Monte Carlo Simulation in Statistical Physics

Monte Carlo Simulation in Statistical Physics

This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results.

Author: Kurt Binder

Publisher: Springer Science & Business Media

ISBN: 9783662046852

Category: Science

Page: 183

View: 378

Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. This fourth edition has been updated and a new chapter on Monte Carlo simulation of quantum-mechanical problems has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was the winner of the Berni J. Alder CECAM Award for Computational Physics 2001.
Categories: Science

The Monte Carlo Simulation Method for System Reliability and Risk Analysis

The Monte Carlo Simulation Method for System Reliability and Risk Analysis

The Monte Carlo Simulation Method for System Reliability and Risk Analysis comprehensively illustrates the Monte Carlo simulation method and its application to reliability and system engineering.

Author: Enrico Zio

Publisher: Springer Science & Business Media

ISBN: 9781447145882

Category: Mathematics

Page: 198

View: 776

Monte Carlo simulation is one of the best tools for performing realistic analysis of complex systems as it allows most of the limiting assumptions on system behavior to be relaxed. The Monte Carlo Simulation Method for System Reliability and Risk Analysis comprehensively illustrates the Monte Carlo simulation method and its application to reliability and system engineering. Readers are given a sound understanding of the fundamentals of Monte Carlo sampling and simulation and its application for realistic system modeling. Whilst many of the topics rely on a high-level understanding of calculus, probability and statistics, simple academic examples will be provided in support to the explanation of the theoretical foundations to facilitate comprehension of the subject matter. Case studies will be introduced to provide the practical value of the most advanced techniques. This detailed approach makes The Monte Carlo Simulation Method for System Reliability and Risk Analysis a key reference for senior undergraduate and graduate students as well as researchers and practitioners. It provides a powerful tool for all those involved in system analysis for reliability, maintenance and risk evaluations.
Categories: Mathematics

Essentials of Monte Carlo Simulation

Essentials of Monte Carlo Simulation

Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically.

Author: Nick T. Thomopoulos

Publisher: Springer Science & Business Media

ISBN: 9781461460220

Category: Mathematics

Page: 174

View: 183

Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run several times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. Over 100 numerical examples are presented as part of the appendix to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. Very little has been published in the area of computer Monte Carlo simulation methods, and this book will appeal to students and researchers in the fields of Mathematics and Statistics.
Categories: Mathematics

Applications of the Monte Carlo Method in Statistical Physics

Applications of the Monte Carlo Method in Statistical Physics

The large number of recent publications dealing either with applications or further development of some aspects of this method is a clear indication that the scientific community has realized the power and versatility of Monte Carlo simula ...

Author: K. Binder

Publisher: Springer Science & Business Media

ISBN: 9783642967887

Category: Science

Page: 311

View: 314

Monte Carlo computer simulations are now a standard tool in scientific fields such as condensed-matter physics, including surface-physics and applied-physics problems (metallurgy, diffusion, and segregation, etc. ), chemical physics, including studies of solutions, chemical reactions, polymer statistics, etc. , and field theory. With the increasing ability of this method to deal with quantum-mechanical problems such as quantum spin systems or many-fermion problems, it will become useful for other questions in the fields of elementary-particle and nuclear physics as well. The large number of recent publications dealing either with applications or further development of some aspects of this method is a clear indication that the scientific community has realized the power and versatility of Monte Carlo simula tions, as well as of related simulation techniques such as "molecular dynamics" and "Langevin dynamics," which are only briefly mentioned in the present book. With the increasing availability of recent very-high-speed general-purpose computers, many problems become tractable which have so far escaped satisfactory treatment due to prac tical limitations (too small systems had to be chosen, or too short averaging times had to be used). While this approach is admittedly rather expensive, two cheaper alternatives have become available, too: (i) array or vector processors specifical ly suited for wide classes of simulation purposes; (ii) special purpose processors, which are built for a more specific class of problems or, in the extreme case, for the simulation of one single model system.
Categories: Science

Simulation and the Monte Carlo Method

Simulation and 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 ...

