University over several years, the book will also appeal to practitioners working in the finance industry, statistics and operations research.

This book gives an overview of the quantum transport approaches for nanodevices and focuses on the Wigner formalism. It details the implementation of a particle-based Monte Carlo solution of the Wigner transport equation and how the technique is applied to typical devices exhibiting quantum phenomena, such as the resonant tunnelling diode, the ultra-short silicon MOSFET and the carbon nanotube transistor. In the final part, decoherence theory is used to explain the emergence of the semi-classical transport in nanodevices.

This broad-based book covers the three major areas of Chemical Engineering. Most of the books in the market involve one of the individual areas, namely, Fluid Mechanics, Heat Transfer or Mass Transfer, rather than all the three. This book presents this material in a single source. This avoids the user having to refer to a number of books to obtain information. Most published books covering all the three areas in a single source emphasize theory rather than practical issues. This book is written with emphasis on practice with brief theoretical concepts in the form of questions and answers, not adopting stereo-typed question-answer approach practiced in certain books in the market, bridging the two areas of theory and practice with respect to the core areas of chemical engineering. Most parts of the book are easily understandable by those who are not experts in the field. Fluid Mechanics chapters include basics on non-Newtonian systems which, for instance find importance in polymer and food processing, flow through piping, flow measurement, pumps, mixing technology and fluidization and two phase flow. For example it covers types of pumps and valves, membranes and areas of their use, different equipment commonly used in chemical industry and their merits and drawbacks. Heat Transfer chapters cover the basics involved in conduction, convection and radiation, with emphasis on insulation, heat exchangers, evaporators, condensers, reboilers and fired heaters. Design methods, performance, operational issues and maintenance problems are highlighted. Topics such as heat pipes, heat pumps, heat tracing, steam traps, refrigeration, cooling of electronic devices, NOx control find place in the book. Mass transfer chapters cover basics such as diffusion, theories, analogies, mass transfer coefficients and mass transfer with chemical reaction, equipment such as tray and packed columns, column internals including structural packings, design, operational and installation issues, drums and separators are discussed in good detail. Absorption, distillation, extraction and leaching with applications and design methods, including emerging practices involving Divided Wall and Petluk column arrangements, multicomponent separations, supercritical solvent extraction find place in the book.

Heat transfer is the area of engineering science which describes the energy transport between material bodies due to a difference in temperature. The three different modes of heat transport are conduction, convection and radiation. In most problems, these three modes exist simultaneously. However, the significance of these modes depends on the problems studied and often, insignificant modes are neglected. Very often books published on Computational Fluid Dynamics using the Finite Element Method give very little or no significance to thermal or heat transfer problems. From the research point of view, it is important to explain the handling of various types of heat transfer problems with different types of complex boundary conditions. Problems with slow fluid motion and heat transfer can be difficult problems to handle. Therefore, the complexity of combined fluid flow and heat transfer problems should not be underestimated and should be dealt with carefully. This book: Is ideal for teaching senior undergraduates the fundamentals of how to use the Finite Element Method to solve heat transfer and fluid dynamics problems Explains how to solve various heat transfer problems with different types of boundary conditions Uses recent computational methods and codes to handle complex fluid motion and heat transfer problems Includes a large number of examples and exercises on heat transfer problems In an era of parallel computing, computational efficiency and easy to handle codes play a major part. Bearing all these points in mind, the topics covered on combined flow and heat transfer in this book will be an asset for practising engineers and postgraduate students. Other topics of interest for the heat transfer community, such as heat exchangers and radiation heat transfer, are also included.

Applications of mathematical heat transfer and fluid flow models in engineering and medicine Abram S. Dorfman, University of Michigan, USA Engineering and medical applications of cutting-edge heat and flow models This book presents innovative efficient methods in fluid flow and heat transfer developed and widely used over the last fifty years. The analysis is focused on mathematical models which are an essential part of any research effort as they demonstrate the validity of the results obtained. The universality of mathematics allows consideration of engineering and biological problems from one point of view using similar models. In this book, the current situation of applications of modern mathematical models is outlined in three parts. Part I offers in depth coverage of the applications of contemporary conjugate heat transfer models in various industrial and technological processes, from aerospace and nuclear reactors to drying and food processing. In Part II the theory and application of two recently developed models in fluid flow are considered: the similar conjugate model for simulation of biological systems, including flows in human organs, and applications of the latest developments in turbulence simulation by direct solution of Navier-Stokes equations, including flows around aircraft. Part III proposes fundamentals of laminar and turbulent flows and applied mathematics methods. The discussion is complimented by 365 examples selected from a list of 448 cited papers, 239 exercises and 136 commentaries. Key features: Peristaltic flows in normal and pathologic human organs. Modeling flows around aircraft at high Reynolds numbers. Special mathematical exercises allow the reader to complete expressions derivation following directions from the text. Procedure for preliminary choice between conjugate and common simple methods for particular problem solutions. Criterions of conjugation, definition of semi-conjugate solutions. This book is an ideal reference for graduate and post-graduate students and engineers.