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Self-organised criticality : theory, models, and characterisation

Author: Gunnar Pruessner
Publisher: Cambridge ; New York : Cambridge University Press, 2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"Giving a detailed overview of the subject, this book takes in the results and methods that have arisen since the term 'self-organised criticality' was coined twenty years ago. Providing an overview of numerical and analytical methods, from their theoretical foundation to the actual application and implementation, the book is an easy access point to important results and sophisticated methods. Starting with the
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Pruessner, Gunnar, 1973-
Self-organised criticality.
Cambridge, UK ; New York : Cambridge University Press, 2012
(DLC) 2011023678
(OCoLC)664324535
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gunnar Pruessner
ISBN: 9781139525602 1139525603 9780511977671 0511977670 9781139527996 1139527991
OCLC Number: 810924644
Description: 1 online resource.
Contents: Cover; Self-Organised Criticality: Theory, Models and Characterisation; Title; Copyright; Dedication; Contents; Tables; Foreword by Henrik J. Jensen; Preface; Style; Structure; Keywords, notes and indices; Numerics; Acknowledgments; Symbols; PART I: INTRODUCTION; 1: Introduction; 1.1 Reviews; 1.2 Basic ingredients; 1.3 Basic observables and observations; 1.3.1 Simple scaling; 1.3.2 1/ f noise; 1.3.3 Edge of chaos; 1.3.4 The signature of SOC; 1.4 Universality; 1.4.1 Universal quantities; 1.4.2 Universality classes of SOC; 2: Scaling; 2.1 Distribution functions; 2.1.1 Upper and lower cutoffs. 2.1.2 Scaling function2.1.2.1 Apparent exponent; 2.1.2.2 Constraints; 2.1.2.3 The bump; 2.1.3 Two examples; 2.2 Moments; 2.2.1 Moment ratios; 2.2.2 Joint distributions and conditional moments; 2.2.3 Moment and cumulant generating functions; 2.3 Algebraic correlations; 2.3.1 Coarse graining and block scaling; 2.4 Multiscaling; 3: Experiments and observations; 3.1 Granular media; 3.2 Superconductors; 3.2.1 Superfluid helium; 3.3 Barkhausen effect; 3.3.1 Mechanical instabilities; 3.4 Earthquakes; 3.5 Evolution; 3.6 Neural networks; 3.7 Other systems; 3.7.1 Meteorology; 3.7.2 High energy physics. 3.7.3 Ecology, epidemiology and population dynamics3.7.4 Physiology; 3.7.5 Financial markets, sociology and psychology; 3.7.6 Virtual, electrical and data networks; 3.8 A very brief conclusion; PART II: MODELS AND NUMERICS; 4: Deterministic sandpiles; 4.1 The BAK-TANG-WIESENFELD Model; 4.1.1 Higher dimensions; 4.1.2 The Abelian symmetry; 4.2 Dhar's Abelian Sandpile Model; 4.2.1 Operator approach to the ASM; 4.2.2 Analytical results for the two-dimensional Abelian BTW Model; 4.2.3 A directed sandpile; 4.2.4 Numerical results; 4.3 The ZHANG Model; 4.3.1 Relation to the BTW Model. 4.3.2 Non-Abelian dynamics4.3.3 Energy histogram; 4.3.4 Analytical approaches; 4.3.5 Numerical results; 5: Dissipative models; 5.1 The BAK-CHEN-TANG Forest Fire Model; 5.1.1 Critique; 5.2 The DROSSEL-SCHWABL Forest Fire Model; 5.2.1 Double separation of time scales; 5.2.2 Lack of scaling in the two-dimensional DS-FFM; 5.2.3 Analytical approaches; 5.2.4 Physical relevance; 5.2.5 Numerical methods; 5.2.5.1 Numerical results; 5.3 The OLAMI-FEDER-CHRISTENSEN Model; 5.3.1 Non-conservation; 5.3.1.1 Average avalanche size; 5.3.1.2 Marginal phase locking.
Responsibility: Gunnar Pruessner.
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An overview of results and methods, written for graduates and researchers in physics, mathematics, biology, sociology, finance, medicine and engineering.  Read more...

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schema:description"Cover; Self-Organised Criticality: Theory, Models and Characterisation; Title; Copyright; Dedication; Contents; Tables; Foreword by Henrik J. Jensen; Preface; Style; Structure; Keywords, notes and indices; Numerics; Acknowledgments; Symbols; PART I: INTRODUCTION; 1: Introduction; 1.1 Reviews; 1.2 Basic ingredients; 1.3 Basic observables and observations; 1.3.1 Simple scaling; 1.3.2 1/ f noise; 1.3.3 Edge of chaos; 1.3.4 The signature of SOC; 1.4 Universality; 1.4.1 Universal quantities; 1.4.2 Universality classes of SOC; 2: Scaling; 2.1 Distribution functions; 2.1.1 Upper and lower cutoffs."@en
schema:description""When Bak, Tang, and Wiesenfeld (1987) coined the term Self-Organised Criticality (SOC), it was an explanation for an unexpected observation of scale invariance and at the same time, a programme of further research. Over the years it developed into a subject area which is concerned mostly with the analysis of computer models that display a form of generic scale invariance. The primacy of the computer model is manifest in the first publication and throughout the history of SOC, which evolved with and revolved around such computer models. That has led to a plethora of computer 'models', many of which are not intended to model much except themselves (also Gisiger, 2001), in the hope that they display a certain aspect of SOC in a particularly clear way. The question whether SOC exists is empty if SOC is merely the title for a certain class of computer models. In the following, the term SOC will therefore be used in its original meaning (Bak et al, 1987), to be assigned to systems with spatial degrees of freedom [which] naturally evolve into a self-organized critical point. Such behaviour is to be juxtaposed to the traditional notion of a phase transition, which is the singular, critical point in a phase diagram, where a system experiences a breakdown of symmetry and long-range spatial and in non-equilibrium, also temporal correlations, generally summarised as (power law) scaling (Widom, 1965a, b; Stanley, 1971)"--"@en
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