Download or read book Chaos and Coarse Graining in Statistical Mechanics written by and published by . This book was released on 2008 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos.
Download or read book Chaos and Coarse Graining in Statistical Mechanics written by Patrizia Castiglione and published by Cambridge University Press. This book was released on 2008-08-21 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos.
Download or read book Chaos and Coarse Graining in Statistical Mathematics written by and published by . This book was released on 2008 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chaos written by Angelo Vulpiani and published by World Scientific. This book was released on 2010 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Download or read book From Phase Transitions to Chaos written by Gza Gyrgyi and published by World Scientific. This book was released on 1992 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Pter Szpfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.
Download or read book Chaos Scattering and Statistical Mechanics written by Pierre Gaspard and published by Cambridge University Press. This book was released on 1998-05-21 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book about chaos in statistical mechanics, in Cambridge Nonlinear Science Series.
Download or read book Equilibrium and Non equilibrium Statistical Mechanics written by Carolyn M. Van Vliet and published by World Scientific. This book was released on 2008 with total page 987 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.
Download or read book Chaotic Flows written by Oleg G. Bakunin and published by Springer Science & Business Media. This book was released on 2011-08-29 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.
Download or read book From Hamiltonian Chaos to Complex Systems written by Xavier Leoncini and published by Springer Science & Business Media. This book was released on 2013-07-14 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems.
Download or read book Hamiltonian Chaos and Fractional Dynamics written by George M. Zaslavsky and published by Oxford University Press on Demand. This book was released on 2005 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This books gives a realistic contemporary image of Hamiltonian dynamics, dealing with the basic principles of the Hamiltonian theory of chaos in addition to very recent and unusual applications of nonlinear dynamics and the fractality of dynamics.
Download or read book Fully Chaotic Maps and Broken Time Symmetry written by Dean J. Driebe and published by Springer Science & Business Media. This book was released on 1999-02-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book providing an introduction to a new approach to the nonequilibrium statistical mechanics of chaotic systems. It shows how the dynamical problem in fully chaotic maps may be solved on the level of evolving probability densities. On this level, time evolution is governed by the Frobenius-Perron operator. Spectral decompositions of this operator for a variety of systems are constructed in generalized function spaces. These generalized spectral decompositions are of special interest for systems with invertible trajectory dynamics, as on the statistical level the new solutions break time symmetry and allow for a rigorous understanding of irreversibility. Several techniques for the construction of explicit spectral decompositions are given. Systems ranging from the simple one-dimensional Bernoulli map to an invertible model of deterministic diffusion are treated in detail. Audience: Postgraduate students and researchers in chaos, dynamical systems and statistical mechanics.
Download or read book Statistical Mechanics written by James Sethna and published by Oxford University Press, USA. This book was released on 2006-04-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sethna distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, and modern biology. He explores everything from chaos through to life at the end of the universe.
Download or read book Coherent Quantum Physics written by Arnold Neumaier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-21 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces mathematicians, physicists, and philosophers to a new, coherent approach to theory and interpretation of quantum physics, in which classical and quantum thinking live peacefully side by side and jointly fertilize the intuition. The formal, mathematical core of quantum physics is cleanly separated from the interpretation issues. The book demonstrates that the universe can be rationally and objectively understood from the smallest to the largest levels of modeling. The thermal interpretation featured in this book succeeds without any change in the theory. It involves one radical step, the reinterpretation of an assumption that was virtually never questioned before - the traditional eigenvalue link between theory and observation is replaced by a q-expectation link: Objective properties are given by q-expectations of products of quantum fields and what is computable from these. Averaging over macroscopic spacetime regions produces macroscopic quantities with negligible uncertainty, and leads to classical physics. - Reflects the actual practice of quantum physics. - Models the quantum-classical interface through coherent spaces. - Interprets both quantum mechanics and quantum field theory. - Eliminates probability and measurement from the foundations. - Proposes a novel solution of the measurement problem.
Download or read book Scale Invariance written by Annick LESNE and published by Springer Science & Business Media. This book was released on 2011-11-04 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
Download or read book Chaos Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
Download or read book Chaos Information Processing And Paradoxical Games The Legacy Of John S Nicolis written by Gregoire Nicolis and published by World Scientific. This book was released on 2014-12-30 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a self-contained survey of the mechanisms presiding information processing and communication. The main thesis is that chaos and complexity are the basic ingredients allowing systems composed of interesting subunits to generate and process information and communicate in a meaningful way. Emphasis is placed on communication in the form of games and on the related issue of decision making under conditions of uncertainty. Biological, cognitive, physical, engineering and societal systems are approached from a unifying point of view, both analytically and by numerical simulation, using the methods of nonlinear dynamics and probability theory. Epistemological issues in connection with incompleteness and self-reference are also addressed.
Download or read book Nonlinear Dynamics and Quantum Chaos written by Sandro Wimberger and published by Springer. This book was released on 2014-05-13 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
