Download or read book The Langevin Equation written by William Coffey and published by World Scientific. This book was released on 1996 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation ? Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem ? Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint ? Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) ? together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.

Download or read book Langevin Equation The With Applications In Physics Chemistry And Electrical Engineering written by William T Coffey and published by World Scientific. This book was released on 1996-07-03 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation — Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem — Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint — Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) — together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.

Download or read book Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering 2nd Edition written by William T Coffey and published by World Scientific. This book was released on 2004-03-03 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on. It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena. The book has been written in such a way that all the material should be accessible to an advanced undergraduate or beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of research papers or scattered review articles.

Download or read book Basic Concepts for Simple and Complex Liquids written by Jean-Louis Barrat and published by Cambridge University Press. This book was released on 2003-03-27 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a unified approach, this book focusses on the concepts and theoretical methods that are necessary for an understanding of the physics and chemistry of the fluid state. The authors do not attempt to cover the whole field in an encyclopedic manner. Instead, important ideas are presented in a concise and rigorous style, and illustrated with examples from both simple molecular liquids and more complex soft condensed matter systems such as polymers, colloids, and liquid crystals.

Download or read book Langevin And Fokker planck Equations And Their Generalizations Descriptions And Solutions written by Sau Fa Kwok and published by World Scientific. This book was released on 2018-03-07 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker-Planck equations (H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed.Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details.Recent research on the integro-differential Fokker-Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems.

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Download or read book The Langevin and Generalised Langevin Approach to the Dynamics of Atomic Polymeric and Colloidal Systems written by Ian Snook and published by Elsevier. This book was released on 2006-12-11 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems.Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book.* Starts from fundamental equations* Gives up-to-date illustration of the application of these techniques to typical systems of interest* Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes

Download or read book Elements of Nonequilibrium Statistical Mechanics written by V. Balakrishnan and published by Springer. This book was released on 2021-12-05 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas. The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments.

Download or read book Fractional Equations and Models written by Trifce Sandev and published by Springer Nature. This book was released on 2019-11-23 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical, chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory, as it might have once seemed. The present book seeks to demonstrate this using various examples of equations and models with fractional and generalized operators. Intended for students and researchers in mathematics, physics, chemistry, biology and engineering, it systematically offers a wealth of useful tools for fractional calculus.

Download or read book Fractional Dynamics Recent Advances written by Joseph Klafter and published by World Scientific. This book was released on 2011-10-14 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject.In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

Download or read book The Fokker Planck Equation written by Hannes Risken and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonequilibrium Statistical Mechanics written by Robert Zwanzig and published by Oxford University Press, USA. This book was released on 2001-05-17 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a presentation of the main ideas and methods of modern nonequilibrium statistical mechanics. It is the perfect introduction for anyone in chemistry or physics who needs an update or background in this time-dependent field. Topics covered include fluctuation-dissipation theorem; linear response theory; time correlation functions, and projection operators. Theoretical models are illustrated by real-world examples and numerous applications such as chemical reaction rates and spectral line shapes are covered. The mathematical treatments are detailed and easily understandable and the appendices include useful mathematical methods like the Laplace transforms, Gaussian random variables and phenomenological transport equations.

Download or read book Stochastic Energetics written by Ken Sekimoto and published by Springer. This book was released on 2010-03-10 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Energetics by now commonly designates the emerging field that bridges the gap between stochastic dynamical processes and thermodynamics. Triggered by the vast improvements in spatio-temporal resolution in nanotechnology, stochastic energetics develops a framework for quantifying individual realizations of a stochastic process on the mesoscopic scale of thermal fluctuations. This is needed to answer such novel questions as: Can one cool a drop of water by agitating an immersed nano-particle? How does heat flow if a Brownian particle pulls a polymer chain? Can one measure the free-energy of a system through a single realization of the associated stochastic process? This book will take the reader gradually from the basics to the applications: Part I provides the necessary background from stochastic dynamics (Langevin, master equation), Part II introduces how stochastic energetics describes such basic notions as heat and work on the mesoscopic scale, Part III details several applications, such as control and detection processes, as well as free-energy transducers. It aims in particular at researchers and graduate students working in the fields of nanoscience and technology.

Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Download or read book Stochastic Processes in Physics and Chemistry written by N.G. Van Kampen and published by Elsevier. This book was released on 1992-11-20 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.

Download or read book Analysis and Data Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

Download or read book Autonomous Mobile Robots and Multi Robot Systems written by Eugene Kagan and published by John Wiley & Sons. This book was released on 2019-12-16 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a theoretical and practical guide to the communication and navigation of autonomous mobile robots and multi-robot systems This book covers the methods and algorithms for the navigation, motion planning, and control of mobile robots acting individually and in groups. It addresses methods of positioning in global and local coordinates systems, off-line and on-line path-planning, sensing and sensors fusion, algorithms of obstacle avoidance, swarming techniques and cooperative behavior. The book includes ready-to-use algorithms, numerical examples and simulations, which can be directly implemented in both simple and advanced mobile robots, and is accompanied by a website hosting codes, videos, and PowerPoint slides Autonomous Mobile Robots and Multi-Robot Systems: Motion-Planning, Communication and Swarming consists of four main parts. The first looks at the models and algorithms of navigation and motion planning in global coordinates systems with complete information about the robot’s location and velocity. The second part considers the motion of the robots in the potential field, which is defined by the environmental states of the robot's expectations and knowledge. The robot's motion in the unknown environments and the corresponding tasks of environment mapping using sensed information is covered in the third part. The fourth part deals with the multi-robot systems and swarm dynamics in two and three dimensions. Provides a self-contained, theoretical guide to understanding mobile robot control and navigation Features implementable algorithms, numerical examples, and simulations Includes coverage of models of motion in global and local coordinates systems with and without direct communication between the robots Supplemented by a companion website offering codes, videos, and PowerPoint slides Autonomous Mobile Robots and Multi-Robot Systems: Motion-Planning, Communication and Swarming is an excellent tool for researchers, lecturers, senior undergraduate and graduate students, and engineers dealing with mobile robots and related issues.