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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]

It is well known that charge density wave systems exhibit a variety of phenomena related to the existence of metastable states: Electric measurements reveal hystereses in both their thermal and electric behavior as well as different kinds of memory effects. Although these integral methods provide strong evidence for metastability, they can not uncover the spatial structure of the charge density wave. As predicted by the theory of Fukuyama, Lee, and Rice, the charge density wave should organize in domains obeying a characteristic length scale. We have performed investigations on a TaS3 sample with a low-temperature scanning electron microscope, using the electron beam as weak local heat source and recording the thermopower as a function of the beam position. We demonstrate that the structures observed can be related to metastable deformations of the charge density wave. [ABSTRACT FROM AUTHOR]

Granular materials differ from ordinary solids and fluids in many respects. One particularly fascinating aspect of granular systems is their ability to reduce their packing fraction under tapping. In this contribution, we review and partly extend recent progress in this area with special emphasis on the nonlinear dynamical modeling of the compaction process. In particular, we also present and discuss a novel minimal model for relaxational granular compaction. [ABSTRACT FROM AUTHOR]

We discuss the theoretical description of the formation of natural cellular patterns by means of rotationally invariant order parameter equations. Starting from the hydrodynamic basic equations it turns out that the order parameter equations have nonlocal character. We present a suitable approximation scheme of the nonlocal terms by local ones which is based on a systematic gradient expansion. A truncation of this expansion leads to model equations which are widely used in the theoretical treatment of pattern formation in complex systems. Its application to spiral turbulence is studied in detail. [ABSTRACT FROM AUTHOR]

Within a light-sensitive Belousov-Zhabotinskii medium we study the interaction of meandering spiral waves. Using an open gel-reactor we find experimental evidence that a small pair of spiral waves undergoes a symmetry-breaking instability, where one member of the spiral pair overwhelms its neighbor and pushes it to the periphery of the medium. To avoid this instability we consider the interaction of a spiral wave with its virtual mirror image close to a plane boundary impermeable to diffusion. The drift of this pseudo-bound state parallel to the boundary occurs on a time scale up to two orders of magnitude larger than the rotation period. The experimental data agree qualitatively with results of numerical simulations obtained within a modified kinematic approach. [ABSTRACT FROM AUTHOR]

We present the combination of microscopic model calculations and direct experimental evidence for ultrafast nonlinear spatio-temporal dynamics of a laser system. In particular, we have studied the nearfield dynamics of a broad area semiconductor laser on picosecond timescales. The mechanisms inducing the complex behavior can be identified as self-focusing, diffraction, and hole burning. We find the onset of dynamical filamentation within the turn-on dynamics of such a laser and demonstrate that this is a non-transient behavior. [ABSTRACT FROM AUTHOR]

In order to be able to visualize spatial pattern formation during low-temperature carrier transport processes in solid state physics, we demonstrate a new concept of a scanning-laser microscope that is integrated inside an encapsulated cryogenic sample stage. All the components of the microscope, i.e., a laser diode, the deflection unit, and the focussing optics, are cooled to the temperature of the sample under investigation. Furthermore, unwanted excitation of the sample, like excitation due to background radiation, is suppressed. Our technical solution meets the challenging experimental claims of a perfect shielding and low-temperature applicability further enables the sample to be exposed to strong magnetic fields. First results on imaging current inhomogeneities in both a semi- and a superconductor experiment will be outlined. [ABSTRACT FROM AUTHOR]

We review recent work on the transition to turbulence in shear flows, in particular plane Couette flow. In the linearized system the non-normality of the linear operator gives rise to non-orthogonal eigenvectors and to a significant amplification of noise. We present a typical result for a Fokker-Planck equation with non-normal relaxation matrix. As the driving becomes stronger, further stationary states are born in a saddle node bifurcation. This is observed in a two degree of freedom phenomenological model, in the a few mode approximation to a simple shear flow and in full numerical studies of plane Couette flow. The stationary states give rise to a fractal border between decaying and turbulent states. [ABSTRACT FROM AUTHOR]

