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 The Fokker planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by Christian Soize and published by World Scientific. This book was released on 1994-05-16 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?
Download or read book Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2015-12-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
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 Particle Accelerator Physics I written by Helmut Wiedemann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition of Particle Accelerator Physics, Vol. 1, is mainly a reprint of the first edition without significant changes in content. The bibliography has been updated to include more recent progress in the field of particle accelerators. With the help of many observant readers a number of misprints and errors could be eliminated. The author would like to express his sincere appreciation to all those who have pointed out such shortcomings and wel comes such information and any other relevant information in the future. The author would also like to express his special thanks to the editor Dr. Helmut Lotsch and his staff for editorial as well as technical advice and support which contributed greatly to the broad acceptance of this text and made a second edition of both volumes necessary. Palo Alto, California Helmut Wiedemann November 1998 VII Preface to the First Edition The purpose of this textbook is to provide a comprehensive introduction into the physics of particle accelerators and particle beam dynamics. Parti cle accelerators have become important research tools in high energy physics as well as sources of incoherent and coherent radiation from the far infra red to hard x-rays for basic and applied research. During years of teaching accelerator physics it became clear that the single most annoying obstacle to get introduced into the field is the absence of a suitable textbook.
Download or read book Asymptotic Methods for the Fokker Planck Equation and the Exit Problem in Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 1999-03-08 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Download or read book Physical and Mathematical Aspects of Symmetries written by Sergio Duarte and published by Springer. This book was released on 2018-01-09 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings records the 31st International Colloquium on Group Theoretical Methods in Physics (“Group 31”). Plenary-invited articles propose new approaches to the moduli spaces in gauge theories (V. Pestun, 2016 Weyl Prize Awardee), the phenomenology of neutrinos in non-commutative space-time, the use of Hardy spaces in quantum physics, contradictions in the use of statistical methods on complex systems, and alternative models of supersymmetry. This volume’s survey articles broaden the colloquia’s scope out into Majorana neutrino behavior, the dynamics of radiating charges, statistical pattern recognition of amino acids, and a variety of applications of gauge theory, among others. This year’s proceedings further honors Bertram Kostant (2016 Wigner Medalist), as well as S.T. Ali and L. Boyle, for their life-long contributions to the math and physics communities. The aim of the ICGTMP is to provide a forum for physicists, mathematicians, and scientists of related disciplines who develop or apply methods in group theory to share their research. The 31st ICGTMP was held in Rio de Janeiro, Brazil, from June 19th to June 25th, 2016. This was the first time that a colloquium of the prestigious and traditional ICGTMP series (which started in 1972 in Marseille, France) took place in South America. (The history of the colloquia can be found at http://icgtmp.blogs.uva.es/)
Download or read book Stochastic Processes for Physicists written by Kurt Jacobs and published by Cambridge University Press. This book was released on 2010-02-18 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Calculus and Differential Equations for Physics and Finance written by Joseph L. McCauley and published by Cambridge University Press. This book was released on 2013-02-21 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
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 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 Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
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 Applied Functional Analysis written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.
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 Hypocoercivity written by Cdric Villani and published by American Mathematical Soc.. This book was released on 2009-10-08 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.
Download or read book Asymptotic Methods for the Fokker Planck Equation and the Exit Problem in Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
