How Nature Works

the science of self-organized criticality

Author: Per Bak

Publisher: Springer Science & Business Media

ISBN: 1475754264

Category: Mathematics

Page: 212

View: 9058

Self-organized criticality, the spontaneous development of systems to a critical state, is the first general theory of complex systems with a firm mathematical basis. This theory describes how many seemingly desperate aspects of the world, from stock market crashes to mass extinctions, avalanches to solar flares, all share a set of simple, easily described properties. "...a'must read'...Bak writes with such ease and lucidity, and his ideas are so intriguing...essential reading for those interested in complex will reward a sufficiently skeptical reader." -NATURE "...presents the theory (self-organized criticality) in a form easily absorbed by the non-mathematically inclined reader." -BOSTON BOOK REVIEW "I picture Bak as a kind of scientific musketeer; flamboyant, touchy, full of swagger and ready to join every fray... His book is written with panache. The style is brisk, the content stimulating. I recommend it as a bracing experience." -NEW SCIENTIST

Self-Organized Criticality

Emergent Complex Behavior in Physical and Biological Systems

Author: Henrik Jeldtoft Jensen

Publisher: Cambridge University Press

ISBN: 9780521483711

Category: Science

Page: 153

View: 1672

A clear and concise introduction to this new, cross-disciplinary field.

Self-Organized Criticality in Astrophysics

The Statistics of Nonlinear Processes in the Universe

Author: Markus Aschwanden

Publisher: Springer Science & Business Media

ISBN: 9783642150012

Category: Science

Page: 416

View: 3535

Markus Aschwanden introduces the concept of self-organized criticality (SOC) and shows that due to its universality and ubiquity it is a law of nature for which he derives the theoretical framework and specific physical models in this book. He begins by providing an overview of the many diverse phenomena in nature which may be attributed to SOC behaviour. The author then introduces the classic lattice-based SOC models that may be explored using numerical computer simulations. These simulations require an in-depth knowledge of a wide range of mathematical techniques which the author introduces and describes in subsequent chapters. These include the statistics of random processes, time series analysis, time scale distributions, and waiting time distributions. Such mathematical techniques are needed to model and understand the power-law-like occurrence frequency distributions of SOC phenomena. Finally, the author discusses fractal geometry and scaling laws before looking at a range of physical SOC models which may be applicable in various aspects of astrophysics. Problems, solutions and a glossary will enhance the pedagogical usefulness of the book. SOC has been receiving growing attention in the astrophysical and solar physics community. This book will be welcomed by students and researchers studying complex critical phenomena.

Self-Organized Criticality in Earth Systems

Author: Stefan Hergarten

Publisher: Springer Science & Business Media

ISBN: 3662043904

Category: Mathematics

Page: 272

View: 451

Self-organized criticality (SOC) has become a magic word in various scientific disciplines; it provides a framework for understanding complexity and scale invariance in systems showing irregular fluctuations. In the first 10 years after Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic appeared. Seismology has been a field in earth sciences where the SOC concept has already deepened the understanding, but there seem to be much more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader into the basics of fractals, chaos and SOC, the book presents established and new applications of SOC in earth sciences, namely earthquakes, forest fires, landslides and drainage networks.


Life at the Edge of Chaos

Author: Roger Lewin

Publisher: University of Chicago Press

ISBN: 9780226476551

Category: Science

Page: 234

View: 1886

Examines the field of complexity science, with sections focusing on how the discipline works within computer simulations, natural ecosystems, and various social systems.

Bak's Sand Pile

Strategies for a Catastrophic World

Author: Theodore Gyle Lewis

Publisher: N.A

ISBN: 9780983074502

Category: Emergency management

Page: 382

View: 2706

Did the terrorist attacks on the United States in 2001, the massive power blackout of 2003, Hurricane Katrina in 2005, and the Gulf oil spill of 2010 'just happen'-or were these shattering events foreseeable? Do such calamities in fact follow a predictable pattern? Can we plan for the unforeseen by thinking about the unthinkable?Ted Lewis explains the pattern of catastrophes and their underlying cause. In a provocative tour of a volatile world, he guides the reader through mega-fires, fragile power grids, mismanaged telecommunication systems, global terrorist movements, migrating viruses, volatile markets and Internet storms. Modern societies want to avert catastrophes, but the drive to make things faster, cheaper, and more efficient leads to self-organized criticality-the condition of systems on the verge of disaster. This is a double-edged sword. Everything from biological evolution to political revolution is driven by some collapse, calamity or crisis. To avoid annihilation but allow for progress, we must change the ways in which we understand the patterns and manage systems. Bak's Sand Pile explains how.

Self-Organised Criticality

Theory, Models and Characterisation

Author: Gunnar Pruessner

Publisher: Cambridge University Press

ISBN: 0521853354

Category: Science

Page: 494

View: 5196

An overview of results and methods, written for graduates and researchers in physics, mathematics, biology, sociology, finance, medicine and engineering.

