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At least 469 records · Page 26Linked to original sources
arXiv1998

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.

patt-sol↗
arXiv1999

Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics

We present results of experiments on the dynamics of Dictyostelium discoideum in a novel set-up which constraints cell motion to a plane. After aggregation, the amoebae collect into round ''pancake" structures in which the cells rotate around the center of the pancake. This vortex state persists for many hours and we have explicitly verified that the motion is not due to rotating waves of cAMP. To provide an alternative mechanism for the self-organization of the Dictyostelium cells, we have developed a new model of the dynamics of self-propelled deformable objects. In this model, we show that cohesive energy between the cells, together with a coupling between the self-generated propulsive force and the cell's configuration produces a self-organized vortex state. The angular velocity profiles of the experiment and of the model are qualitatively similar. The mechanism for self-organization reported here can possibly explain similar vortex states in other biological systems.

patt-sol↗
arXiv1999

Extended parametric resonances in nonlinear Schrodinger systems

We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schrödinger type. It is also conjectured how related models not exactly solvable should behave in the same way. The results have applicability in recent experiments in Bose-Einstein condensation and to classical problems in Nonlinear Optics.

patt-sol↗
arXiv1999

Transitions to Line-Defect Turbulence in Complex Oscillatory Media

The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nucleation, proliferation and erratic motion of synchronization defect lines which separate domains of different oscillation phases. The line defect dynamics is controlled by the competition between diffusion, which reduces line length and curvature, and phase-gradient-induced growth. The onset of each type of defect-line turbulence is identified with a non-equilibrium phase transition characterized by non-trivial critical exponents.

chao-dyn↗
arXiv1999

Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems

Numerical simulations of two dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong correlations along one of the principal axes. Equations that describe the dependence of front motion on the angle illustrate the mechanism leading to stratified chaos.

patt-sol↗
arXiv1999

Diffusion-induced vortex filament instability in 3-dimensional excitable media

We studied the stability of linear vortex filaments in 3-dimensional (3D) excitable media, using both analytical and numerical methods. We found an intrinsic 3D instability of vortex filaments that is diffusion-induced, and is due to the slower diffusion of the inhibitor. This instability can result either in a single helical filament or in chaotic scroll breakup, depending on the specific kinetic model. When the 2-dimensional dynamics were in the chaotic regime, filament instability occurred via on-off intermittency, a failure of chaos synchronization in the third dimension.

patt-sol↗
arXiv1999

Stability of multi-hump optical solitons

We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the experimental results reported by M. Mitchell, M. Segev, and D. Christodoulides [Phys. Rev. Lett. v. 80, p. 4657 (1998)].

patt-sol↗
arXiv1998

Faraday waves on a viscoelastic liquid

We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external drive competes with the usual subharmonic Faraday instability. Close to the bicriticality the nonlinear wave interaction gives rise to a variety of novel surface states: Localised patches of hexagons, hexagonal superlattices, coexistence of hexagons and lines. Theoretical stability calculations and qualitative resonance arguments support the experimental observations.

patt-sol↗
arXiv1999

Braided Rivers and Superconducting Vortex Avalanches

Magnetic vortices intermittently flow through preferred channels when they are forced in or out of a superconductor. We study this behavior using a cellular model, and find that the vortex flow can make braided rivers strikingly similar to aerial photographs of braided fluvial rivers, such as the Brahmaputra. By developing an analysis technique suitable for characterizing a self-affine (multi)fractal, the scaling properties of the braided vortex rivers in the model are compared with those of braided fluvial rivers. We suggest that avalanche dynamics leads to braiding in both cases.

cond-mat.stat-mech↗
arXiv1999

Shock-Like Dynamics of Inelastic Gases

We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity distribution are identical to those of a perfectly inelastic sticky gas, which in turn is described by the inviscid Burgers equation. Asymptotic predictions of this continuum theory, including the t^{-2/3} temperature decay and the development of discontinuities in the velocity profile, are verified numerically for inelastic gases.

cond-mat.stat-mech↗
arXiv1999

Interplay between Coherence and Incoherence in Multi-Soliton Complexes

We analyze photo-refractive incoherent soliton beams and their interactions in Kerr-like nonlinear media. The field in each of M incoherently interacting components is calculated using an integrable set of coupled nonlinear Schrodinger equations. In particular, we obtain a general N-soliton solution, describing propagation of multi-soliton complexes and their collisions. The analysis shows that the evolution of such higher-order soliton beams is determined by coherent and incoherent contributions from fundamental solitons. Common features and differences between these internal interactions are revealed and illustrated by numerical examples.

patt-sol↗
arXiv1999

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.

patt-sol↗
arXiv1999

Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions

The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small scale (e.g., cellular) structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the KPZ universality class.

cond-mat.soft↗
arXiv1999

Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models

A system of first-order differential-difference equations with time lag describes the formation of density waves, called as quasi-solitons for dissipative systems in this paper. For co-moving density waves, the system reduces to some exactly solvable lattice models. We construct a shock-wave solution as well as one-quasi-soliton solution, and argue that there are pseudo-conserved quantities which characterize the formation of the co-moving waves. The simplest non-trivial one is given to discuss the presence of a cascade phenomena in relaxation process toward the pattern formation.

patt-sol↗
arXiv1999

On-off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics

We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of spatially regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over several decades by a power law with exponent -3/2. The experimental findings agree with simulations of the linearized electrohydrodynamic equations near the sample stability threshold.

patt-sol↗
arXiv1999

Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators

Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.

patt-sol↗
arXiv1999

Influence of four-wave mixing and walk-off on the self-focusing of coupled waves

Four-wave mixing and walk-off between two optical beams are investigated for fo cusing Kerr media. It is shown that four-wave mixing reinforces the self-focusi ng of mutually-trapped waves by lowering their power threshold for collapse, on ly when their phase mismatch is small. On the contrary, walk-off inhibits the c ollapse by detrapping the beams, whose partial centroids experience nonlinear o scillations.

patt-sol↗