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Microtubules, dynamic protein fibers of eukaryotic cells, can be formed by in vitro polymerization in aqueous solutions of the constituent protein tubulin. The kinetics of microtubule self-assembly can be studied by light or X-ray scattering and by video-enhanced light microscopy. While the first method records ensemble averages of microtubules, the latter allows observation of single microtubules. At conditions of overall microtubule formation, microtubules switch stochastically between phases of growth and phases of rapid shortening ("dynamic instability"). At high tubulin concentrations, length-excursions of the microtubules can be correlated, resulting in synchronous changes of microtubule assembly in time and space (oscillations, spatial patterns). First, a short review of the structure and biological functions of microtubules will be presented. Then, the dynamics of individual microtubules and collective phenomena in ensembles of large numbers of microtubules will be discussed. [ABSTRACT FROM AUTHOR]

Selforganisation in biology is a phenomenon of major interest, especially from a microbiological point of view. The question, how cells communicate to gather or to find their final destination in large associations of cells, like in mophogenesis, is not completely understood. In this paper a reinforced random walk is introduced and its approximating system of partial differential equations. Both models deal with selforganization of organisms due to an external stimulus. The first motivation to adress this question was the gliding and aggregation of starving myxobacteria Therefor in this paper the case is discussed, where the organisms do not only detect the signal but also modify the environment themselves in a strictly local manner. In Othmer and Stevens (1996) the related one dimensional models were analyzed. Here the two dimensional models will be discussed and compared to the former results. [ABSTRACT FROM AUTHOR]

Impurity breakdown induced current filamentation has been investigated in n-GaAs epitaxial layers applying a new method based on the quenching of photoluminescence in spatial regions of high free carrier density and using a laser scanning microscope. Well below breakdown an elevated free electron concentration in the vicinity of contacts, in the regime of relaxation oscillations lateral vibrations of the electron distribution, and above breakdown well developed filaments have been identified in samples with point contacts. In Corbino discs multifilamentary structures have been observed, demonstrating symmetry breaking and self-organization of current filamentation. Discontinuities and hysteresis in current-voltage characteristics at filamentary current flow, which are observed with practically all semiconductors at low temperatures, could clearly be attributed to a pinning of filaments and filament borders by material imperfections. [ABSTRACT FROM AUTHOR]

Experimental techniques for the investigation of spatial structure formation in semiconductor systems are limited in spatial resolution and will eventually change the intrinsic system behavior drastically. Scanning probe techniques can probably overcome these constraints. We present first experimental results of Low-temperature Scanning tunneling microscopy on current filaments in p-Germanium. Possible applications of related probe techniques are briefly discussed. [ABSTRACT FROM AUTHOR]

We investigate pattern formation by means of stochastic algorithms. We present three different approaches based on- i)Active Brownian particles- ii)Stochastic cellular automata- iii)master-equation approach We apply all three algorithms to a simple activator-inhibitor dynamics and show the emergence of spirals, moving and standing spots. The stochastic algorithms during the simulations were very stable and under some conditions faster than the numerical integration of their corresponding mean-field approximations. We also discuss several differences occurring due to the inclusion of fluctuations in the consideration. [ABSTRACT FROM AUTHOR]

We apply the thermodynamic formalism to discrete random walks on infinite lattices. This generalizes the case of the widely used finite Markov models. It is shown analytically that new scenarios for phase transitions become possible. Their relevance for the coding of fractals and chaotic systems is elaborated. [ABSTRACT FROM AUTHOR]

Dynamically generated multifractal measures are a generic model for the observation of fractal structures in nature. We investigate the effects obtained from the superposition of such structures. In our approach, this problem is discussed from the generalised entropy point of view. In the limit of a large number of systems contributing to the superposition, a universal entropy function is obtained. We discuss explicitly all commonly measured specific fluctuation spectra. We show that the generic existence of second order phase transitions manifests in stopping points of specific entropy functions. This yields new explanations for different phenomena which are observed in the fluctuation spectra obtained from experimental systems. [ABSTRACT FROM AUTHOR]

Many combinatorial optimization problems in industry can be reduced to a so-called assignment problem. This assignment problem can be handled by an adapted form of the nonlinear differential equations which are used to model the macroscopic behavior of complex physical systems. To get the necessary adaption specific coupling terms are used to result in a suitable selection and feasible solutions as stable points of the dynamical system. In comparison to many other methods this approach has the advantage that additional constraints of the optimization problem can easily be considered. Furthermore, parallel hardware realizations of this approach are possible because of the similarity to models of complex physical and chemical systems. A realization with coupled chemical reaction cells is suggested in this paper. [ABSTRACT FROM AUTHOR]