At Home in the Universe

The Search for the Laws of Self-Organization and Complexity

Author: Stuart Kauffman

Publisher: Oxford University Press

ISBN: 019976185X

Category: Science

Page: 336

View: 5585

A major scientific revolution has begun, a new paradigm that rivals Darwin's theory in importance. At its heart is the discovery of the order that lies deep within the most complex of systems, from the origin of life, to the workings of giant corporations, to the rise and fall of great civilizations. And more than anyone else, this revolution is the work of one man, Stuart Kauffman, a MacArthur Fellow and visionary pioneer of the new science of complexity. Now, in At Home in the Universe, Kauffman brilliantly weaves together the excitement of intellectual discovery and a fertile mix of insights to give the general reader a fascinating look at this new science--and at the forces for order that lie at the edge of chaos. We all know of instances of spontaneous order in nature--an oil droplet in water forms a sphere, snowflakes have a six-fold symmetry. What we are only now discovering, Kauffman says, is that the range of spontaneous order is enormously greater than we had supposed. Indeed, self-organization is a great undiscovered principle of nature. But how does this spontaneous order arise? Kauffman contends that complexity itself triggers self-organization, or what he calls "order for free," that if enough different molecules pass a certain threshold of complexity, they begin to self-organize into a new entity--a living cell. Kauffman uses the analogy of a thousand buttons on a rug--join two buttons randomly with thread, then another two, and so on. At first, you have isolated pairs; later, small clusters; but suddenly at around the 500th repetition, a remarkable transformation occurs--much like the phase transition when water abruptly turns to ice--and the buttons link up in one giant network. Likewise, life may have originated when the mix of different molecules in the primordial soup passed a certain level of complexity and self-organized into living entities (if so, then life is not a highly improbable chance event, but almost inevitable). Kauffman uses the basic insight of "order for free" to illuminate a staggering range of phenomena. We see how a single-celled embryo can grow to a highly complex organism with over two hundred different cell types. We learn how the science of complexity extends Darwin's theory of evolution by natural selection: that self-organization, selection, and chance are the engines of the biosphere. And we gain insights into biotechnology, the stunning magic of the new frontier of genetic engineering--generating trillions of novel molecules to find new drugs, vaccines, enzymes, biosensors, and more. Indeed, Kauffman shows that ecosystems, economic systems, and even cultural systems may all evolve according to similar general laws, that tissues and terra cotta evolve in similar ways. And finally, there is a profoundly spiritual element to Kauffman's thought. If, as he argues, life were bound to arise, not as an incalculably improbable accident, but as an expected fulfillment of the natural order, then we truly are at home in the universe. Kauffman's earlier volume, The Origins of Order, written for specialists, received lavish praise. Stephen Jay Gould called it "a landmark and a classic." And Nobel Laureate Philip Anderson wrote that "there are few people in this world who ever ask the right questions of science, and they are the ones who affect its future most profoundly. Stuart Kauffman is one of these." In At Home in the Universe, this visionary thinker takes you along as he explores new insights into the nature of life.


The Emerging Science at the Edge of Order and Chaos

Author: Mitchell M. Waldrop

Publisher: Simon and Schuster

ISBN: 0671872346

Category: Mathematics

Page: 380

View: 7863

A look at the rebellious thinkers who are challenging old ideas with their insights into the ways countless elements of complex systems interact to produce spontaneous order out of confusion


A Deep Natural History of the Indian Subcontinent

Author: Pranay Lal

Publisher: Random House India

ISBN: 9385990365


Page: 384

View: 4624

Few places have been as influential as the Indian subcontinent in shaping the course of life on Earth. Yet its evolution has remained largely unchronicled. Indica: A Deep Natural History of the Indian Subcontinent fills this gap. From the oldest rocks, formed three billion years ago in Karnataka, to the arrival of our ancestors 50,000 years ago on the banks of the Indus, the author meticulously sifts through wide-ranging scientific disciplines and through the layers of earth to tell us the story of India, filled with a variety of fierce reptiles, fantastic dinosaurs, gargantuan mammals and amazing plants. Beautifully produced in full colour, with a rare collection of images, illustrations and maps, Indica is full of fascinating, lesser-known facts. It shows us how every piece of rock and inch of soil is a virtual museum, and how, over billions of years, millions of spectacular creatures have reproduced, walked and lived over and under it.

