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The Nonlinear Universe

Author: Alwyn C. Scott

Publisher: Springer Science & Business Media

Published: 2007-10-02

Total Pages: 371

ISBN-13: 3540341536

Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.

The (1+ 1)-nonlinear Universe Of The Parabolic Map And Combinatorics

Author: James D Louck

Publisher: World Scientific

Published: 2014-12-30

Total Pages: 192

ISBN-13: 9814632430

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This monograph develops chaos theory from properties of the graphs inverse to the parabolic map of the interval [0, 2], where the height at the midpoint x = 1 may be viewed as a time-like parameter, which together with the x-coordinate, provide the two parameters that uniquely characterize the parabola, and which are used throughout the monograph. There is only one basic mathematical operation used: function composition. The functions studied are the n-fold composition of the basic parabola with itself. However, it is the properties of the graph inverse to this n-fold composition that are the objects whose properties are developed. The reflection symmetry of the basic parabola through the vertical line x = 1 gives rise to two symmetry classes of inverse graphs: the inverse graphs and their conjugates. Quite remarkably, it turns out that there exists, among all the inverse graphs and their conjugates, a completely deterministic class of inverse graphs and their conjugates. Deterministic in the sense that this class is uniquely determined for all values of the time-like parameter and the x-coordinate, the entire theory, of course, being highly nonlinear — it is polynomial in the time-like parameter and in the x-coordinate. The deterministic property and its implementation are key to the argument that the system is a complex adaptive system in the sense that a few axioms lead to structures of unexpected richness.This monograph is about working out the many details that advance the notion that deterministic chaos theory, as realized by a complex adaptive system, is indeed a new body of mathematics that enriches our understanding of the world around us. But now the imagination is also opened to the possibility that the real universe is a complex adaptive system.* deceased

Self-Organized Criticality in Astrophysics

Author: Markus Aschwanden

Publisher: Springer Science & Business Media

Published: 2011-01-11

Total Pages: 416

ISBN-13: 3642150012

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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.

Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Gravity and the Quantum

Author: Jasjeet Singh Bagla

Publisher: Springer

Published: 2017-03-01

Total Pages: 0

ISBN-13: 9783319516998

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This book provides a compilation of in-depth articles and reviews on key topics within gravitation, cosmology and related issues. It is a celebratory volume dedicated to Prof. Thanu Padmanabhan ("Paddy"), the renowned relativist and cosmologist from IUCAA, India, on the occasion of his 60th birthday. The authors, many of them leaders of their fields, are all colleagues, collaborators and former students of Paddy, who have worked with him over a research career spanning more than four decades. Paddy is a scientist of diverse interests, who attaches great importance to teaching. With this in mind, the aim of this compilation is to provide an accessible pedagogic introduction to, and overview of, various important topics in cosmology, gravitation and astrophysics. As such it will be an invaluable resource for scientists, graduate students and also advanced undergraduates seeking to broaden their horizons.

Nonlinear Psychoanalysis

Author: Robert M. Galatzer-Levy

Publisher: Taylor & Francis

Published: 2017-06-26

Total Pages: 272

ISBN-13: 1351970216

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Nonlinear concepts from chaos theory, complexity studies, and fractal geometry have transformed the way we think about the mind. Nonlinear Psychoanalysis shows how nonlinear dynamics can be integrated with psychoanalytic thinking to shed new light on psychological development, therapeutic processes, and fundamental psychoanalytic concepts. Starting with a personal history of the author’s engagement with nonlinear dynamics and psychoanalysis, this book describes how his approach applies to diagnosis of psychological conditions, concepts of normal and pathological development, gender, research methods, and finally the theory and practice of psychoanalysis and psychodynamic psychotherapy. This book is full of new ideas about the basic nonlinear processes of human development, nonlinear views of gender and fundamental psychoanalytic process like working through, and the nature of the therapeutic process as conceptualized in terms of the theory of coupled oscillators. Galatzer-Levy questions many standard psychoanalytic formulations and points to a freer practice of psychoanalysis and psychoanalytic thinking. His new approach opens the reader’s eyes to ways in which development and treatment can occur through processes not now included in standard psychoanalytic theory. The book not only provides useful theories but also helps readers take note of commonly passed over phenomena that were unseen for lack of a theory to explain them. Galatzer-Levy brings an unusual combination of training in psychiatry, psychoanalysis, and mathematics to this unique study, which summarizes his forty years of exploration of nonlinearity and psychoanalysis. Nonlinear Psychoanalysis will appeal to psychoanalysts and psychotherapists as well as students of nonlinear dynamics systems.

Structure Formation in the Universe

Author: T. Padmanabhan

Publisher: Cambridge University Press

Published: 1993

Total Pages: 504

ISBN-13: 9780521424868

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This text provides an up-to-date and pedagogical introduction to this exciting area of research.

Quest for the Origin of Particles and the Universe

Author: Yasumichi Aoki

Publisher: World Scientific

Published: 2013

Total Pages: 416

ISBN-13: 9814412325

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The Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI) was founded at Nagoya University in 2010 under the directorship of T Maskawa, in celebration of the 2008 Nobel Prize in Physics for M Kobayashi and T Maskawa, both who are alumni of Nagoya University. In commemoration of the new KMI building in 2011, the KMI Inauguration Conference (KMIIN) was organized to discuss perspectives of various fields OCo both theoretical and experimental studies of particle physics and astrophysics OCo as the main objectives of the KMI activity.This proceedings contains a welcome address by T Maskawa conveying his hopes for KMI to create new revolutionary directions in the spirit of Shoichi Sakata, a great mentor of both Maskawa and Kobayashi. Invited speakers, world-leading scientists in the fields, and the young scientists at KMI contributed to this volume containing theoretical studies of strongly coupled gauge theories in view of LHC phenomenology, string theory approach and lattice studies as well as hot/dense QCD system, and also super-symmetric GUT models, etc., together with experimental studies of LHC physics, B physics, neutrino physics and the related astrophysics and cosmology. The volume yields a unique synergy of particle physics and astrophysics, closely related to the main activity of KMI encompassing particle theory (including lattice computer simulations), particle physics experiments, cosmology, and astrophysics observations."

Nonlinear Dynamics

Author: Muthusamy Lakshmanan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 628

ISBN-13: 3642556884

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This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Plasmas in the Universe

Author: Società italiana di fisica

Publisher: IOS Press

Published: 2000-10-25

Total Pages: 528

ISBN-13: 1614992274

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This book illustrates new developments in the fields of space and solar physics, stellar physics, extragalactic physics and cosmology. It also elaborates upon the progress of laboratory plasma physics. One of the topics discussed is the existence of collective processes, both linear and non-linear, that can explain key elements of accretion physics, magnetic reconnection, the formation of ‘strange’ particle distributions, particle scattering phenomena, etc. Astrophysical plasma are dominated by turbulent or quasi-turbulent processes which interactively associate instabilities, radiation processes and plasma-wave scattering. The resulting scenario, which is outside thermodynamics and conventional statistical physics, is too difficult to describe theoretically, but today there are large-scale experiments and powerful computational tools allowing for the exploration of an almost similarly complex variety of phenomena. Several contributions to this book present indications of the influence of nonlinear phenomena in astrophysical applications. This work marks the fast growth of plasma astrophysics thanks to new observations in the high energy band of the spectrum on the one hand and the possibility of validating and bringing to light relevant new theories by increasingly sophisticated machines on the other.