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An overview of spatial patterns emerging in a system containing methyleneblue, sulfide and molecular oxygen (MBO-system) in the presence of polyacry-lamide (PA) gel components is presented. In this so-called PA-MBO-System the gel plays an important role in the pattern formation process. In experiments conducted in a spatially twodimensional system we have found several different Turing-type structures such as hexagons, stripes and zig-zag patterns similar to those observed in the well known CIMA reaction. We examined the effect of an externally applied electrical field on the observed structures. The electrical field leads to the formation of striped patterns under conditions which favour the formation of hexagons in the absence of the field. The orientation of the stripes relative to the electrical filed vector depends on the intensity of the field: While a weak electrical field leads to stripes parallel to the field vector, higher field intensities lead to an orientation of the stripes perpendicular to it. In a spatially onedimensional system coexisting domains of stationary and Hopf-modes are formed under the influence of an electrical field. Moreover, we present experiments showing that pattern formation can be controlled by visible light. A selective illumination of the gel-sheet leads to distinct regions of activity which generates stripes instead of hexagons. Using illumination patterns of hexagonal symmetry and tunable wavelength we demonstrate spatial entrainment of the Turing-like patterns. [ABSTRACT FROM AUTHOR]

Since the seminal paper "The chemical basis of morphogenesis" by Alan Turing, the temporal and spatial self-organization phenomena produced in chemically reacting and diffusing systems are often thought as paradigms for biological development. The basic theoretical principles on which the development of stationary concentration patterns (Turing structures) rely on are briefly presented. We review different aspects of our contribution to the experimental observation of reaction-diffusion patterns in iodine-oxychlorine systems. The experimental techniques are emphasized. Phase diagrams gathering different standing and travelling patterns are presented, analyzed and modeled. A special attention is also given to some peculiar pattern growth dynamics (spot division, finger splitting). It has been suggested that a reaction-diffusion instability could be involved in the cell mitosis mechanism. In an attempt to test for such a contribution, we have performed a systematic study of the effect of geometric deformations (flattening) on the division of sea urchin eggs. [ABSTRACT FROM AUTHOR]

Spiral breakup is a phenomenon that leads to destruction of regular spirals with periodic dynamics and is often responsible for the emergence of spatiotemporal chaos in two-dimensional reaction-diffusion media. In recent years, spiral breakup has been investigated in a variety of reaction-diffusion models of chemical reactions, cardiac tissue and calcium waves. Here, we analyze the main ingredients of the instability and illustrate them with two examples: one chemical reaction model and a model of intracellular calcium wave propagation. In both cases, wave trains become unstable by an Eckhaus instability below a critical wavelength. Nevertheless, two different scenarios of breakup, namely breakup near and far away from the center, are found in these systems. By reduction to a one-dimensional problem describing the radial dynamics in the far-field of the spiral, we are able to relate the two phenomenologies to different variants of the Eckhaus instability. Breakup far away from the center appears only if the Eckhaus instability is convective. [ABSTRACT FROM AUTHOR]

Wave propagation in excitable media with fast inhibitor diffusion is investigated by analytical and numerical methods. The curvature dependence of the velocity of propagating waves is derived and used to explain the appearance of instabilities with respect to transverse perturbations. Numerical simulations show that this instability may lead to the development of spiral turbulence. On the other hand, the computations also demonstrate that in narrow stripes of such excitable media and/or in media with especially chosen nonhomogeneity the spiral turbulence can be suppressed and steadily propagating wave patterns are found instead. [ABSTRACT FROM AUTHOR]

From a physical point of view many biological (sub)systems are strongly driven through chemical and electrical signals. The strong interactions between different elements of the system transforms such "input" signals, into a nonequilibrium, cooperative dynamics. Perhaps the simplest physical system for modeling how external, random input is transformed by a population of correlated elements, is the magnetic Ising model, modulated by the presence of a fast but randomly switching external field. We present a full analysis of the DRIM, including the mean field theory, one- and two dimensional analytic and numerical results. The multifractal structure of the stationary state is discussed in detail, suggesting-in principle-a dynamic information storage scheme going beyond the 1 bit capacity of the ferromagnetic state. [ABSTRACT FROM AUTHOR]

A method for analyzing fluctuating data sets of complex systems is presented. The algorithm will deliver deterministic and stochastic parts of the dynamics of the investigated process for a special class of systems. The results of an application of the analysis to simulated data sets of one- and two-dimensional stochastic systems are shown. [ABSTRACT FROM AUTHOR]