We investigate the generalized Rössler system introduced by Baier and Sahle. They have linearly coupled additional degrees of freedom to the original Rössler system, in order to construct a set of equations which shows maximum instability at arbitrary dimension N, i.e., N — 2 positive Lyapunov exponents. We present a transformation into a mode picture. It enables a qualitative understanding of the mechanism generating the dynamics of this complex system. The advantages of our approach are demonstrated for the exemplary case N=5. [ABSTRACT FROM AUTHOR]

We present a novel technique for stabilizing unstable periodic orbits of chaotic systems. It uses a continuous feedback loop in the form of the difference between an actual and a delayed output signal of the system with a variable delay time. This time is chosen to be equal to the interval between the last and the k-th previous maximum of the output signal and is changed at every k-th maximum. During the procedure, the delay time asymptotically tends to the period of the period-k unstable periodic orbits and the control signal vanishes. The method is illustrated with the help of the Rössler ordinary differential equations and the Mackey-Glass delay differential equations. Eventually, the experimental realization of the control method is demonstrated. [ABSTRACT FROM AUTHOR]

We propose a method that is able to analyze chaotic time series, gained from experimental data. The method allow to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form $$\frac{{dy(t)}}{{dt}} = h(y(t),y(t - \tau _0 ))$$ , the delay time τo and the function h can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. The method turns out to be insensitive to noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators. [ABSTRACT FROM AUTHOR]

Nonlinear time series analysis offers an approach to the understanding of complex systems on the basis of observed data, if the dynamics is effectively lowdimensional deterministic. Since only a small subset out of all interesting signals with irregular time dependence falls into this class, extensions of the methods towards deterministic systems coupled to random noises and towards systems with more than a few active degrees of freedom are required. [ABSTRACT FROM AUTHOR]

We present synergetic hardware concepts for self-organizing feature representations, i.e., for the Kohonen map, the "neural-gas" vector quantization network, and generalizations of these basic procedures. Ignition of fronts and filaments in suitably designed semiconductor devices are universal synergetic mechanisms proposed to implement the interactive parts of the algorithms. Basically, the best matching unit ("winner neuron") is determined in parallel by the (first) ignition. Learning is controlled by the intrinsic dynamics of the semiconductor device, i.e., either by front propagation or by successive ignition of further filaments when a global control parameter such as the supply voltage is increased. The architectures presented in this article operate in a highly parallel manner whereas connectivity within the network is maintained very low. [ABSTRACT FROM AUTHOR]

After a brief description of the goals of synergetics, basic concepts of this interdisciplinary field, such as order parameters and the slaving principles, are sketched. Close to instability points the dynamics of a complex system can be reduced to low dimensional dynamics, where fluctuations can be included. First steps towards the extension of the slaving principle towards delay equations and towards situations far away from instability points are outlined. While the problem of pattern formation has been at the focus of synergetics, new lines of research are the analysis of observed patterns and pattern recognition. The principle of the synergetic computer requires further elaborations. Teaching robots, using concepts of synergetics, may be an important task. New kinds of devices that may return to analogue processes seem to be feasible; here the parallelism of processes will be in the foreground of future research. First steps into this direction were done by studies of lasers and new kinds of semiconductor devices. According to this author's opinion, physics will play an increasingly important role in medicine, especially in medical diagnosis. Here synergetics can be of help for instance in analysing MEG and EEG recordings, where first steps are reported. A challenging problem remains in how far physical devices can mimick brain functions. Pattern recognition by the synergetic computer and related devices as well as learning by robots are only first steps. It is hoped that the concept of order parameters and the slaving principle will be of use here also. [ABSTRACT FROM AUTHOR]

Spiral waves are a typical phenomenon of spatio-temporal pattern formation. They are observed in various biological and chemical systems, for example in the catalysis on platinum surfaces and in the Belousov-Zhabotinsky reaction. We develop a mathematical theory for the Hopf bifurcation from rigidly rotating spiral waves to meandering spiral waves; we prove the transition to drifting spiral waves if the rotation frequency of the rigidly rotating spiral wave is a multiple of the module of the Hopf eigenvalue and we study the parameter-dependence of the drift velocity near the bifurcation from rigidly rotating spiral waves. Furthermore we prove that analogous phenomena occur if a rigidly rotating spiral wave is subjected to external periodic forcing. Our results hold for a general class of reaction-diffusion systems and provide a rigorous mathematical explanation of experiments on the meandering transition in autonomous and periodically forced systems. [ABSTRACT FROM AUTHOR]

The effects of global coupling in oscillatory reaction-diffusion systems near the Hopf bifurcation are investigated. Global coupling, typical for the catalytic surface chemical reactions, significantly influences the properties of pattern formation. New kinds of patterns, such as cellular structures formed by standing waves and self-confined local turbulence, are found. [ABSTRACT FROM AUTHOR]

