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.

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.

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

Vol. 1. I. Introduction -- II. Review of the standard 123 theory -- III. Grand unification -- IV. SO(10) -- V. Exceptional unification -- VI. Reality and complexity of the world -- VII. Proton decay -- VIII. Family problem and orthogonal unification -- IX. Fermion mass hierarchy -- Vol. 2. X.A short course in cosmology -- XI. Genesis of matter -- XII. Introduction to the theory of galaxy formation -- XIII. Neutrinos and galaxies -- XIV. Monopoles and inflation -- XV. Hierarchy, technicolor, supersymmetry, and variations -- XVI. Invisible axions -- XVII. Composite quarks and leptons -- XVIII. Gravity and grand unification

The Young Universe presents four major physical and astrophysical themes related to these extreme phases of the primordial universe. In particular, it presents the physics of the primordial plasma and the concepts of quantum and particle physics necessary to describe this extreme state. It discusses the cosmological background radiation and explores inflation, an extremely rapid expansion phase that is believed to have occurred very early in cosmological history and to have shaped our present universe. The book also provides a synthesis of the dark matter problem.

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.

The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the Einstein-Vlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.