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Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon’s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods. This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners. Provides a concise treatment of generic Monte Carlo methods Proofs for each chapter Appendixes include Certain mathematical functions; Bose Einstein functions, Fermi Dirac functions, Watson functions
The Monte Carlo method has become the de facto standard in radiation transport. Although powerful, if not understood and used appropriately, the method can give misleading results. Monte Carlo Methods for Particle Transport teaches appropriate use of the Monte Carlo method, explaining the method’s fundamental concepts as well as its limitations. Concise yet comprehensive, this well-organized text: Introduces the particle importance equation and its use for variance reduction Describes general and particle-transport-specific variance reduction techniques Presents particle transport eigenvalue issues and methodologies to address these issues Explores advanced formulations based on the author’s research activities Discusses parallel processing concepts and factors affecting parallel performance Featuring illustrative examples, mathematical derivations, computer algorithms, and homework problems, Monte Carlo Methods for Particle Transport provides nuclear engineers and scientists with a practical guide to the application of the Monte Carlo method.
Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.
This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.
Diffusion in Crystalline Solids addresses some of the most active areas of research on diffusion in crystalline solids. Topics covered include measurement of tracer diffusion coefficients in solids, diffusion in silicon and germanium, atom transport in oxides of the fluorite structure, tracer diffusion in concentrated alloys, diffusion in dislocations, grain boundary diffusion mechanisms in metals, and the use of the Monte Carlo Method to simulate diffusion kinetics. This book is made up of eight chapters and begins with an introduction to the measurement of diffusion coefficients with radioisotopes. The following three chapters consider diffusion in materials of substantial technological importance such as silicon and germanium. Atomic transport in oxides of the fluorite structure is described, and diffusion in concentrated alloys, including intermetallic compounds, is analyzed. The next two chapters delve into diffusion along short-circuiting paths, focusing on the effect of diffusion down dislocations on the form of the tracer concentration profile. The book also discusses the mechanisms of diffusion in grain boundaries in metals by invoking considerable work done on grain-boundary structure. The last two chapters are concerned with computer simulation, paying particular attention to machine calculations and the Monte Carlo method. The book concludes by exploring the fundamental atomic migration process and presenting some state-of-the-art calculations for defect energies and the topology of the saddle surface. Students and researchers of material science will find this book extremely useful.
Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This edition now contains material describing powerful new algorithms that have appeared since the previous edition was published, and highlights recent technical advances and key applications that these algorithms now make possible. Updates also include several new sections and a chapter on the use of Monte Carlo simulations of biological molecules. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory.
This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'

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