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Author: Anton Bovier Publisher: Springer ISBN: 3319247778 Category : Mathematics Languages : en Pages : 578
Book Description
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.
Author: Anton Bovier Publisher: Springer ISBN: 3319247778 Category : Mathematics Languages : en Pages : 578
Book Description
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.
Author: Christof Schütte Publisher: American Mathematical Soc. ISBN: 0821843591 Category : Mathematics Languages : en Pages : 141
Book Description
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.
Author: Seiji Miyashita Publisher: Springer Nature ISBN: 9811966680 Category : Science Languages : en Pages : 260
Book Description
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.
Author: Pablo G. Debenedetti Publisher: Princeton University Press ISBN: 9780691085951 Category : Science Languages : en Pages : 432
Book Description
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.
Author: Stephen Z.D. Cheng Publisher: Elsevier ISBN: 0080558208 Category : Science Languages : en Pages : 325
Book Description
A classical metastable state possesses a local free energy minimum at infinite sizes, but not a global one. This concept is phase size independent. We have studied a number of experimental results and proposed a new concept that there exists a wide range of metastable states in polymers on different length scales where their metastability is critically determined by the phase size and dimensionality. Metastable states are also observed in phase transformations that are kinetically impeded on the pathway to thermodynamic equilibrium. This was illustrated in structural and morphological investigations of crystallization and mesophase transitions, liquid-liquid phase separation, vitrification and gel formation, as well as combinations of these transformation processes. The phase behaviours in polymers are thus dominated by interlinks of metastable states on different length scales. This concept successfully explains many experimental observations and provides a new way to connect different aspects of polymer physics.* Written by a leading scholar and industry expert* Presents new and cutting edge material encouraging innovation and future research* Connects hot topics and leading research in one concise volume
Author: Alexander V. Kolobov Publisher: John Wiley & Sons ISBN: 3527608664 Category : Science Languages : en Pages : 436
Book Description
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
Author: Sumiyoshi Abe Publisher: American Institute of Physics ISBN: 9780735404816 Category : Science Languages : en Pages : 370
Book Description
All papers have been peer-reviewed. This volume gives an updated overview of current interdisciplinary studies on complex systems and nonextensive statistical mechanics. It is an ideal starting point for scientists and graduate students who wish to enter the field. The book features a diverse collection of the latest research work not found in a single volume elsewhere. Among the highly regarded contributors to the volume are the 2004 Boltzmann medalist H. E. Stanley and numerous internationally renowned experts, such as S. Abe, P-H. Chavanis, C. Beck, G. Casati, D. Farmer, H. Herrmann, R. Mantegna, J. Naudts, A. Plastino, A Robledo, B. Spagnolo C. Tsallis and many others.
Author: Alice Wang Publisher: Springer Science & Business Media ISBN: 0387764720 Category : Technology & Engineering Languages : en Pages : 312
Book Description
This book is about various adaptive and dynamic techniques used to optimize processor power and performance. It is based on a very successful forum at ISSCC which focused on Adaptive Techniques. The book looks at the underlying process technology for adaptive designs and then examines different circuits, architecture and software that address the different aspects. The chapters are written by people both in academia and the industry to show the scope of alternative practices.
Author: Robert Bogdan Staszewski Publisher: John Wiley & Sons ISBN: 0470041943 Category : Technology & Engineering Languages : en Pages : 281
Book Description
A new and innovative paradigm for RF frequency synthesis and wireless transmitter design Learn the techniques for designing and implementing an all-digital RF frequency synthesizer. In contrast to traditional RF techniques, this innovative book sets forth digitally intensive design techniques that lead the way to the development of low-cost, low-power, and highly integrated circuits for RF functions in deep submicron CMOS processes. Furthermore, the authors demonstrate how the architecture enables readers to integrate an RF front-end with the digital back-end onto a single silicon die using standard ASIC design flow. Taking a bottom-up approach that progressively builds skills and knowledge, the book begins with an introduction to basic concepts of frequency synthesis and then guides the reader through an all-digital RF frequency synthesizer design: Chapter 2 presents a digitally controlled oscillator (DCO), which is the foundation of a novel architecture, and introduces a time-domain model used for analysis and VHDL simulation Chapter 3 adds a hierarchical layer of arithmetic abstraction to the DCO that makes it easier to operate algorithmically Chapter 4 builds a phase correction mechanism around the DCO such that the system's frequency drift or wander performance matches that of the stable external frequency reference Chapter 5 presents an application of the all-digital RF synthesizer Chapter 6 describes the behavioral modeling and simulation methodology used in design The final chapter presents the implementation of a full transmitter and experimental results. The novel ideas presented here have been implemented and proven in two high-volume, commercial single-chip radios developed at Texas Instruments: Bluetooth and GSM. While the focus of the book is on RF frequency synthesizer design, the techniques can be applied to the design of other digitally assisted analog circuits as well. This book is a must-read for students and engineers who want to learn a new paradigm for RF frequency synthesis and wireless transmitter design using digitally intensive design techniques.
Author: Anton Bovier
Author: Anton Bovier
Author: Christof Schütte
Author: Enzo Olivieri
Author: Seiji Miyashita
Author: Pablo G. Debenedetti
Author: Stephen Z.D. Cheng
Author: Alexander V. Kolobov
Author: Sumiyoshi Abe
Author: Alice Wang
Author: Robert Bogdan Staszewski