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Über dieses Buch

The concept of this book was developed during the Winter Seminar held in the Austrian mountains at the Alpengasthof Zeinisjoch, Tirol-Vorarlberg, from February 27 to March 3, 1988. Leading experts and advanced students in math­ ematics, physics, chemistry and computer science met to present and discuss their most recent results in an informal seminar. These were the circumstances that led to the idea of compiling some of the essential contributions presented at this seminar together with others describing basic features of "optimal struc­ tures in heterogeneous reaction systems". The aim of this book is to present the scientific results of the intensive work carried out in each of the specific fields of research. Each contribution therefore presents the current state of the art together with a deeper treatment enabling a more comprehensive understanding of that particular field of work. The common ideas which unite all the different contributions are already ex­ pressed in the title of this book. The nature of heterogeneous reaction systems is quite varied. An example is provided by the chemical systems such as noble metal particles which may act as heterogeneous catalysts for gaseous chemical compounds. Under these circumstances the metal particles and/or their sur­ faces may undergo phase transitions during reaction. Imbihl and Plath report on special catalytic systems of this kind, which are of industrial importance.



Modelling of Heterogeneously Catalyzed Reactions by Cellular Automata of Dimension Between One and Two

Experiments on the catalytic oxidation of CO on palladium supporting catalysts are modelled by the use of cellular automata. The discrete character of the models does not represent the molecular events, but reflects the microscopic origin of the macroscopic patterns that are observed. With one-dimensional automata it is mainly the temporal patterns of the oscillating reaction that can be modelled, whereas automata with a fractal dimension between one and two are used to study spatial pattern formation on an idealized model for amorphous catalytic material.
P. J. Plath

The Study of Kinetic Oscillations in the Catalytic CO-Oxidation on Single Crystal Surfaces

In the past decade the study of non-equilibrium systems has attracted a great deal of interest as more and more mathematical tools and theoretical concepts have been developed to try to understand the complex dynamical behavior of these systems. Although the prototype of such a chemical reaction system is still the Belousov-Zabotinskii (BZ)-reaction which takes place in the homogeneous fluid phase, there have also been numerous investigations of kinetic oscillations in heterogeneously catalyzed reactions amongst which the catalytic CO-oxidation has attracted most interest [1,2]. This can be attributed to the simplicity of the chemistry CO+1/2O2→CO2: However, despite numerous studies, reviewed recently by Schmitz [2] there still exists no commonly accepted mechanism among the different models which have been proposed.
R. Imbihl

Optimization of Heterogeneous-Catalyst Structure: Simulations and Experiments with Fractal and Non-Fractal Systems

We explore the effects that the geometric details of heterogeneous catalysts have on their performance, in order to suggest guide-lines for the design of catalysts with optimal structures. The following geometric parameters are investigated: (a) The (fractal and non-fractal) distribution pattern of surface active sites; (b) the particle size of the catalyst; (c) the surface fractal dimension; (d) the average pore size.
D. Avnir, O. Citri, D. Farin, M. Ottolenghi, J. Samuel, A. Seri-Levy

Reaction Kinetics in Disordered Systems: Hierarchical Models

We investigate diffusion-limited reactions of the types A + A → 0 and A + B → 0 in disordered systems by modelling the dynamics through random walks. By introducing hierarchical structures, two aspects of disorder are considered: (a) temporal and (b) energetic. The temporal disorder is accounted for by continuous time random walks (CTRW), whose waiting times distribution displays long time tails. The energetic disorder is modelled using ultrametric spaces (UMS) with hierarchically distributed energy barriers. We discuss the interplay between these two disorder aspects in terms of subordination.
G. Zumofen, A. Blumen, J. Klafter

Optimization and Complexity in Molecular Biology and Physics

Many optimization problems in physics and biology lead to highly rugged cost functions. The most important examples come from the theory of spin glasses and from biological evolution. During the last decade new algorithms were developed in order to deal with such complex systems. Two techniques — known as simulated annealing and genetic algorithms — are applied to study the optimization of polynucleotide replication. Ruggedness of value landscapes in evolutionary optimization has its origin in the complexity of genotype-phenotype-relations. Folding of RNA molecules into spatial structures represents an example of a complex relation which is particularly important in virology and cell metabolism. A model of polynucleotide folding and optimization of replication rates through mutation and selection is presented and discussed. It enables us to extend the concepts of conventional population genetics into the realm of frequent mutations.
P. Schuster

Explicit Observers

A new approach to the brain and the world is presented. A chaotic Hamiltonian universe is set up, in 1 D, such that an explicit internal observer — an excitable system — becomes amenable to complete understanding. The Gibbs symmetry and the Wigner symmetry, when taken into explicit regard, imply that to this observer, his world appears quite different from what one would expect at first sight — such as when one is doing a molecular dynamics simulation of the same system, for example. Specifically, both stochastic mechanics and the quantum nonlorcality turn out to be formal implications of the present “deterministic local hidden variables” approach to quantum mechanics — despite the fact that it never was an approach to quantum mechanics in the first place. Bell’s well-known impossibility theorem is circumvented because all quantum effects arising are nonexistent objectively. They are valid only within the “interface” that develops internally between the observer and his world. For the first time, the Kantian notion that the world is objectively different from the way we perceive it can be demonstrated — not for our own world, but for a lower-level model world as it appears to an artificial observer living inside.
O. E. Rössler

Dynamics of Networks and Pattern Processing

The dynamics of networks is closely connected with the development of the modern science of non-linear irreversible processes [1–6].
W. Ebeling, I. Schimansky-Geier, Ch. Zülicke

Synergetics Applied to Pattern Formation and Pattern Recognition

Synergetics is the study and analysis of complex systems which are composed of many subsystems. These systems show the ability to selforganize spontaneously on macroscopic scales, i.e. we may observe highly ordered spatial, temporal, or spatio-temporal structures on scales which are much larger than the corresponding characteristic scales of the subsystems. As a result, we conclude that there must be very many subsystems coherently involved in order to produce these highly regular states on characteristic scales of the composed system. Synergetics offers a unified viewpoint to the emergence of such patterns and the underlying processes. Furthermore, powerful mathematical methods have been developed in this field to understand and predict the spontaneous occurrence of order, qualitatively as well as quantitatively.
M. Bestehorn, R. Friedrich, A. Fuchs, H. Haken, A. Kuhn, A. Wunderlin


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