Shock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations

Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the time-averaged patterns for the case of stepwise fixed boundary conditions. Our results show that the shock structure for the noisy KdV-Burgers equation has an oscillating tail, even for the time averaged pattern. Also, we find that the width of the shock and the intensity of the velocity fluctuations in the shock region increase with system size.Comment: 9 pages, 5 figure

Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation

Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one soliton, when there is no phase shift. If a phase difference is given to the two solitons, the Josephson oscillation is induced. The Josephson oscillation is amplified near the junction. The two solitons are reflected when the initial velocity is below a critical value.Comment: 3 pages, 2 figure

Domain-size control by global feedback in bistable systems

We study domain structures in bistable systems such as the Ginzburg-Landau equation. The size of domains can be controlled by a global negative feedback. The domain-size control is applied for a localized spiral pattern

Electromagnetic emission from hot medium measured by the PHENIX experiment at RHIC

Electromagnetic radiation has been of interest in heavy ion collisions because they shed light on early stages of the collisions where hadronic probes do not provide direct information since hadronization and hadronic interactions occur later. The latest results on photon measurement from the PHENIX experiment at RHIC reflect thermodynamic properties of the matter produced in the heavy ion collisions. An unexpectedly large positive elliptic flow measured for direct photons can not be explained by any of the current models.Comment: Talk contributed to Rutherford Centennial Conference, Aug 8-12, 2011, held in Manchester, U

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