Cooperative jump motions of jammed particles in a one-dimensional periodic potential

Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated and it is compared with theoretical estimates. We find that the size distribution of the cooperative jump motions obeys an exponential law in a large system.Comment: 5 pages, 4 figure

Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation

We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to \emph{stable} fully localized 2D pulses, which are spatiotemporal ``light bullets'', existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system's parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.Comment: 16pages, 9figure

Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice

We predict new generic types of vorticity-carrying soliton complexes in a class of physical systems including an attractive Bose-Einstein condensate in a square optical lattice (OL) and photonic lattices in photorefractive media. The patterns include ring-shaped higher-order vortex solitons and supervortices. Stability diagrams for these patterns, based on direct simulations, are presented. The vortex ring solitons are stable if the phase difference \Delta \phi between adjacent solitons in the ring is larger than \pi/2, while the supervortices are stable in the opposite case, \Delta \phi <\pi /2. A qualitative explanation to the stability is given.Comment: 9 pages, 4 figure

Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1+1 dimensions

The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1+1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in the sense that they have scale invariant solutions with the same scaling exponents in the long-wavelength limit. The RG analysis reveals that the RG flow for the parameters of the noisy KS equation rapidly approach the KPZ fixed point with increasing the strength of the noise. This is supplemented by the numerical simulations of the KS equation with a stochastic noise, in which the scaling behavior of the KPZ equation can be easily observed even in the moderate system size and time.Comment: 12pages, 7figure

Self-organized criticality in an interface-growth model with quenched randomness

We study a modified model of the Kardar-Parisi-Zhang equation with quenched disorder, in which the driving force decreases as the interface rises up. A critical state is self-organized, and the anomalous scaling law with roughness exponent alpha=0.63 is numerically obtained.Comment: 4 pages, 4 figure