Author: Reuven Y. Rubinstein

Publisher: John Wiley & Sons

ISBN: 9781118632161

Category: Mathematics

Page: 432

View: 476

"[This third edition] reflects the latest developments in the field and presents a fully updates and comprehensive account of 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 facilitating 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 addressing the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss 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 a importance (re)sampling and the transform likelihood ratio method, score function method for sensitivity analysis, stochastic approximation method and stochastic counter-part method for Monte Carlo optimization, 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." (source : 4ème de couverture).
Categories: Mathematics

Handbook in Monte Carlo Simulation

Handbook in Monte Carlo Simulation

The Handbook in Monte Carlo Simulation features: ■ An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials ■ Carefully crafted examples in ...

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 9781118593646

Category: Business & Economics

Page: 688

View: 424

An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.
Categories: Business & Economics

Monte Carlo Simulation im Operations Research

Monte Carlo Simulation im Operations Research

Einfuhrung und einfache beispiele; Die erzeugung von zufallszahlen; Die simulation stochastischer prozesse; Die statistischen grundlagen der Monte Carlo simulation.

Author: Jürg Kohlas

Publisher: Springer

ISBN: UOM:39015009808935

Category: Business & Economics

Page: 162

View: 530

Einfuhrung und einfache beispiele; Die erzeugung von zufallszahlen; Die simulation stochastischer prozesse; Die statistischen grundlagen der Monte Carlo simulation.
Categories: Business & Economics

Reliability Assessment of Electric Power Systems Using Monte Carlo Methods

Reliability Assessment of Electric Power Systems Using Monte Carlo Methods

It is hoped that this textbook will help formalize the many existing applications of Monte Carlo simulation and assist in their integration in teaching programs. This book presents the basic concepts associated with Monte Carlo simulation.

Author: Billinton

Publisher: Springer Science & Business Media

ISBN: 0306447819

Category: Technology & Engineering

Page: 352

View: 99

The application of quantitative reliability evaluation in electric power sys tems has now evolved to the point at which most utilities use these techniques in one or more areas of their planning, design, and operation. Most of the techniques in use are based on analytical models and resulting analytical evaluation procedures. Improvements in and availability of high-speed digi tal computers have created the opportunity to analyze many of these prob lems using stochastic simulation methods and over the last decade there has been increased interest in and use made of Monte Carlo simulation in quantitative power system reliability assessment. Monte Carlo simulation is not a new concept and recorded applications have existed for at least 50 yr. However, localized high-speed computers with large-capacity storage have made Monte Carlo simulation an available and sometimes preferable option for many power system reliability applications. Monte Carlo simulation is also an integral part of a modern undergrad uate or graduate course on reliability evaluation of general engineering systems or specialized areas such as electric power systems. It is hoped that this textbook will help formalize the many existing applications of Monte Carlo simulation and assist in their integration in teaching programs. This book presents the basic concepts associated with Monte Carlo simulation.
Categories: Technology & Engineering

The Monte Carlo Method for Semiconductor Device Simulation

The Monte Carlo Method for Semiconductor Device Simulation

This volume presents the application of the Monte Carlo method to the simulation of semiconductor devices, reviewing the physics of transport in semiconductors, followed by an introduction to the physics of semiconductor devices.

Author: Carlo Jacoboni

Publisher: Springer Science & Business Media

ISBN: 9783709169636

Category: Technology & Engineering

Page: 359

View: 357

This volume presents the application of the Monte Carlo method to the simulation of semiconductor devices, reviewing the physics of transport in semiconductors, followed by an introduction to the physics of semiconductor devices.
Categories: Technology & Engineering

Monte Carlo Methods

Monte Carlo Methods

Author: J. M. Hammersley

Publisher:

ISBN: UOM:39015013200285

Category: Monte Carlo method

Page: 178

View: 359

Categories: Monte Carlo method

Monte Carlo Methods in Financial Engineering

Monte Carlo Methods in Financial Engineering

The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not.

