Synergetics Of Molecular Systems

Synergetics is the quantitative study of multicomponent systems that exhibit nonlinear dynamics and cooperativity. This book specifically considers basic models of the nonlinear dynamics of molecular systems and discusses relevant applications in biological physics and the polymer sciences. Emphasis is placed on specific solutions to the dynamical equations that correspond to the coherent formation of spatial-temporal structures, such as solitons, kinks and breathers, in particular. The emergence of these patterns in molecular structures provides a variety of information on their structural properties and plays a significant part in energy transfer processes, topological defects, dislocations, and related structure transitions. Real media, in which solitons take the form of solitary waves, are also considered. In this context, the formation of nonlinear waves in a continuous medium described by nonlinear equations is associated with spontaneous breaking of the local symmetry of the homogeneous system, which produces a range of interesting phenomena. A particular feature of this text is its combination of analytic and computational strategies to tackle difficult nonlinear problems at the molecular level of matter.

This book addresses both multi robot systems and miniaturization to the nanoscale from a unifying point of view, but without leaving aside typical particularities of either. The unifying aspect is based on the concept of information minimization whose precise formulation is the Haken-Levi-principle. The authors introduce basic concepts of multi-component self-organizing systems such as order parameters (well known from equilibrium and non-equilibrium phase transitions) and the slaving principle (which establishes a link to dynamical systems). Among explicit examples is the docking manoeuvre of two robots in two and three dimensions. The second part of the book deals with the rather recently arising field of molecular robotics. It is particularly here where nature has become a highly influential teacher for the construction of robots. In living biological cells astounding phenomena occur: there are molecules (proteins) that literally walk on polymer strands and transport loads that are heavier than their carriers, or molecules that, by joint action, contract muscles. The book provides the reader with an insight into these phenomena, especially by a detailed theoretical treatment of the molecular mechanism of muscle contraction. At the molecular level, for an appropriate approach the use of quantum theory is indispensable. The authors introduce and use it in a form that avoids all the clumsy calculations of wave-functions. They present a model which is based on an elementary version of quantum field theory and allows taking into account the impact of the surrounding on the quantum mechanical activity of a single molecule. By presenting explicit and pedagogical examples, the reader gets acquainted with the appropriate modelling of the walking behaviour of single molecular robots and their collective behaviour. The further development of multi-robot systems and particularly of molecular robots will require the cooperation of a variety of disciplines. Therefore the book appeals to a wide audience including researchers, instructors, and advanced graduate students.

This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.

At a first glance the reader of this book might be puzzled by the variety of its topics which range from phase-transition-like phenomena of chemical reactions, lasers and electrical currents to biological systems, like neuron networks and membranes, to population dynamics and socio­ logy. When looking more closely at the different subjects the reader will recognize, however, that this book deals with one main problem: the behaviour of systems which are composed of many elements of one or a few kinds. We are sure the reader will be surprised in the same way as the participants of a recent symposium on synergetics, who recognized that such systems have amazingly common features. Though the subsystems (e. g. electrons, cells, human beings) are quite different in nature, their joint action is governed by only a few principles which lead to strikingly similar phenomena. It hardly needs to be mentioned that once such common principles are established, they are of an enormous stimulus and help for future research. Though the articles of this book are based on invited papers given at the first International Symposium on Synergetics at Schlof. l. Elmau from April 30 to May 6, 1972, it differs from usual conference proceedings in a distinct way. The authors and subjects were chosen from the very beginning so that fmally a well organized total book arises. We hope that the reader will feel the same pleasure and enthusiasm the participants at the symposium had.

The spontaneous formation of well organized structures out of germs or even out of chaos is one of the most fascinating phenomena and most challenging problems scientists are confronted with. Such phenomena are an experience of our daily life when we observe the growth of plants and animals. Thinking of much larger time scales, scientists are led into the problems of evolution, and, ultimately, of the origin of living matter. When we try to explain or understand in some sense these extremely complex biological phenomena it is a natural question, whether pro cesses of self-organization may be found in much simpler systems of the un animated world. In recent years it has become more and more evident that there exist numerous examples in physical and chemical systems where well organized spatial, temporal, or spatio-temporal structures arise out of chaotic states. Furthermore, as in living of these systems can be maintained only by a flux of organisms, the functioning energy (and matter) through them. In contrast to man-made machines, which are to exhibit special structures and functionings, these structures develop spon devised It came as a surprise to many scientists that taneously-they are self-organizing. numerous such systems show striking similarities in their behavior when passing from the disordered to the ordered state. This strongly indicates that the function of such systems obeys the same basic principles. In our book we wish to explain ing such basic principles and underlying conceptions and to present the mathematical tools to cope with them.

This proceedings volume contains talks and poster presentations from the International Symposium "Self-Organization in Complex Systems: The Past, Present, and Future of Synergetics", which took place at Hanse-Wissenschaftskolleg, an Institute of Advanced Studies, in Delmenhorst, Germany, during the period November 13 - 16, 2012. The Symposium was organized in honour of Hermann Haken, who celebrated his 85th birthday in 2012. With his fundamental theory of Synergetics he had laid the mathematical-physical basis for describing and analyzing self-organization processes in a diversity of fields of research. The quest for common and universal principles of self-organization in complex systems was clearly covered by the wide range of interdisciplinary topics reported during the Symposium. These extended from complexity in classical systems and quantum systems over self-organisation in neuroscience even to the physics of finance. Moreover, by combining a historical view with a present status report the Symposium conveyed an impression of the allure and potency of this branch of research as well as its applicability in the future.

Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifica tion schemes. The draw upon widely different sections of mathematics.

Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifica tion schemes. The draw upon widely different sections of mathematics.