10 edition of **Chaos and coarse graining in statistical mathematics** found in the catalog.

- 17 Want to read
- 9 Currently reading

Published
**2008**
by Cambridge University Press in New York
.

Written in English

- Chaotic behavior in systems,
- Dynamics,
- Statistical mechanics,
- Mathematical statistics

**Edition Notes**

Includes bibliographical references and index.

Statement | Patrizia Castigilione ... [et al.]. |

Contributions | Castiglione, Patrizia, 1968- |

Classifications | |
---|---|

LC Classifications | QC174.8 .C475 2008 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL16727756M |

ISBN 10 | 9780521895934 |

LC Control Number | 2008013430 |

Don't show me this again. Welcome! This is one of over 2, courses on OCW. Find materials for this course in the pages linked along the left. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.. No enrollment or registration. DOI: /bjps/axy Corpus ID: Asymmetry, Abstraction, and Autonomy: Justifying Coarse-Graining in Statistical Mechanics @article{RobertsonAsymmetryAA, title={Asymmetry, Abstraction, and Autonomy: Justifying Coarse-Graining in Statistical Mechanics}, author={Katie Robertson}, journal={The British Journal for the Philosophy of .

The coarse-graining also modifies the time-step between applications of the rule that is then applied to the coarse-grained system, effectively skipping through some of the states. For each of Wolfram's cellular automata, Goldenfeld and Israeli explored the consequences of a large number of possible coarse grainings. This book begins with the entropy of a state and through the entropy of coarse graining it proceeds to the quantum dynamical entropy. A bunch of topics shows the direct physical relevance of the entropy methods. The math ematical formalism is based on operator theory and mostly the language of operator algebras is used.

An aggregated or ‘coarse-grained’ Markov chain (in discrete time and on a finite state-space) is a special case of a hidden Markov model, a type of model well known in the statistics literature and extensively applied in a wide variety of time-series or similar analyses. ‘Coarse-graining’ is a standard method of extracting a simple Markov process from a more complicated one by identifying states. We extend coarse-graining to open Markov processes. An ‘open’ Markov process is one where probability can flow in .

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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 by: Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical Chaos and coarse graining in statistical mathematics book 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.5/5(1).

Chaos and Coarse Graining in Statistical Mechanics on *FREE* shipping on qualifying offers.5/5(1). In addition, the authors also discuss the relevance that many degrees of freedom, coarse-graining procedure, and instability mechanisms, have in justifying a statistical description of macroscopic bodies.

The book introduces the tools to characterize the non- asymptotic behaviors of chaotic systems. A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Chaos and coarse graining in statistical mathematics / Patrizia Castigilione [et al.].

Basic concepts of dynamical systems theory; 2. Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond; 3. Coarse graining, entropies and Lyapunov exponents at work; 4. Foundation of the statistical mechanics and dynamical systems; 5.

On the origin of irreversibility; 6. The role of chaos in non-equilibrium statistical mechanics; 7. Coarse-graining. Mathematics and Statistics Department Faculty Publication Series. Title. Numerical and statistical methods for the coarse-graining of many-particle stochastic systems.

Authors. MA Katsoulakis, University of Massachusetts - Amherst Follow P Plechac L Rey-Bellet. Publication Date. Journal or Book Title.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer.

How can a reversible micro-description be adapted to the dissipative macroscopic model. These crucial questions, as well as many other related problems, are discussed in this book. Mathematics and Statistics Department Faculty Publication Series. Title. Numerical and statistical methods for the coarse-graining of many-particle stochastic systems.

Authors. MA Katsoulakis, P Plechac L Rey-Bellet, University of Massachusetts - Amherst Follow. Publication Date. Journal or Book Title. Coarse graining technology is one of the important methods to study large-scale complex networks currently.

Here, we propose a generalized-degree-based coarse graining (GDCG) approach to extract respectively the undirected or directed coarse-grained networks by merging the nodes with same or similar generalized degree. Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form.- Coarse-Graining and Ideas of Statistical Physics.- Basic Types of Coarse-Graining.- Renormalization Group Methods for Coarse-Graining of Evolution Equations.- A Stochastic Process Behind Boltzmann's Kinetic Equation and Issues of Coarse Graining A reexamination is conducted of the 'coarse graining' concept in statistical physics, in view of the appearance of macroscopic chaos in dynamical systems and with attention to formal and physical aspects.

With respect to the formal aspect, chaos onset should be modeled after 'intrinsic coarsening', due to the limitation in self-evaluation.

The coarse graining procedure is designed such that it manifestly preserves the thermodynamic structure of the equations. The relevant thermodynamic structure and the coarse graining recipes suggested by statistical mechanics are described in detail and are illustrated by the example of hydrodynamics.

The book then moves on to explore the role of ergodicity and chaos for the validity of statistical laws.

The last part of the book is devoted to the treatment of problems characterized by the presence of more than one significant scale. In addition, the authors also discuss the relevance that many degrees of freedom, coarse graining procedure, and instability mechanisms, have in justifying a statistical.

Coarse Graining in Statistical Mechanicstqw darksiderg rapidshare hotfile megaupload, Chaos and Coarse Graining in Statistical Mechanicstqw darksiderg torrent download. I learned from Debra helped me learn a few insider tips on tools, and years of development observed in the same cream color as the winter months.

About the role of chaos and coarse graining in Statistical Mechanics Article in Physica A: Statistical Mechanics and its Applications May with 65.

School of Applied Mathematics and Physical Sciences. NTU, Athens, Greece. Coarse-Graining the Dynamics of (Pol. Chaos basis functions) Gfeller, D. & Rios, P. L., Spectral coarse graining and synchronization in oscillator networks.

Phys Rev Lett,() y. Newman, M. J., Finding community structure in networks using the. the collision integral is of order Nσ2×typical velocity thevolumeofthegas and the errors we introduced in the coarse-graining are of order Nσ3.

e.g., Nσ2 =cm2 (if N∼,σ∼10−8cm), then Nσ3 ∼10−ore, our approximation is good. Applied Mathematics and Computation, Vol. Issue. 4, p. Chaos and coarse-grainings in non equilibrium statistical mechanics, Springer-Verlag (to appear).

Chernov, N. and Lebowitz, J. () Stationary nonequilibrium states in () Generalized Markov coarse-graining and spectral decompositions of chaotic piecewise linear.

Mac Kernan, D. [] "Generalized Markov coarse graining and the observables of chaos," PhD thesis, Centre for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles. Google Scholar. Chaos and Coarse Graining in Statistical Mechanics.

by Patrizia Castiglione. As for all books authored by A. Vulpiani, this book is also excellent. The topics of this book are extremely deep and the authors render them justice. Maybe only for the pros, but absolutely a must-read.Chaos and Coarse Graining in Statistical Mechanics Patrizia Castiglione, Massimo Falcioni, Annick Lesne, Angelo Vulpiani Category: Thermodynamics, statistical physics.This book highlights the state-of-art in coarse-grained modeling of biomolecules, covering both fundamentals as well as various cutting edge applications.

Coarse-graining of biomolecules is an area of rapid advances, with numerous new force fields having appeared recently and significant progress made in developing a systematic theory of coarse.