Author: Paul Glasserman

Publisher: Springer Science & Business Media

ISBN: 9780387216171

Category: Mathematics

Page: 596

View: 301

From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
Categories: Mathematics

Introductory Econometrics

Introductory Econometrics

This accessible textbook and supporting web site use Excel (R) to teach introductory econometrics.

Author: Humberto Barreto

Publisher: Cambridge University Press

ISBN: 0521843197

Category: Business & Economics

Page: 774

View: 570

This accessible textbook and supporting web site use Excel (R) to teach introductory econometrics.
Categories: Business & Economics

Monte Carlo Methods

Monte Carlo Methods

This is the second, completely revised and extended edition of the successful monograph which brings the treatment up to date while retaining its elementary but general approach.

Author: Malvin H. Kalos

Publisher: John Wiley & Sons

ISBN: 9783527626229

Category: Science

Page: 215

View: 455

This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Categories: Science

The Monte Carlo Methods in Atmospheric Optics

The Monte Carlo Methods in Atmospheric Optics

The authors of this book have contributed to the development of mathemati cal methods of simulation and to the interpretation of optical observations. A series of general method using Monte Carlo techniques has been developed.

Author: G.I. Marchuk

Publisher: Springer

ISBN: 9783540352372

Category: Technology & Engineering

Page: 210

View: 743

This monograph is devoted to urgent questions of the theory and applications of the Monte Carlo method for solving problems of atmospheric optics and hydrooptics. The importance of these problems has grown because of the increas ing need to interpret optical observations, and to estimate radiative balance precisely for weather forecasting. Inhomogeneity and sphericity of the atmos phere, absorption in atmospheric layers, multiple scattering and polarization of light, all create difficulties in solving these problems by traditional methods of computational mathematics. Particular difficulty arises when one must solve nonstationary problems of the theory of transfer of narrow beams that are connected with the estimation of spatial location and time characteristics of the radiation field. The most universal method for solving those problems is the Monte Carlo method, which is a numerical simulation of the radiative-transfer process. This process can be regarded as a Markov chain of photon collisions in a medium, which result in scattering or absorption. The Monte Carlo tech nique consists in computational simulation of that chain and in constructing statistical estimates of the desired functionals. The authors of this book have contributed to the development of mathemati cal methods of simulation and to the interpretation of optical observations. A series of general method using Monte Carlo techniques has been developed. The present book includes theories and algorithms of simulation. Numerical results corroborate the possibilities and give an impressive prospect of the applications of Monte Carlo methods.
Categories: Technology & Engineering

Monte Carlo Simulation

Monte Carlo Simulation

Aimed at researchers across the social sciences, this book explains the logic behind the Monte Carlo simulation method and demonstrates its uses for social and behavioural research.

Author: Christopher Z. Mooney

Publisher: SAGE

ISBN: 0803959435

Category: Education

Page: 103

View: 855

Aimed at researchers across the social sciences, this book explains the logic behind the Monte Carlo simulation method and demonstrates its uses for social and behavioural research.
Categories: Education

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field.

Author: Dirk P. Kroese

Publisher: John Wiley & Sons

ISBN: 1118014952

Category: Mathematics

Page: 772

View: 260

A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
Categories: Mathematics

Explorations in Monte Carlo Methods

Explorations in Monte Carlo Methods

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.

Author: Ronald W. Shonkwiler

Publisher: Springer Science & Business Media

ISBN: 9780387878362

Category: Mathematics

Page: 243

View: 240

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.
Categories: Mathematics

Markov Chains

Markov Chains

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling.

Author: Pierre Bremaud

Publisher: Springer Science & Business Media

ISBN: 0387985093

Category: Mathematics

Page: 445

View: 745

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.
Categories: Mathematics

Monte Carlo Simulation and Resampling Methods for Social Science

Monte Carlo Simulation and Resampling Methods for Social Science

The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project.

Author: Thomas M. Carsey

Publisher: SAGE Publications, Incorporated

ISBN: 1452288909

Category: Social Science

Page: 304

View: 345

Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, Monte Carlo Simulation and Resampling Methods for Social Science, by Thomas M. Carsey and Jeffrey J. Harden, examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.
Categories: Social Science