Energy, Information, Feedback, Adaptation, and Self-organization

The Fundamental Elements of Life and Society

Author: Spyros G Tzafestas

Publisher: Springer

ISBN: 3319669990

Category: Technology & Engineering

Page: 668

View: 1406

This unique book offers a comprehensive and integrated introduction to the five fundamental elements of life and society: energy, information, feedback, adaptation, and self-organization. It is divided into two parts. Part I is concerned with energy (definition, history, energy types, energy sources, environmental impact); thermodynamics (laws, entropy definitions, energy, branches of thermodynamics, entropy interpretations, arrow of time); information (communication and transmission, modulation–demodulation, coding–decoding, information theory, information technology, information science, information systems); feedback control (history, classical methodologies, modern methodologies); adaptation (definition, mechanisms, measurement, complex adaptive systems, complexity, emergence); and self-organization (definitions/opinions, self-organized criticality, cybernetics, self-organization in complex adaptive systems, examples in nature). In turn, Part II studies the roles, impacts, and applications of the five above-mentioned elements in life and society, namely energy (biochemical energy pathways, energy flows through food chains, evolution of energy resources, energy and economy); information (information in biology, biocomputation, information technology in office automation, power generation/distribution, manufacturing, business, transportation), feedback (temperature, water, sugar and hydrogen ion regulation, autocatalysis, biological modeling, control of hard/technological and soft/managerial systems), adaptation and self-organization (ecosystems, climate change, stock market, knowledge management, man-made self-organized controllers, traffic lights control).

Philosophy of Complex Systems

Author: N.A

Publisher: Elsevier

ISBN: 9780080931227

Category: Philosophy

Page: 952

View: 506

The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Dynamic Patterns

The Self-organization of Brain and Behavior

Author: J. A. Scott Kelso

Publisher: MIT Press

ISBN: 9780262611312

Category: Psychology

Page: 334

View: 5258

foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels -- from neurons to mind -- is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency.Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics.Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.

Toward a Unified Theory of Development

Connectionism and Dynamic Systems Theory Re-considered

Author: John P. Spencer,Michael S. C. Thomas,James L. McClelland

Publisher: Oxford University Press, USA


Category: Psychology

Page: 389

View: 498

This resource defines and refines two major theoretical approaches within developmental science that address the central issues of development-connectionism and dynamical systems theory.

Deterministic Abelian Sandpile Models and Patterns

Author: Guglielmo Paoletti

Publisher: Springer Science & Business Media

ISBN: 3319012045

Category: Science

Page: 163

View: 5380

The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters. The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site and not only ensemble average or coarse graining. Very complex and amazingly beautiful periodic patterns are often generated by the dynamics involved, especially in deterministic protocols in which the sand is added at chosen sites. For example, the author studies the appearance of allometric structures, that is, patterns which grow in the same way in their whole body, and not only near their boundaries, as commonly occurs. The local conservation laws which govern the evolution of these patterns are also presented. This work has already attracted interest, not only in non-equilibrium statistical mechanics, but also in mathematics, both in probability and in combinatorics. There are also interesting connections with number theory. Lastly, it also poses new questions about an old subject. As such, it will be of interest to computer practitioners, demonstrating the simplicity with which charming patterns can be obtained, as well as to researchers working in many other areas.

System Effects

Complexity in Political and Social Life

Author: Robert Jervis

Publisher: Princeton University Press

ISBN: 9781400822409

Category: Political Science

Page: 328

View: 3960

Based on more than three decades of observation, Robert Jervis concludes in this provocative book that the very foundations of many social science theories--especially those in political science--are faulty. Taking insights from complexity theory as his point of departure, the author observes that we live in a world where things are interconnected, where unintended consequences of our actions are unavoidable and unpredictable, and where the total effect of behavior is not equal to the sum of individual actions. Jervis draws on a wide range of human endeavors to illustrate the nature of these system effects. He shows how increasing airport security might actually cost lives, not save them, and how removing dead trees (ostensibly to give living trees more room) may damage the health of an entire forest. Similarly, he highlights the interconnectedness of the political world as he describes how the Cold War played out and as he narrates the series of events--with their unintended consequences--that escalated into World War I. The ramifications of developing a rigorous understanding of politics are immense, as Jervis demonstrates in his critique of current systemic theories of international politics--especially the influential work done by Kenneth Waltz. Jervis goes on to examine various types of negative and positive feedback, bargaining in different types of relationships, and the polarizing effects of alignments to begin building a foundation for a more realistic, more nuanced, theory of international politics. System Effects concludes by examining what it means to act in a system. It shows how political actors might modify their behavior in anticipation of system effects, and it explores how systemic theories of political behavior might account for the role of anticipation and strategy in political action. This work introduces powerful new concepts that will reward not only international relations theorists, but also all social scientists with interests in comparative politics and political theory.

Fractals, Chaos, Power Laws

Minutes from an Infinite Paradise

Author: Manfred Schroeder

Publisher: Courier Corporation

ISBN: 0486472043

Category: Science

Page: 448

View: 6971

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.

Proving Darwin

Making Biology Mathematical

Author: Gregory Chaitin

Publisher: Vintage

ISBN: 1400077982

Category: Science

Page: 123

View: 7576

A metamathematician best known for his discovery of the Omega number explains how Darwin's theory of evolution succeeds on a mathematic level and argues that no one can be certain about evolution without a proven mathematical theory. Original.