Universal calcium fluctuations inmorphogenesis.

Understanding the collective physical processes that drive robust morphological transitions in animal development necessitates the characterization of the relevant fields involved in morphogenesis. Calcium (Ca) is recognized as one such field. In this study, we demonstrate that the spatial fluctuations of Caduringregeneration exhibit universal characteristics.

Laplacian growth with an isolated bubble near a tip.

We construct exact solutions for the Saffman-Taylor problem in a planar Hele-Shaw cell for the case of an isolated bubble near the tip of an expanding bubble in the limit of zero surface tension. This construction utilizes the integrability of the problem in the limit of vanishing surface tension. It exploits the connection, brought by the Schwarz function, between the constants of motion and the shape of the bubbles.

Observation of universal ageing dynamics in antibiotic persistence.

Stress responses allow cells to adapt to changes in external conditions by activating specific pathways. Here we investigate the dynamics of single cells that were subjected to acute stress that is too strong for a regulated response but not lethal. We show that when the growth of bacteria is arrested by acute transient exposure to strong inhibitors, the statistics of their regrowth dynamics can be predicted by a model for the cellular network that ignores most of the details of the underlying molecular interactions.

Lineage correlations of single cell division time as a probe of cell-cycle dynamics.

Stochastic processes in cells are associated with fluctuations in mRNA, protein production and degradation, noisy partition of cellular components at division, and other cell processes. Variability within a clonal population of cells originates from such stochastic processes, which may be amplified or reduced by deterministic factors. Cell-to-cell variability, such as that seen in the heterogeneous response of bacteria to antibiotics, or of cancer cells to treatment, is understood as the inevitable consequence of stochasticity.

Fluctuations in the relaxation dynamics of mixed chaotic systems.

The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for this exponent. In order to reconcile these results, we consider an ensemble of mixed chaotic systems approximated by rate equations and analyze the fluctuations in the distribution of Poincaré recurrence times.

Localized rayleigh instability in evaporation fronts.

A qualitatively different manifestation of the Rayleigh instability is demonstrated, where, instead of the usual extended undulations and breakup of the liquid into many droplets, the instability is localized, leading to an isolated narrowing of the liquid filament. The localized instability, caused by a nonuniform curvature of the liquid domain, plays a key role in the evaporation of thin liquid films off solid surfaces.

Viscous fingering in volatile thin films.

A thin water film on a cleaved mica substrate undergoes a first-order phase transition between two values of film thickness. By inducing a finite evaporation rate of the water, the interface between the two phases develops a fingering instability similar to that observed in the Saffman-Taylor problem. We draw the connection between the two problems, and construct solutions describing the dynamics of evaporation in this system.

Correlated tunneling and the instability of the fractional quantum Hall edge.

We consider a class of interaction terms that describes correlated tunneling of composite fermions between effective Landau levels. Despite being generic and of similar strength to that of the usual density-density couplings, these terms are not included in the accepted theory of the edges of fractional quantum Hall systems. Here we show that they may lead to an instability of the edge towards a new reconstructed state with additional channels, and thereby demonstrate the incompleteness of the traditional edge theory.

Long-range correlations in the speckle patterns of directed waves.

We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of classical fluctuations. We apply the method to the case where the incident wave experiences many small angle scattering events during propagation, but the total angle change remains small.

Singularities of the Hele-Shaw flow and shock waves in dispersive media.

We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Korteveg-de Vriez equation.

Statistical properties of spike trains: universal and stimulus-dependent aspects.

Statistical properties of spike trains measured from a sensory neuron in vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike trains exhibit universal behavior over a short time, modulated by a stimulus-dependent envelope over a long time.

Viscous fingering and the shape of an electronic droplet in the quantum Hall regime.

We show that the semiclassical dynamics of an electronic droplet, confined in a plane in a quantizing inhomogeneous magnetic field in the regime where the electrostatic interaction is negligible, is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to 10(-9). We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.

Adaptation of autocatalytic fluctuations to diffusive noise.

Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes negative, growth rate fluctuations induced by the discrete nature of the agents are shown to allow for an active phase, where reactants proliferate as their spatial configuration adapts to the fluctuations of the catalyst density. The model is explored by employing field theoretical techniques, numerical simulations, and strong coupling analysis.

Projecting the Kondo effect: theory of the quantum mirage.

A microscopic theory is developed for the projection (quantum mirage) of the Kondo resonance from one focus of an elliptic quantum corral to the other focus. The quantum mirage is shown to be independent of the size and the shape of the ellipse, and experiences lambdaF/4 oscillations ( lambdaF is the surface-band Fermi wavelength) with an increasing semimajor axis length. We predict an oscillatory behavior of the mirage as a function of a weak magnetic field applied perpendicular to the sample.

Relaxation to the invariant density for the kicked rotor.

The relaxation rates to the invariant density in the chaotic phase space component of the kicked rotor (standard map) are calculated analytically for a large stochasticity parameter K. These rates are the logarithms of the poles of the matrix elements of the resolvent, Rinsertion mark(z)=(z-Uinsertion mark)(-1), of the classical evolution operator Uinsertion mark. The resolvent poles are located inside the unit circle.

Leading ruelle resonances of chaotic maps.

The leading Ruelle resonances of typical chaotic maps, the perturbed cat map and the standard map, are calculated by variation. It is found that, excluding the resonance associated with the invariant density, the next subleading resonances are, approximately, the roots of the equation z(4)=gamma, where gamma is a positive number that characterizes the amount of stochasticity of the map. The results are verified by numerical computations, and the implications to the form factor of the corresponding quantum maps are discussed.

Diagrammatic approach for open chaotic systems.

A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving Wigner representations of the observables. The formalism is used to explain a recent microwave experiment on the four-disk problem, and to characterize the two-point function of the photodissociation cross section of complex molecules.

Shot noise in chaotic systems: "classical" to quantum crossover.

This paper is devoted to study of the classical-to-quantum crossover of the shot noise in chaotic systems. This crossover is determined by the ratio of the particle dwell time in the system, tau(d), to the characteristic time for diffraction t(E) approximately lambda(-1)|lnh, where lambda is the Lyapunov exponent. The shot noise vanishes when t(E)>>tau(d), while it reaches a universal value in the opposite limit.