Complex Spatiotemporal Behavior Research Articles

Periodic and irregular wave patterns in an open tubular gel reactor

In an open quasi-one-dimensional Belousov-Zhabotinsky reaction-diffusion system we investigated simple periodic, complex and irregular spatiotemporal concentration patterns emerging under oscillatory boundary conditions. Symmetric (identical) feed concentrations were used at each boundary of a tabular gel reactor and the length of the system was varied. For tubes shorter than 11 mm the intrinsic wavelength is larger than half the length of the tube. In this case regular pairs of pulse waves are generated. When the length of the tube was increased we found more complex spatiotemporal behavior. Small inevitable differences in the oscillation frequencies at the boundaries finally lead to irregular patterns. The Karhunen-Loeve decomposition technique was applied for an analysis of the observed patterns.

Whirling modes and parametric instabilities in the discrete Sine-Gordon equation: Experimental tests in Josephson rings.

We analyze the damped driven discrete sine-Gordon equation. For underdamped, highly discrete systems, we show that whirling periodic solutions undergo parametric instabilities at certain drive strengths. The theory predicts novel resonant steps in the current-voltage characteristics of discrete Josephson rings, occurring in the return path of the subgap region. We have observed these steps experimentally in a ring of 8 underdamped junctions. An unusual prediction, verified experimentally, is that such steps occur even if there are no vortices in the ring. Numerical simulations indicate that complex spatiotemporal behavior occurs past the onset of instability.

Weakly multimode dynamics of a photorefractive oscillator

The dynamics of a photorefractive oscillator has been studied in the weakly multimode case. It is shown that the eigenmodes of the empty cavity provide the bases in which the transverse patterns of this oscillator should be analysed. The concept of mode families I.e. sets of frequency degenerate modes, is very efficient to classify the different ranges of operation of the oscillator with Fresnel number up to 5-7. As the complexity of the pattems increases, the interpretation in terms of optical defects or phase singularities greatly simplifies the analysis. Photorefractive materials have been shown to be efficient in many applications, such as pattern recognition, volume hologriphic storage, phase conjugated lasers, II. The knowledge and the understanding of the dynamics that they could develop when they are placed inside a cavity is important from two points of view (I) they can help in building devices whose stable pattems are used as a basis for the manipulation of complex images, for example by reducing images to the components of their projection on a limited number of « eigen-patterns » (2) (it) more fundamentally, photorefractive oscillators (PRO) have analogies with lasers (3), and thus could contribute to understand the spatio-temporal dynamics of nonlinear optical systems. Indeed, some properties of PROS, and in particular their relatively long response time, allow us to access more easily to the inforrnation needed to analyse the spatio-temporal behavior of nonlinear optical systems. In fact, as the analogy with lasers has been demonstrated through the Ginzburg-Landau equation, dynamics of photorefractive oscillators should show analogies with a much larger class of physical systems, namely those in which complex spatio-temporal behaviors lead to turbulence. In order to determine the basic mechanisms of transverse dynamics in nonlinear optical systems, we have chosen to study first the behavior of a simple system with few spatio- temporal degrees of freedom. Here we have used an optical cavity whose gain is provided by two-wave mixing (2 WM) in a photorefractive crystal, and with small transverse dimensions such that only few modes are able to oscillate in the empty cavity. By varying the diameter of an intracavity aperture, we change the number of degrees of freedom of the transverse variables and study the evolution of transverse patterns in situations of different complexity. The dynamics is interpreted in terms of the empty-cavity modes (ec modes) and of their

Oscillations, complex spatiotemporal behavior, and information transport in networks of excitatory and inhibitory neurons.

Various types of spatiotemporal behavior are described for two-dimensional networks of excitatory and inhibitory neurons with time delayed interactions. It is described how the network behaves as several structural parameters are varied, such as the number of neurons, the connectivity, and the values of synaptic weights. A transition from spatially uniform oscillations to spatiotemporal chaos via intermittentlike behavior is observed. The properties of spatiotemporally chaotic solutions are investigated by evaluating the largest positive Lyapunov exponent and the loss of correlation with distance. Finally, properties of information transport are evaluated during uniform oscillations and spatiotemporal chaos. It is shown that the diffusion coefficient increases significantly in the spatiotemporal phase similar to the increase of transport coefficients at the onset of fluid turbulence. It is proposed that such a property should be seen in other media, such as chemical turbulence or networks of oscillators. The possibility of measuring information transport from appropriate experiments is also discussed.

Stick-slip dynamics in the relaxation of stresses in a continuous elastic medium.

We report on experimental results on the dynamical behavior of the stress relaxation in a model system for earthquakelike dynamics. In the experiments, a continuous elastic medium, namely, a transparent gel, is sheared at a very slow rate in between two coaxial circular cylinders. The stress relaxations are investigated locally by means of photoelastic techniques. We find four different stick-slip dynamical regimes. Three of them are reminiscent of the unstable solutions of the Burridge-Knopoff model: the sliding, the global relaxation, and the solitonlike propagating solutions. The fourth regime shows complex spatiotemporal behavior involving events of all sizes. For this last type of behavior the statistics of event duration, event separation, and amplitude show exponential behavior.