A new application of the theory of Markov processes to the characterization of fractals is presented. We show under which condition distinct stochastic processes of a cascade lead to multifractal scaling behavior. We apply our method to analyze the spatial disorder of the velocity field of fully developed turbulence and the roughness of a gold film of granular-like structure. The results obtained from these experimental data are compared with results from synthetic data of a fractal basin boundary. [ABSTRACT FROM AUTHOR]

In this paper we investigate chemical reaction equations of pollutants in the troposphere and compare it with a simple model. We show that time averages are possible, in the model they represent a very good approximation. The averaged equations are of a special polynomial type, thus the formalism of Groebner bases is one possibility to detect all fixed points. Of particular interest are fixed points in the physical regime. Varying the source strengths — they serve as control parameters — bifurcations originating from these fixed points are expected. We have tested this in the model: The formalism of Groebner bases let us find 12 fixed points. However, in the chosen range of the control parameters there exists only one physically important fixed point. This can become unstable undergoing a Hopf bifurcation. Beyond the instability strong variations of the pollutant concentrations occur. Use of the center manifold theorem can reduce the dimension of the problem considerably. [ABSTRACT FROM AUTHOR]

In electrochemical systems, the range of the spatial coupling through the electric field can vary widely, giving rise to new spatiotemporal phenomena, i.e. the acceleration of fronts. In the axial symmetric electrode arrangement, the non-local coupling can be even negative, giving rise to phenomena typical for an integral constraint, i.e. a rotating wave in a quasi one dimensional, oscillatory system with periodic boundary conditions. In addition to the more general aspects of spatial coupling in different electrode geometries, the electrodissolution of cobalt into phosphoric acid shows modulated waves in the excitable system. [ABSTRACT FROM AUTHOR]

The human brain may behave as an excitable medium, at least up to a certain degree. Although increasing evidence supports this statement, the experimental basis for investigations in the field is small. However, the spreading depression, a propagating wave of depression of the electrical activity in neural tissue, is a tempting example of self-organisation in the brain and also occurs in the retina as a true part of CNS. There it can be easily investigated and can be used as a tool for studying self-organisation in the brain. We will shortly introduce some of the experimental advances of the retinal model of the CNS and the retinal spreading depression in this article, together with some conclusion from experiments which have been done with it. [ABSTRACT FROM AUTHOR]

Evolutionary dynamics, especially dynamics on bio-molecular scale, bear inherent nonlinear properties. We analyze these dynamics of evolution by subdividing it in less sophisticated processes: population dynamics, population-support dynamics, and genotype-phenotype mapping. Molecular evolutionary biology provides a sufficiently simple experimental setup for a quantitative analysis of these subsystems. RNA secondary structures serve as model of reasonable phenotype mapping. Preimages of these mappings reveal neutral behavior and percolate genotype-space as so called neutral networks. The spatial organization of these networks significantly determine evolutionary dynamics: By stochastic flow transitions between two networks (two phenotypes) take place, by neutral drift better phenotypes are explored and evolutionary optimization towards a global maximum is possible, and by diffusion complex dynamical units (such as hypercycles) are competitive against parasites. [ABSTRACT FROM AUTHOR]

Bovine spongiform encephalopathy (BSE) is proposed to be a "dynamical disease" in the sense of Mackey and Glass. It according to the Prusiner-Gajduesek model involves an autocatalysis with an exceedingly low threshold for "going off." A few trigger molecules are believed to be sufficient. This extreme sensitivity — combined with the fact that only natural body constituents are involved — paradoxically makes intervention rather easy: "Increase the wall reactions". Hence increasing the scavenging of the autocatalytic bodily constituent may suffice. Homologous antibodies against the spontaneously occurring "folded-sheet" isoform (PrPSc) of the natural prion protein (PrPC) should therefore be effective. A single injection may abolish the disease in an earliest stage. [ABSTRACT FROM AUTHOR]