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.

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.

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

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.

Carl Sagan once noted that there is only one generation that gets to see things for the first time. We are in the midst of such a time right now, standing on the threshold of discovery in the young and remarkable field of X-ray astronomy. In The Restless Universe, astronomer Eric Schlegel offers readers an informative survey of this cutting-edge science. Two major space observatories launched in the last few years--NASA's Chandra and the European Newton--are now orbiting the Earth, sending back a gold mine of data on the X-ray universe. Schlegel, who has worked on the Chandra project for seven years, describes the building and launching of this space-based X-ray observatory. But the book goes far beyond the story of Chandra. What Schlegel provides here is the background a nonscientist would need to grasp the present and follow the future of X-ray astronomy. He looks at the relatively brief history of the field, the hardware used to detect X-rays, the satellites--past, present, and future--that have been or will be flown to collect the data, the way astronomers interpret this data, and, perhaps most important, the insights we have already learned as well as speculations about what we may soon discover. And throughout the book, Schlegel conveys the excitement of looking at the universe from the perspective brought by these new observatories and the sharper view they deliver. Drawing on observations obtained from Chandra, Newton, and previous X-ray observatories, The Restless Universe gives a first look at an exciting field which significantly enriches our understanding of the universe.

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

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 — both theoretical and experimental studies of particle physics and astrophysics — 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.

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

This advanced textbook provides an up-to-date and comprehensive introduction to the very active field of structure formation in cosmology. It is written by eleven world-leading authorities. Written in a clear and pedagogical style appropriate for graduate students in astronomy and physics, this textbook introduces the reader to a wide range of exciting topics in contemporary cosmology: from recent advances in redshift surveys, to the latest models in gravitational lensing and cosmological simulations. The authors are all world-renowned experts both for their research and teaching skills. In the fast-moving field of structure formation, this book provides advanced undergraduate and graduate students with a welcome textbook which unites the latest theory and observations.