Phase Defects as a Measure of Disorder in Traveling-Wave Convection

A versatile cortical pattern-forming circuit based on Rho, F-actin, Ect2, and RGA-3/4

Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, “chases” Rho waves in an F-actin–dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, and we demonstrate that the immature oocyte is a powerful model for characterizing these dynamics.

Frequency clusters and defect structures in nonlinear dust-density waves under microgravity conditions

Density waves in a dusty plasma emerge spontaneously at low gas pressures and high dust densities. These acousticlike wave modes were studied in a radio-frequency discharge under microgravity conditions. The complex three-dimensional wave pattern shows a spatially varying wavelength that leads to bifurcations, i.e., topological defects, where wave fronts split or merge. The calculation of instantaneous wave attributes from the spatiotemporal evolution of the dust density allows a precise analysis of those structures. Investigations of the spatial frequency distribution inside the wave field revealed that the wave frequency decreases from the bulk to the edge of the cloud in terms of frequency jumps. Between those jumps, regions of almost constant frequency appear. The formation of frequency clusters is strongly correlated with defects that occur exclusively at the cluster boundaries. It is shown that the nonlinearity of the waves has a significant influence on the topology of the wave pattern.

Husimi–Wigner representation of chaotic eigenstates

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements.

The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of non-classical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual two-dimensional Wigner functions resemble those of semiclassically quantized states.

Defect turbulence in a spiral wave pattern in the torsional Couette flow

Our experimental study is devoted to the transition to defect turbulence of a periodic spiral wave pattern occurring in the flow between a rotating and a stationary disk. As the rotation rate Omega of the disk is increased, the radial phase velocity of the waves changes its sign: The waves that propagate first outward on average, then become stationary and finally propagate inward. As they become stationary, the nucleation of topological defects breaks the periodicity of the pattern. For higher Omega, more and more defects are generated in the flow pattern. This article presents the statistical study of this defect mediated turbulence.

Effects of lateral boundaries on traveling-wave dynamics in binary fluid convection

The global dynamics of traveling-wave patterns in convection in a mixture of ethanol in water is studied in different cell geometries: circular, rectangular, and stadium-shaped cells. The dynamics in these cells differ greatly, changing from a globally rotating state in the circular cell, to one large domain of locally parallel traveling waves in the rectangular cell, to a continually chaotic state in the stadium cell. In all three cases, the patterns can be described in terms of the phase of the complex order parameter. Disorder in the patterns is quantified in terms of topological defects in the phase field. While the numbers, net charge, and dynamics of defects differ greatly in the patterns in the three cells, the local dynamics of the defects, as measured by the defect-defect correlation functions, are similar.

Critical behavior of crisis-induced transition to spatiotemporal chaos in parameter space

In previous works we reported a transition mechanism from a temporal chaos (TC) to spatiotemporal chaos (STC) through a crisis due to a collision to a saddle steady wave (SSW). However, the transition also displays as a critical phenomenon in parameter space. In the present work the time variations of mode interaction energy, deltaE(I)(k)(t), of the perturbation wave (PW) with its carrier SSW are calculated. In the TC state in all the dimensions the motion is dominated by negative deltaE(I)(k)(t). With variation of the parameter in one dimension deltaE(I)(k=1)(t) becomes smaller and smaller while statistically more balanced in its negative and positive values. The critical parameter point for the crisis is right at the place where the time-averaged negative and positive deltaE(I)(k=1)(t) are equal. A power-law behavior is observed when approaching to the point. After the crisis in the STC state the motion with positive deltaE(I)(k=1)(t) suddenly becomes much stronger than that with negative ones. In addition, it is shown that stable orbit of the SSW is a boundary of the PW motion, it behaves like a potential well that constrains the PW motion.

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequilibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.