Metastability
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Metastability
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Author : Anton Bovier
language : en
Publisher:
Release Date : 2015
Metastability written by Anton Bovier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Metastability is a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise. This monograph provides a concise presentation of mathematical approach to metastability based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focus on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hopping dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.
Metastability
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Author : Anton Bovier
language : en
Publisher: Springer
Release Date : 2016-02-11
Metastability written by Anton Bovier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Mathematics categories.
This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.
Large Deviations And Metastability
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Author : Enzo Olivieri
language : en
Publisher: Cambridge University Press
Release Date : 2005-02-21
Large Deviations And Metastability written by Enzo Olivieri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-21 with Mathematics categories.
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Collapse Of Metastability
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Author : Seiji Miyashita
language : en
Publisher: Springer Nature
Release Date : 2022-11-05
Collapse Of Metastability written by Seiji Miyashita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-05 with Science categories.
To understand phenomena in nature, it is important to focus not only on properties of stationary states, but also their changes in time, that is, the dynamics between bistable states. This book reviews the mechanics of first-order phase transitions and discusses relaxation and collapses of metastable states from various viewpoints, including Kramers' method for the lifetime of metastability, Langer’s analysis on the singularity, effects of thermal fluctuation studied by Néel and Brown, and eigenvalue structures of the transfer-matrix for the phase transitions. The book also goes into the mechanics of metastability in quantum systems from the viewpoints of the eigenvalue problem of the Hamiltonian and the Liouvillian for a dynamical process and discusses relations between quantum tunneling processes and metastability therein. Lastly, the coercivity of magnets consisting of an ensemble of grains is reviewed. The book is beneficial for those new in the field as a primer on first-order phase transition from modern perspectives. The comprehensive content offers overviews of related topics and allows readers to quickly catch up with developments in the field.
Metastasis And Metastability
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Author : Kane X. Faucher
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19
Metastasis And Metastability written by Kane X. Faucher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-19 with Education categories.
The word “information” carries a number of connotations depending on context, and can be said to be one of the most problematic words to define despite many efforts by statistical theorists, mathematicians, physicists, cyberneticians, communication theorists, computer scientists, and philosophers. Is information physical or non-physical? Is the universe digital, analog, or a “chaosmic” mixture of the two? This book explores a Deleuzian way of understanding information by retracing Deleuze’s ontology of difference back to Gilbert Simondon’s concepts of transduction, metastability, and perpetual individuation as a source for Deleuze’s concept of the virtual. Although Deleuze did not address information specifically in his oeuvre, this book attempts to construct what a Deleuzian theory of information might look like as a consequence of his philosophical insights. The reader is presented with a brief survey of information theories, capsule explanations of the philosophy of Gilbert Simondon and Gilles Deleuze, and a discussion on the roles of metastasis and metastability as a means of addressing the problematic known as information outside of computing regimes, and as a critique of cybernetics, informatics, and memetics. Can information be reconfigured as affirmative difference, transformed into a “nomad science,” or must it remain consigned to the realm of probabilism?
Metastability And Markov State Models In Molecular Dynamics
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Author : Christof Schütte
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-26
Metastability And Markov State Models In Molecular Dynamics written by Christof Schütte and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-26 with Mathematics categories.
Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a consequence, there is an increasing need for reduced models that describe the relevant dynamical properties while at the same time being less complex. In this book the authors exploit the existence of metastable sets for constructing such a reduced molecular dynamics model, the so-called Markov state model (MSM), with good approximation properties on the long timescales. With its many examples and illustrations, this book is addressed to graduate students, mathematicians, and practical computational scientists wanting an overview of the mathematical background for the ever-increasing research activity on how to construct MSMs for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Metastability And Incompletely Posed Problems
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Author : Stuart S. Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Metastability And Incompletely Posed Problems written by Stuart S. Antman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This IMA Volume in Mathematics and its Applications Metastability and Incompletely Posed Problems represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EOIIATIONS. We are grateful to the Scientific Committee: ,I.L. Eri cksen D. Kinderlehrer H. Rrezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger Preface Most equilibrium events in nature do not realize configurations of minimum energy. They are only metastable. Available knowledge of constitutive relations and environmental interactions may be limiterl. As a result, many configurations may he compatible with the rlata. Such questions are incompletely poserl. The papers in this volume address a wide variety of these issues as they are perceived by the material scientist and the mathematician. They represent a portion of the significant activity which has been underway in recent years, from the experimental arena and physical theory to the analysis of differential equations and computation.
Photo Induced Metastability In Amorphous Semiconductors
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Author : Alexander V. Kolobov
language : en
Publisher: John Wiley & Sons
Release Date : 2006-12-13
Photo Induced Metastability In Amorphous Semiconductors written by Alexander V. Kolobov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-13 with Science categories.
A review summarising the current state of research in the field, bridging the gaps in the existing literature. All the chapters are written by world leaders in research and development and guide readers through the details of photo-induced metastability and the results of the latest experiments and simulations not found in standard monographs on this topic. A useful reference not only for graduates but also for scientific and industrial researchers. With a foreword of Kazunobu Tanaka
Complexity Metastability And Nonextensivity
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Author :
language : en
Publisher:
Release Date :
Complexity Metastability And Nonextensivity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Metastable Liquids
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Author : Pablo G. Debenedetti
language : en
Publisher: Princeton University Press
Release Date : 2020-06-16
Metastable Liquids written by Pablo G. Debenedetti and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-16 with Science categories.
Metastable Liquids provides a comprehensive treatment of the properties of liquids under conditions where the stable state is a vapor, a solid, or a liquid mixture of different composition. It examines the fundamental principles that govern the equilibrium properties, stability, relaxation mechanisms, and relaxation rates of metastable liquids. Building on the interplay of kinetics and thermodynamics that determines the thermophysical properties and structural relaxation of metastable liquids, it offers an in-depth treatment of thermodynamic stability theory, the statistical mechanics of metastability, nucleation, spinodal decomposition, supercooled liquids, and the glass transition. Both traditional topics--such as stability theory--and modern developments--including modern theories of nucleation and the properties of supercooled and glassy water--are treated in detail. An introductory chapter illustrates, with numerous examples, the importance and ubiquity of metastable liquids. Examples include the ascent of sap in plants, the strategies adopted by many living organisms to survive prolonged exposure to sub-freezing conditions, the behavior of proteins at low temperatures, metastability in mineral inclusions, ozone depletion, the preservation and storage of labile biochemicals, and the prevention of natural gas clathrate hydrate formation. All mathematical symbols are defined in the text and key equations are clearly explained. More complex mathematical explanations are available in the appendixes.