Regular and Chaotic Spatiotemporal Patterns in a Model of Slime Mold Aggregation11The project supported by National Natural Science Foundation of China

In this paper we proposed a spatial modulated two-variable Martiel–Goldbeter model to describe the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17. As the nonlinear modulated parameter A and diffusion coefficient varied, the system shows: 1) multiperiodic phase, 2) co-existence phase of chaotic and multi-periodic state, 3) spatiotemporal chaotic phase, 4) co-existence phase of chaotic, multi-periodic and steady state, and 5) co-existence phase of chaotic and steady state. These phases can be described by spatiotemporal power spectra, pattern distribution function and Lyapunov spectra. We believed that the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17 is a spatiotemporal chaotic state.

Experiments on Earthquakes in a Continuous Elastic Medium

We report on experiments on the dynamical behaviour in a model system for earthquake-like dynamics. Shear is imposed on a transparent gel in between two coaxial circular cylinders. The stress relaxations are investigated locally by means of photoelastic techniques. We found several dynamical regimes; three of them are reminiscent of the unstable solutions of the Burridge-Knopoff model. The fourth regime shows complex spatiotemporal behaviour involving events of many different sizes. For this last type of behaviour the statistics of event duration, event separation, and amplitude show exponential behaviour.

Spatio-temporal dynamics in twin-stripe semiconductor lasers

The twin-stripe semiconductor laser, a system of two evanescently coupled nonlinear oscillators, shows complex spatio-temporal behaviour. Its dynamics is studied theoretically by numerical integration of a model system of coupled partial differential equations. The overlap of the evanescent optical fields and the diffusion of charge carriers determine the amount of nonlinear transverse coupling between the laser stripes. The concept of cumulants of the bit-number of a dynamical system composed of two sub-systems, and a characteristic spatio-temporal correlation function are introduced and applied to quantity the complexities in space and time as they are observed in the output signal of the twin-stripe laser. Depending on the distance between the adjacent oscillators, three dynamical regimes are identified: Sufficiently far apart, the two laser oscillators are uncoupled and the device shows a steady constant output signal. In the regime of medium coupling, randomly oscillating light pulses dominate the output signal. If both stripes are strongly coupled, both lasers oscillate with a (fixed) phase lag but chaotic intensities.

Spatiotemporal oscillations in a semiconductor étalon.

We show theoretically that competing optical nonlinearities in a semiconductor \'etalon, with transverse effects included, result in complex spatiotemporal behavior. A theoretical framework is developed that explains many features of the oscillatory behavior. Numerical simulations exhibit kinks, switching waves, whole-beam, and edge oscillations. Simulations compare favorably with recent experiments.

Mean flow effects in the electro-hydrodynamic convection in nematic liquid crystals

On the basis of the weakly nonlinear analysis a set of two coupled amplitude equations is derived, which lead to a better understanding of the electro-hydrodynamic instability in nematic liquid crystals near onset. It is shown that the normal convective patterns are very sensitive against large scale flow (mean flow) modes, which are systematically included. Simulation of the equations shows typically a complex spatio-temporal behavior (“defect turbulence”) very similar to the situation often observed in experiments.

Dispersion relation and spiral rotation in an excitable surface reaction

A kinetic model of the catalytic CO oxidation on a Pt(110) surface is used to describe effects of spatiotemporal self-organization, which have been observed experimentally with this system. After some simplification and taking advantage of the strong separation of fast and slow variables the model can be used to obtain analytical expressions for front and pulse velocities, pulse width and the dispersion relation, as well as for the dependency of pinned spiral rotation on the core size. Comparison with experimentally observed wave velocities and spiral rotation allows to draw conclusions about defects on the surface. Possible extensions of the model in order to explain more complex spatiotemporal behavior are briefly discussed.

Quasi-steady state self-trapping of first, second and third order subnanosecond soliton beams

Self-trapping of pulsed laser beams exhibits a complex spatio-temporal behaviour, due to the temporal dependence of the intensity during the whole exciting laser pulse duration. Here we suppress the temporal dependence of self-induced convergence thanks to a well-suited excitation of the nonlinear medium: a temporal shaping device transforms gaussian laser pulses in ”flat topped“ subnanosecond pulses of high power (transient edges of these pulses are carrying negligible energies). Then the intensity dependence of the refractive index induces a quasi-steady state, stable beam self-trapping patterns agree satisfactorily with well known features of soliton propagation.

Spatio-temporal behaviour of flows with circular constraints

Observations of the evolution of time-dependent flows and their associated spatial structure in two flows with strong circular symmetry constraints are reviewed. Some of these observations may be interpreted in terms of simple time dependent structures, associated with identifiable instability processes, which interact nonlinearly to give complex spatio-temporal behaviour. Such specially simple geometries offer the possibility of rational mathematical models which will expose the interactive processes and their role in the progress to turbulence.

Heating of Continuous Thermoluminescent Layers with Localised Laser Beams

Abstract Thin uniform continuous layers of thermoluminescent materials are convenient dosemeter configurations for laser-heated thermoluminescence dosimetry. Rapid heating of a small circular spot determined by the Gaussian laser beam profile together with thermal diffusion yields characteristic glow curve shapes. The complex spatio-temporal behaviour of the thermoluminescence emission, which results from this particular situation of heat transfer and diffusion, was calculated as a function of time and compared with experimental data.

Heating of Continuous Thermoluminescent Layers with Localised Laser Beams

Thin uniform continuous layers of thermoluminescent materials are convenient dosemeter configurations for laser-heated thermoluminescence dosimetry. Rapid heating of a small circular spot determined by the Gaussian laser beam profile together with thermal diffusion yields characteristic glow curve shapes. The complex spatio-temporal behaviour of the thermoluminescence emission, which results from this particular situation of heat transfer and diffusion, was calculated as a function of time and compared with experimental data.