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Stochastic Methods

Author: Crispin Gardiner
Publisher: Springer
ISBN: 9783642089626
Size: 75.37 MB
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In the third edition of this classic the chapter on quantum Marcov processes has been replaced by a chapter on numerical treatment of stochastic differential equations to make the book even more valuable for practitioners.

Handbook Of Stochastic Methods For Physics Chemistry And The Natural Sciences

Author: Crispin W. Gardiner
Publisher: Springer Verlag
ISBN: 9783540208822
Size: 60.37 MB
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This valuable and highly-praised reference collects and explains, in simple language and reasonably deductive form, those formulas and methods and their applications used in modern Statistical Physics, including the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations, and quantum-mechanical Markov processes. The practical orientation and broad coverage appeal to researchers and academics working in theoretical physics, physical chemistry, and related fields. In the third edition of this classic the chapter on quantum Marcov processes has been replaced by a chapter on numerical treatment of stochastic differential equations to make the book even more valuable for practitioners. From the reviews: "Extremely well written and informative... clear, complete, and fairly rigorous treatment of a larger number of very basic concepts in stochastic theory." (Journal of Quantum Electronics) "A first class book." (Optica Acta) "Ideal for people who need a clear introduction to stochastic mathematics and their applications in physical sciencesa ] an excellent self study and reference book." (Quantnotes.com) "This well-established volume takes a supreme position [among the many books on the subject].. This extremely valuable contribution to the field of applied stochastic methods can be recommended to graduate students, researchers, and university teachers." (Optimization)

Stochastic Processes In Physics And Chemistry

Author: N.G. Van Kampen
Publisher: Elsevier
ISBN: 9780080475363
Size: 55.67 MB
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The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992) W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004) * Comprehensive coverage of fluctuations and stochastic methods for describing them * A must for students and researchers in applied mathematics, physics and physical chemistry

Stochastic Processes For Physicists

Author: Kurt Jacobs
Publisher: Cambridge University Press
ISBN: 1139486799
Size: 53.42 MB
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Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.

The Fokker Planck Equation

Author: Hannes Risken
Publisher: Springer Science & Business Media
ISBN: 3642615449
Size: 25.52 MB
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This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.

Non Equilibrium Thermodynamics And Statistical Mechanics

Author: Phil Attard
Publisher: Oxford University Press
ISBN: 0199662762
Size: 60.88 MB
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This title builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. It is a pedagogic introduction, a comprehensive reference manual, and an original research monograph--

Markov Processes

Author: Daniel T. Gillespie
Publisher: Gulf Professional Publishing
ISBN: 9780122839559
Size: 31.70 MB
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Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level. A self-contained, prgamatic exposition of the needed elements of random variable theory Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples Clear treatments of first passages, first exits, and stable state fluctuations and transitions Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

Quantum Noise

Author: Crispin Gardiner
Publisher: Springer Science & Business Media
ISBN: 9783540223016
Size: 30.53 MB
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This title is included in the Springer Complexity programme.

Synchronization

Author: Alexander Balanov
Publisher: Springer Science & Business Media
ISBN: 3540721282
Size: 18.30 MB
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This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.

Simulating Social Complexity

Author: Bruce Edmonds
Publisher: Springer
ISBN: 3540938133
Size: 62.44 MB
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Social systems are among the most complex known. This poses particular problems for those who wish to understand them. The complexity often makes analytic approaches infeasible and natural language approaches inadequate for relating intricate cause and effect. However, individual- and agent-based computational approaches hold out the possibility of new and deeper understanding of such systems. Simulating Social Complexity examines all aspects of using agent- or individual-based simulation. This approach represents systems as individual elements having each their own set of differing states and internal processes. The interactions between elements in the simulation represent interactions in the target systems. What makes these elements "social" is that they are usefully interpretable as interacting elements of an observed society. In this, the focus is on human society, but can be extended to include social animals or artificial agents where such work enhances our understanding of human society. The phenomena of interest then result (emerge) from the dynamics of the interaction of social actors in an essential way and are usually not easily simplifiable by, for example, considering only representative actors. The introduction of accessible agent-based modelling allows the representation of social complexity in a more natural and direct manner than previous techniques. In particular, it is no longer necessary to distort a model with the introduction of overly strong assumptions simply in order to obtain analytic tractability. This makes agent-based modelling relatively accessible to a range of scientists. The outcomes of such models can be displayed and animated in ways that also make them more interpretable by experts and stakeholders. This handbook is intended to help in the process of maturation of this new field. It brings together, through the collaborative effort of many leading researchers, summaries of the best thinking and practice in this area and constitutes a reference point for standards against which future methodological advances are judged. This book will help those entering into the field to avoid "reinventing the wheel" each time, but it will also help those already in the field by providing accessible overviews of current thought. The material is divided into four sections: Introductory, Methodology, Mechanisms, and Applications. Each chapter starts with a very brief section called ‘Why read this chapter?’ followed by an abstract, which summarizes the content of the chapter. Each chapter also ends with a section of ‘Further Reading’ briefly describing three to eight items that a newcomer might read next.