7,516 research outputs found
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
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