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 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 Nonlinear Fokker Planck Equations written by T.D. Frank and published by Springer Science & Business Media. This book was released on 2005-01-07 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.
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 Uniqueness of Solutions to Fokker Planck Equations Related to Singular SPDE Driven by L vy and Cylindrical Wiener Noise written by Sven Wiesinger and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytical and Numerical Solutions of Generalized Fokker Planck Equations Final Report written by and published by . This book was released on 2000 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset are amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Encyclopedia of Bioinformatics and Computational Biology written by and published by Elsevier. This book was released on 2018-08-21 with total page 3421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases
Download or read book Theory and Applications of Colloidal Suspension Rheology written by Norman J. Wagner and published by Cambridge University Press. This book was released on 2021-04-15 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential text on practical application, theory and simulation, written by an international coalition of experts in the field and edited by the authors of Colloidal Suspension Rheology. This up-to-date work builds upon the prior work as a valuable guide to formulation and processing, as well as fundamental rheology of colloidal suspensions. Thematically, theory and simulation are connected to industrial application by consideration of colloidal interactions, particle properties, and suspension microstructure. Important classes of model suspensions including gels, glasses and soft particles are covered so as to develop a deeper understanding of industrial systems ranging from carbon black slurries, paints and coatings, asphalt, cement, and mine tailings, to natural suspensions such as biocolloids, protein solutions, and blood. Systematically presenting the established facts in this multidisciplinary field, this book is the perfect aid for academic researchers, graduate students, and industrial practitioners alike.
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 Stationary Solutions of the Vlasov Fokker Planck Equation written by Klaus Dressler and published by . This book was released on 1986 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 1248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Soviet Physics JETP written by and published by . This book was released on 1990 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Order Systems written by Ahmed G. Radwan and published by Academic Press. This book was released on 2021-10-13 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. - Presents a simple and comprehensive understanding of the field of fractional-order systems - Offers practical knowledge on the design of fractional-order systems for different applications - Exposes users to possible new applications for fractional-order systems
Download or read book Statistical Thermodynamics And Stochastic Theory Of Nonequilibrium Systems written by Ebeling Werner and published by World Scientific Publishing Company. This book was released on 2005-09-23 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.
