This collection of articles introduces the idea of a hierarchical order in chaotic systems and natural phenomena. To understand nature, nonlinear sciences use a multidisciplinary perspective. Therefore the book integrates research work of different fields: experimental evidence for the theory drawn from physics, biology and chemistry; theoretical progress in mathematical treatment, numerical techniques and graphical methods of nonlinear sciences; and to not-yet-understood philosophical and fundamental problems related to chaos and cosmos, chaos and quantum mechanics or evolutionary dynamics. Featuring the most recent advances in nonlinear dynamics this collection should provide an indispensable reference source and starting point for further research concerning dynamical and hierarchical chaotic systems. Besides this book is in honor of Professor O E Rössler, one of the pioneers of Chaos Theory, who celebrated his 50th birthday in May 1990.

In this vital new study, Andrew Abbott presents a fresh and daring analysis of the evolution and development of the social sciences. Chaos of Disciplines reconsiders how knowledge actually changes and advances. Challenging the accepted belief that social sciences are in a perpetual state of progress, Abbott contends that disciplines instead cycle around an inevitable pattern of core principles. New schools of thought, then, are less a reaction to an established order than they are a reinvention of fundamental concepts. Chaos of Disciplines uses fractals to explain the patterns of disciplines, and then applies them to key debates that surround the social sciences. Abbott argues that knowledge in different disciplines is organized by common oppositions that function at any level of theoretical or methodological scale. Opposing perspectives of thought and method, then, in fields ranging from history, sociology, and literature, are to the contrary, radically similar; much like fractals, they are each mutual reflections of their own distinctions.

Chaos, catastrophe, self-organization, and complexity theories (nonlinear dynamics) now have practical and measurable roles in the functioning of work organizations. Managing Emergent Phenomena begins by describing how the concept of an organization has changed from a bureaucracy, to a humanistic and organic system, to a complex adaptive system. The dynamics concepts are then explained along with the most recent research methods for analyzing real data. Applications include: work motivation, personnel selection and turnover, creative thinking by individuals and groups, the development of social networks, coordination in work groups, the emergence of leaders, work performance in organizational hierarchies, economic problems that are relevant to organizations, techniques for predicting the future, and emergency management. Each application begins with a tight summary of standard thinking on a subject, followed by the new insights that are afforded by nonlinear dynamics and the empirical data supporting those ideas. Unusual concepts are also encountered, such as the organizational unconscious, collective intelligence, and the revolt of the slaved variables. The net results are a new perspective on what is really important in organizational life, original insights on familiar experiences, and some clear signposts for the next generation of nonlinear social scientists.

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never been published elsewhere. The manuscript has now been edited by Christophe Letellier - involved in chaos theory for almost three decades himself, as well as being active in the history of sciences - with a minimum of changes to the original text. Finally released for the benefit of specialists and non-specialists alike, this book is equally interesting from the historical and the scientific points of view: an unconventionally modern approach to chaos theory, it can be read as a classic introduction and short monograph as well as a collection of original insights into advanced topics from this field.

Identitarians and others making up the European resistance lack a doctrine that truly serves as a political and ideological synthesis of who they are - a doctrine that speaks above parties and sects, above rival sensibilities and wounded feelings, that brings the resistance together around clear ideas and objectives, uniting them in opposition to the Europeans' dramatic decline. Our people today face the gravest peril in their entire history: demographic collapse, submission to an alien colonisation and to Islam, the bastardisation of the European Union, prostration before American hegemony, the forgetting of our cultural roots, and so on. In the form of an introductory text and a dictionary of 177 key words, Guillaume Faye, one of the most creative writers of the European 'Right', makes a diagnosis of the present situation and proposes a program of resistance, reconquest, and regeneration. He holds out the prospect of a racial and revolutionary alternative to the present decayed civilisation. The manifesto's principal objective is thus to unify the resistance by developing a common doctrine that unites everyone and every tendency seeking to constitute a European network of resistance - a doctrine that goes beyond the old sectarian quarrels and superficial divisions. All relevant subjects, including politics, economics, geopolitics, demographics, and biology are broached. As it was for the Nineteenth-century Left with Marx's Communist Manifesto, Why We Fight is destined to become the key work for Twenty-first century identitarians. This edition of Why We Fight contains the complete text of the original French edition, as well as additional material that was added for the German edition. Also included is an original Foreword by translator Michael O'Meara, author of New Culture, New Right, as well as a Foreword by Dr. Pierre Krebs, Chairman of the Thule-Seminar in Germany. With a doctorate in political science from Paris' Institute of Political Science, the essayist Guillaume Faye was one of the principal theoreticians of the French Nouvelle Droite in the 1970s and '80s prior to his growing sympathy for the identitarian movement. He has also been a journalist at Figaro-Magazine, Paris-Match, Magazine-Hebdo, Valeurs Actuelles, and a radio commentator. For several years he was the editor of J'ai tout compris (I Understood Everything), a private newsletter.

Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.

This book presents the construction of an asymptotic technique for solving the Liouville equation, which is to some degree an analogue of the Enskog-Chapman technique for solving the Boltzmann equation. Because the assumption of molecular chaos has been given up at the outset, the macroscopic variables at a point, defined as arithmetic means of the corresponding microscopic variables inside a small neighborhood of the point, are random in general. They are the best candidates for the macroscopic variables for turbulent flows. The outcome of the asymptotic technique for the Liouville equation reveals some new terms showing the intricate interactions between the velocities and the internal energies of the turbulent fluid flows, which have been lost in the classical theory of BBGKY hierarchy.

This book provides a good coverage of the recent developments and future directions in the study of dissipative systems. The primary thrust here is in exposing the reader to the frontiers of chaos, pointing out clues for further work in nonlinear science. With the aid of various types of mappings, the collapse of tori is investigated. The book contains much valuable introductory material and copious reference lists. Some notes on the historical development of the subject are interspersed in this volume.

Biomateriomics is the holistic study of biological material systems. While such systems are undoubtedly complex, we frequently encounter similar components -- universal building blocks and hierarchical structure motifs -- which result in a diverse set of functionalities. Similar to the way music or language arises from a limited set of music notes and words, we exploit the relationships between form and function in a meaningful way by recognizing the similarities between Beethoven and bone, or Shakespeare and silk. Through the investigation of material properties, examining fundamental links between processes, structures, and properties at multiple scales and their interactions, materiomics explains system functionality from the level of building blocks. Biomateriomics specifically focuses the analysis of the role of materials in the context of biological processes, the transfer of biological material principles towards biomimetic and bioinspired applications, and the study of interfaces between living and non-living systems. The challenges of biological materials are vast, but the convergence of biology, mathematics and engineering as well as computational and experimental techniques have resulted in the toolset necessary to describe complex material systems, from nano to macro. Applying biomateriomics can unlock Nature’s secret to high performance materials such as spider silk, bone, and nacre, and elucidate the progression and diagnosis or the treatment of diseases. Similarly, it contributes to develop a de novo understanding of biological material processes and to the potential of exploiting novel concepts in innovation, material synthesis and design.