The diffusive transport and mixing times of regulatory molecules in micrometer and sub-micrometer reaction volumes can be shorter than characteristic times of conformational transformations in single enzyme molecules. Under these conditions, mutual synchronization of individual molecular turnover cycles takes place when strong allosteric activation by the reaction products is present. Using simple automaton models to describe the cycles of single molecules, we analyze properties of the synchronization transition. [ABSTRACT FROM AUTHOR]

We present an overview of the various types of dynamic behaviour observed in the peroxidase-oxidase reaction in homogeneous solution. These behaviours range from simple periodic oscillations over complex periodic oscillations to chaotic dynamics and quasiperiodicity. [ABSTRACT FROM AUTHOR]

The electrophoretic mobility μ of charged 0.3 µm Polystyrene spheres suspended in water was measured over a wide range of salt concentrations c and packing fractions Φ. To observe isolated spheres at packing fractions Φ ≤ 2 × 10−7 a newly developed optical tweezing electrophoresis (OTE) apparatus was used. At deionised conditions μ=2.5 × 10−8 m2V−1s−1, it decreases further upon increasing the salt concentration c. Measurements at larger Φ generally show much larger μ and a qualitatively different dependence on c. At no added salt μ increases in the unordered state but a saturation at μ=6.8 × 10−8 m2V−1s−1 is observed, as the system develops fluid order. The fluid-crystal phase transition is of no influence on μ and the conductivity σ. In the ordered regime μ is extremely sensible to the addition of spurious amounts of salt. Qualitatively similar behaviour is reported for particles of different size and surface chemistry and also under conditions of large amounts of added salt. Most of the presently observed trends cannot be understood in terms of the standard electrokinetic model. Possible extensions are discussed. [ABSTRACT FROM AUTHOR]

A survey is given on the effects of large amplitude oscillatory shear (LAOS) flow on the orientation behavior of lamellar poly (styrene-b- isoprene) (PS-b-PI) diblock copolymers with emphasis on the elucidation of common behavior with other layered complex fluids like lyotropic lamellar phases. It is described that for LAOS at temperatures close to the order-disorder-transition temperature, TODT, three orientation regimes related to the dynamic shear viscosity of the block copolymers are observed: parallel orientation at high, perpendicular orientation at intermediate, and parallel orientation again at very low shear frequencies. It is demonstrated that one of the key issues to understand these non- equilibrium type experiments is the behavior of instabilities leading to flips of orientation from parallel to perpendicular alignment and vice versa. An orientation diagram showing the position of these instabilities in the amplitude-frequency space is derived experimentally suggesting a consistent phenomenological picture of orientation phenomena of layered systems under shear. [ABSTRACT FROM AUTHOR]

Traveling waves of high concentration of Ca2+ are observed in many different cells and have attracted great interest in experimental and theoretical biological research in recent years. They are created by the nonlinear dynamics of the release and uptake of Ca2+ by intracellular Ca2+ stores like the endoplasmatic or sarcoplasmatic reticulum. Their characteristics depend on other cellular organelles and components like mitochondria and Ca2+ buffers too. Here, we present some mathematical models and results of recent research on intracellular Ca2+ waves generated by the inositol 1,4,5-trisphosphate receptor channel including the modeling of Calcium induced Calcium release, buffer dynamics, impact of mitochondria on wave formation and the effect of the spatial discreteness of the channels releasing Ca2+. Modeling of the communication of Ca2+ waves to adjacent cells through gap junctions concludes this report. [ABSTRACT FROM AUTHOR]

The propagation dynamics of traveling calcium waves in rat cardiac myocytes have been investigated by means of confocal laser scanning microscopy. We found, that the calcium waves behave as reaction-diffusion waves, demonstrating the velocity-curvature relationship as well as the dispersion relation. We conclude that thes spatio-temporal pattern of calcium are governed by the properties of an excitable medium. [ABSTRACT FROM AUTHOR]