Recent trends in the experimentation on chemical and biochemical excitation waves are presented. In the Belousov-Zhabotinsky reaction, which is the most suitable chemical laboratory system for the study of wave propagation in excitable medium, the efficient control of wave dynamics by electrical fields and by light illumination is illustrated. In particular, the effects of a feedback control are shown. Further new experiments in this system are concerned with three-dimensional topologies and boundary effects. Important biological applications are found in the aggregation of slime mould amoebae, in proton waves during oscillatory glycolysis, and in waves of spreading depression in neuronal tissue as studied by experiments in chicken retina. Numerical simulations with appropriate reaction-diffusion models complement a large number of these experimental findings. [ABSTRACT FROM AUTHOR]

We study a strongly nonlinear equation describing the long-wave asymptotic behaviour of rapid directional solidification with weak convective coupling. Taking into account kinetic and disequilibrium effects in the basic equation, we are able to identify various nontrivial integrable subproblems that are absent in previous equations derived for this asymtotic regime. Applying then the averaging method to obtain an approximate description of solutions to the full equation, we are led to a new way of looking at wavelength selection problems, revealing a common framework for temporal and spatial processes. The method allows to establish quantitative relations between the drift velocity of parity-breaking solutions and their wavelength. Furthermore, it suggests a new wavelength-selection mechanism for equations without parity symmetry under conditions where a lateral drift is suppressed. [ABSTRACT FROM AUTHOR]

A new class of non-equilibrium critical phenomena is defined, which can appear during the growth of one phase at the expense of a second phase. We assume that the growing phase consists of several sub-phases or species or even of several dynamically defined growth patterns, and that the growth takes place by the propagation of an extended front which separates the growing from the shrinking phase. A coarsening process then takes place during growth, leaving a decreasing number of species or sub-phases immediately behind the front as time increases. This directional coarsening process can be described as a critical phenomenon in terms of a scaling theory. We define the relevant parameters, critical exponents and scaling functions, and give explicit values for these quantities for M-species front-growth in two dimensions. The results are compared with Monte-Carlo simulations and implications for experiments are discussed. [ABSTRACT FROM AUTHOR]

Sound driven gas bubbles in water can emit light pulses (sonoluminescence). Experiments show a strong dependence on the type of gas dissolved in water. Air is found to be one of the most friendly gases towards this phenomenon. Recently, Lohse et al. (1996) have suggested a chemical mechanism to account for the strong dependence on the gas mixture: the dissociation of nitrogen at high temperatures and its subsequent chemical reactions to highly water soluble gases such as NO, NO2, and/or NH3. Here, we analyze the consequences of the theory and offer detailed comparison with the experimental data of Putterman's UCLA group. We can quantitatively account for heretofore unexplained results. In particular, we understand why the argon percentage in air is so essential for the observation of stable SL. [ABSTRACT FROM AUTHOR]

We discuss various kinds of instabilities in smectic liquid crystal films. Instabilities of the layer structure, within the layer structure, and combined ones can be discriminated. [ABSTRACT FROM AUTHOR]

Statistical properties of a turbulent cascade are evaluated by considering the joint probability distribution p(v1, L1; v2, L2) for two velocity increments v1, v2 of different lenght scales L1, L2. We present experimental evidence that the conditional probability distribution p(v2, L2v1, L1) obeys a Chapman-Kolmogorov equation. We evaluate the Kramers-Moyal coefficients and show that the third and fourth order coefficients vanish. The turbulent cascade is described by a drift and diffusion coefficient and the joint probability distributions obey a Fokker-Planck equation. We calculate the drift and diffusion coefficients and discuss their relationship to universal behaviour in the scaling region of the turbulent cascade. [ABSTRACT FROM AUTHOR]

A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and Rayleigh-Bénard systems subject to an externally imposed through-flow. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the boundary conditions in addition to the driving rate and the through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation elucidates how the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation. [ABSTRACT FROM AUTHOR]

It is known that spontaneous density waves appear in granular material flowing through pipes or hoppers. A similar phenomenon is known from traffic jams on highways. Using numerical simulations we show that several types of waves exist and find that the density fluctuations follow a power law spectrum. We also investigate one-dimensional traffic models. If positions and velocities are continuous variables the model shows self-organized criticality driven by the slowest car. Lattice gas and lattice Boltzmann models reproduce the experimentally observed effects. Density waves are spontaneously generated when the viscosity has a non-linear dependence on density or shear rate as it is the case in traffic or granular flow. [ABSTRACT FROM AUTHOR]

A subset of complex physical systems are those for which the basic equations describing the system are known. An example are the Navier-Stokes equations describing turbulent flows in arbitrary geometrical configurations. Based on energy type balances, bounds on transport quantities can be derived rigorously. In many cases of turbulent fluid flow the extremalizing vector fields show surprising similarities with the observed turbulent velocity fields. [ABSTRACT FROM AUTHOR]