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 The Langevin Equation written by William Coffey and published by World Scientific. This book was released on 2004 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 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 Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering Fourth Edition written by William T Coffey and published by World Scientific. This book was released on 2017-03-22 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker-Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.
Download or read book Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering 3rd Edition written by Yuri P Kalmykov and published by World Scientific. This book was released on 2012-07-31 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles.
Download or read book The Langevin Equation written by William Coffey and published by . This book was released on 2017 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker–Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject."--Publisher's website.
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 An Introduction to Anomalous Diffusion and Relaxation written by Luiz Roberto Evangelista and published by Springer Nature. This book was released on 2023-01-01 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.
Download or read book Fractional Calculus Theory and Applications written by Francesco Mainardi and published by MDPI. This book was released on 2018-09-20 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics
Download or read book Modified Maxwell Equations in Quantum Electrodynamics written by Henning F. Harmuth and published by World Scientific. This book was released on 2001 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divergencies in quantum field theory referred to as ?infinite zero-point energy? have been a problem for 70 years. Renormalization has always been considered an unsatisfactory remedy.In 1985 it was found that Maxwell's equations generally do not have solutions that satisfy the causality law. An additional term for magnetic dipole currents corrected this shortcoming. Rotating magnetic dipoles produce magnetic dipole currents, just as rotating electric dipoles in a material like barium titanate produce electric dipole currents. Electric dipole currents were always part of Maxwell's equations.This book shows that the correction of Maxwell's equations eliminates the infinite zero-point energy in quantum electrodynamics. In addition, it presents many more new results.
Download or read book Advances in Chemical Physics Volume 129 written by Stuart A. Rice and published by John Wiley & Sons. This book was released on 2004-08-02 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. Volume 129 in the series continues to report recent advances with significant, up-to-date chapters by internationally recognized researchers.
Download or read book Harmonic Analysis for Engineers and Applied Scientists written by Gregory S. Chirikjian and published by Courier Dover Publications. This book was released on 2016-07-20 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
Download or read book Introduction to Computational Materials Science written by Richard LeSar and published by Cambridge University Press. This book was released on 2013-03-28 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasising essential methods and universal principles, this textbook provides everything students need to understand the basics of simulating materials behavior. All the key topics are covered from electronic structure methods to microstructural evolution, appendices provide crucial background material, and a wealth of practical resources are available online to complete the teaching package. Modeling is examined at a broad range of scales, from the atomic to the mesoscale, providing students with a solid foundation for future study and research. Detailed, accessible explanations of the fundamental equations underpinning materials modelling are presented, including a full chapter summarising essential mathematical background. Extensive appendices, including essential background on classical and quantum mechanics, electrostatics, statistical thermodynamics and linear elasticity, provide the background necessary to fully engage with the fundamentals of computational modelling. Exercises, worked examples, computer codes and discussions of practical implementations methods are all provided online giving students the hands-on experience they need.
Download or read book Dielectric Relaxation And Dynamics Of Polar Molecules written by Myron W Evans and published by World Scientific. This book was released on 1999-04-29 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics covered in this book provide a qualitative and sometimes quantitative classic description of the wide-band 0-THz dielectric spectra of polar liquids, molecular libration-rotation (which is the reason for dielectric loss and absorption of electromagnetic waves), simple molecular models differing by the intermolecular-potential profiles, and present a comparison between the theoretical and experimental dependencies and derivation of the main results. A new feature is the application of a number of analytical models to different substances, including strongly absorbing nonassociating liquids, liquid water, water bound by macromolecules, and gas-like liquids. The presentation of the theory in this book is also new. It is based on the dynamic method in which the Brownian reorientations are considered implicitly, without direct solution of stochastic equations. This approach simplifies the theory. Senior students and experimentalists will find many of the results valuable.
Download or read book Phase In Optics written by Myron W Evans and published by World Scientific. This book was released on 1998-10-05 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the classical and quantum phases in wave and particle optics from the viewpoint of both theory and applications. Wave and beam light optics are reviewed in considerable detail, featuring optical imaging and holography in linear optics and phase conjugation methods in nonlinear optics. Photon optics is embodied here as quantum optics with the modes treated as quantum harmonic oscillators. The importance of the Wigner function for the phase space description in the context of canonical quantization is respected and the method of quasidistributions related to operator orderings in the second-quantized theory is exposed. The history of the quantum phase problem, characterized by renewed interest in the solution to the problem, is included and brought up to date. Approaches based on exponential phase operators, discrete phase states, the enlargement of the Hilbert space of the harmonic oscillator leading to the phase representations and distributions, together with solutions motivated by the quasidistributions, are introduced. The operational approach to the quantum phase is contrasted with the previous formalisms. The results of the study of the coherent states and the ordinary squeezed states from the viewpoint of the quantum phase and those of the analysis of the quantum statistics of phase-related special states of the light field are provided. The quantum phase is also treated with respect to quantum interferometry, particle interferometry, nonlinear optical processes, and quantum nondemolition measurements.The book will prove indispensable to research workers in general optics, quantum optics and electronics, optoelectronics, and nonlinear optics, as well as to students of physics, optics, optoelectronics, photonics, and optical engineering.
Download or read book Structure And Transport Properties In Organized Polymeric Materials written by Emo Chiellini and published by World Scientific. This book was released on 1998-03-19 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-authored book includes selected contributions reviewing the results achieved in the synthesis and characterization of organized polymeric materials. The focus is on competitive materials with liquid crystalline or electroconductive properties. The fine tuning of the properties offered by advanced chemical synthesis has been investigated by a large number of state-of-the-art techniques, including both microscopic (ESR, NMR, dielectrometry, fluorescence, IR, Raman spectroscopy) and macroscopic (calorimetric, mechanical) methodologies. The book also provides an updated coverage of the most challenging applications of organized polymers as functional materials in the fields of electrooptical devices, information retrieval and organic electroconductors.