This contribution is devoted to modeling of cell or vesicle dynamics during chemotaxis, haptotaxis, and under shear flow. There are several mechanisms in general that enable cells to migrate. These mechanisms involve the interaction of the cell surfaces with molecules. The cell migration is caused by molecules which are either in solution, chemotaxis, or bound to a substratum and spatially distributed in a graded fashion, haptotaxis. We present a model of migration by considering a phospholipidic membrane adhering to a substrate. The cell shape may adapt to the environment. The hydrodynamic flow inside and outside the vesicle is taken as a major dissipation mechanism, albeit a discussion will also be devoted to other kinds of dissipation (e.g. bond breaking and restoring with the substratum). Analytical scaling laws are derived such as for migration velocity as function of the relevant parameters (the membrane rigidity, the cell size …). These scaling laws are also in good agreement with numerical solutions. Cells do not only crawl in the body. They can also be transported by hydrodynamic flows, such as the blood cells. In a shear flow, the leucocyte moving along the endothelial wall of a venule experiences, beside the drag force, an orthogonal force trying to keep it away from the substrate. This is analogous to the Magnus lift force, well known in many fields (aircraft, football…), which originates from inertia. For biological cells inertia is small, so that viscous effects prevail. A spherical object with pure viscous effects moving along a wall fells no lift force owing to the reversibility of the hydrodynamic equations. However, the shape of a cell under shear flow deviates considerably from a sphere. This asymmetry destroys the time-reversal symmetry leading thus to an orthogonal force, which we call here rising force for sake of distinction from a Magnus force. Beyond a critical shear rate, the vesicle, which is initially making adhesion with the wall, detaches from the wall. We provide analytical results on the critical shear rate and on the rising force as function of the relevant parameters. These analytical laws are in good agreement with numerical results. [ABSTRACT FROM AUTHOR]

The amoeboid microorganism Dictyostelium discoideum is a paradigm model system for the study of cell-cell signalling, chemotaxis and biological pattern formation. During a phase of its life cycle, many inbividual amoebae aggregate to form a fruiting body. Aggregation proceeds under the influence of concentration waves of the signalling molecule cAMP to which cells respond chemotactically. Mathematical models of the chemotactic response are briefly reviewed. They are integrated with a kinetic description of cAMP signalling into a model of the aggregation process. [ABSTRACT FROM AUTHOR]

Excitation waves of actin filament (F-actin) polymerization and depolymerization have been visualized in fixed and in living Dictyostelium cells by confocal and fluorescence resonance energy transfer (FRET) microscopy. F-actin waves generate supramolecular F-actin patterns, typical of chemical wave systems. Scroll waves distinguishable as sphere, ring and spiral patterns propagate up to several micrometres in diameter in a few seconds at wavefront speeds measured at up to 25 µm/min. These newly identified nonlinear F-actin dynamics drive eukaryotic cell locomotion. F-actin autowaves also induce oscillatory modi of temporally variable frequency and amplitude as cell surface projections, including pseudopodia and lamellipodia, which may traverse the cell surface as waves. F-actin waves may also govern a range of cell functions and behaviours, including phagocytosis, chemotaxis, cell surface receptor activity and biological rhythms. [ABSTRACT FROM AUTHOR]

We review the properties of biological motor proteins which move along linear filaments that are polar and periodic. The physics of the operation of such motors can be described by simple stochastic models which are coupled to a chemical reaction. We analyze the essential features of force and motion generation and discuss the general properties of single motors in the framework of two-state models. Systems which contain large numbers of motors such as muscles and flagella motivate the study of many interacting motors within the framework of simple models. In this case, collective effects can lead to new types of behaviors such as dynamic instabilities of the steady states and oscillatory motion. [ABSTRACT FROM AUTHOR]

Following a short review of the biological function and the structure of molecular motors, we discuss the state of the art of research on the molecular motor actin-myosin. We show how the so called motility assay can been improved by the use of antibodies, yielding clean and reproducible data of the speed of actin on a myosin coated surface. We discuss the dependence of the measured speed on parameters such as ATP concentration, myosin density and temperature; we furthermore show that the specific anchoring of the myosin molecule to the substrate is important for a clean measurement. Using PMMA (poly(methylmethacrylate)) gratings as guidance for the moving actin filaments, we are able to control the mechanical load of the motor via an electric field and to establish a force-speed diagram. The numerical values of duty ratio, internal friction and stalling force of the motor can be deduced from it. The observation of an instability of the motor around stalling conditions is particularly surprising and suggests the existence of a dynamic phase transition. [ABSTRACT FROM AUTHOR]

In the visual cortex of the brain, neurons specialized to process particular aspects of the visual input are arranged in complex spatial patterns, called cortical maps, and interact through a dense network of intracortical connections. Many experimental results are consistent with the hypothesis that the precise organization of patterns and connections within the cortex is not predetermined by genetic instructions, but emerges through activity-dependent self-organization during the first months of life. In this chapter, we will first survey the layout of visual cortical maps and the structure of intracortical connections, and then discuss their activity-dependent development. In the subsequent sections of the chapter, we will discuss the formation of patterns in the developing visual cortex from a nonlinear dynamics perspective. In particular, we will analyze the instability mechanisms, through which cortical patterns presumably emerge early in development. We will also discuss the intriguing possibility that cortical patterns undergo substantial rearrangement during the first months of life. [ABSTRACT FROM AUTHOR]

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]