Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth

We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex envelope to a dendritic one with an overall concave morphology. We have also constructed an order parameter which describes the transition quantitatively. The transition is shown to be continuous, which can be verified by noting the non-existence of any hysteresis.Comment: 16 pages, 5 figure

Vector solitons in (2+1) dimensions

We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.Comment: 3 pages, 5 figures, submitted to Opt. Let

Spatiotemporal chaotic dynamics of solitons with internal structure in the presence of finite-width inhomogeneities

We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of coordinates and a localized impurity with finite-width. The soliton solution of the Klein-Gordon-like equations is usually treated as a structureless point-like particle. A richer dynamics is unveiled when the extended character of the soliton is taken into account. We show that interesting spatiotemporal phenomena appear when the structure of the soliton interacts with finite-width inhomogeneities. We solve an inverse problem in order to have external perturbations which are generic and topologically equivalent to well-known bifurcation models and such that the stability problem can be solved exactly. We also show the different quasiperiodic and chaotic motions the soliton undergoes as a time-dependent force pumps energy into the traslational mode of the kink and relate these dynamics with the excitation of the shape modes of the soliton.Comment: 10 pages Revtex style article, 22 gziped postscript figures and 5 jpg figure

Square patterns in Rayleigh-Benard convection with rotation about a vertical axis

We present experimental results for Rayleigh-Benard convection with rotation about a vertical axis at dimensionless rotation rates in the range 0 to 250 and upto 20% above the onset. Critical Rayleigh numbers and wavenumbers agree with predictions of linear stability analysis. For rotation rates greater than 70 and close to onset, the patterns are cellular with local four-fold coordination and differ from the theoretically expected Kuppers-Lortz unstable state. Stable as well as intermittent defect-free square lattices exist over certain parameter ranges. Over other ranges defects dynamically disrupt the lattice but cellular flow and local four-fold coordination is maintained.Comment: ReVTeX, 4 pages, 7 eps figures include

Thermally Induced Fluctuations Below the Onset of Rayleigh-B\'enard Convection

We report quantitative experimental results for the intensity of noise-induced fluctuations below the critical temperature difference $\Delta T_c$ for Rayleigh-B\'enard convection. The structure factor of the fluctuating convection rolls is consistent with the expected rotational invariance of the system. In agreement with predictions based on stochastic hydrodynamic equations, the fluctuation intensity is found to be proportional to $1/\sqrt{-\epsilon}$ where $\epsilon \equiv \Delta T / \Delta T_c -1$. The noise power necessary to explain the measurements agrees with the prediction for thermal noise. (WAC95-1)Comment: 13 pages of text and 4 Figures in a tar-compressed and uuencoded file (using uufiles package). Detailed instructions of unpacking are include

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.Comment: 5 pages, 5 figures, to appear in PRL (September, 1999