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At least 415 records · Page 23Linked to original sources
arXiv1995

Hexagons, Kinks and Disorder in Oscillated Granular Layers

Experiments on vertically oscillated granular layers in an evacuated container reveal a sequence of well-defined pattern bifurcations as the container acceleration is increased. Period doublings of the layer center of mass motion and a parametric wave instability interact to produce hexagons and more complicated patterns composed of distinct spatial domains of different relative phase separated by kinks (phase discontinuities). Above a critical acceleration, the layer becomes disordered in both space and time.

patt-sol↗
arXiv1995

Coexisting Pulses in a Model for Binary-Mixture Convection

We address the striking coexistence of localized waves (`pulses') of different lengths which was observed in recent experiments and full numerical simulations of binary-mixture convection. Using a set of extended Ginzburg-Landau equations, we show that this multiplicity finds a natural explanation in terms of the competition of two distinct, physical localization mechanisms; one arises from dispersion and the other from a concentration mode. This competition is absent in the standard Ginzburg-Landau equation. It may also be relevant in other waves coupled to a large-scale field.

patt-sol↗
arXiv1996

Competing Patterns of Signaling Activity in Dictyostelium discoideum

Quantitative experiments are described on spatio-temporal patterns of coherent chemical signaling activity in populations of {\it Dictyostelium discoideum} amoebae. We observe competition between spontaneously firing centers and rotating spiral waves that depends strongly on the overall cell density. At low densities, no complete spirals appear and chemotactic aggregation is driven by periodic concentric waves, whereas at high densities the firing centers seen at early times nucleate and are apparently entrained by spiral waves whose cores ultimately serve as aggregation centers. Possible mechanisms for these observations are discussed.

cond-mat↗
arXiv1996

Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency. For forcing above a threshold the modulated standing waves unlock, bifurcating into a temporally periodic state. Below the threshold the system presents a kind of excitability.

patt-sol↗
arXiv1995

Parametric Generation of Second Sound by First Sound in Superfluid Helium

We report the first experimental observation of parametric generation of second sound (SS) by first sound (FS) in superfluid helium in a narrow temperature range in the vicinity of $T_λ$. The temperature dependence of the threshold FS amplitude is found to be in a good quantitative agreement with the theory suggested long time ago and corrected for a finite geometry. Strong amplitude fluctuations and two types of the SS spectra are observed above the bifurcation. The latter effect is quantitatively explained by the discreteness of the wave vector space and the strong temperature dependence of the SS dissipation length.

cond-mat↗
arXiv1995

Rifts in Spreading Wax Layers

We report experimental results on the rift formation between two freezing wax plates. The plates were pulled apart with constant velocity, while floating on the melt, in a way akin to the tectonic plates of the earth's crust. At slow spreading rates, a rift, initially perpendicular to the spreading direction, was found to be stable, while above a critical spreading rate a "spiky" rift with fracture zones almost parallel to the spreading direction developed. At yet higher spreading rates a second transition from the spiky rift to a zig-zag pattern occurred. In this regime the rift can be characterized by a single angle which was found to be dependent on the spreading rate. We show that the oblique spreading angles agree with a simple geometrical model. The coarsening of the zig-zag pattern over time and the three-dimensional structure of the solidified crust are also discussed.

chao-dyn↗
arXiv1996

Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy

Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly nonlinear analysis leading to amplitude equations which couple the short-wavelength patterning mode with the Goldstone mode resulting from the broken isotropy. The new coefficients in these equations are calculated from the hydrodynamics. Simulations exhibit a new type of spatio-temporal chaos at onset. The results are compared with experiments.

patt-sol↗
arXiv1996

Breathing Spots in a Reaction-Diffusion System

A quasi-2-dimensional stationary spot in a disk-shaped chemical reactor is observed to bifurcate to an oscillating spot when a control parameter is increased beyond a critical value. Further increase of the control parameter leads to the collapse and disappearance of the spot. Analysis of a bistable activator-inhibitor model indicates that the observed behavior is a consequence of interaction of the front with the boundary near a parity breaking front bifurcation.

patt-sol↗
arXiv1996

A Variational Principle for Eigenvalue Problems of Hamiltonian Systems

We consider the bifurcation problem $u'' + λu = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $λ$. We give a variational characterization of the bifurcating branch $λ$ as a function of the amplitude of the solution. As an application we show how it can be used to obtain simple approximate closed formulae for the period of large amplitude oscillations.

patt-sol↗
arXiv1996

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $ρ(t)$ is studied using an expansion in $ρ$; in particular, in the limit $γ\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $γ$. Generically $|E_k|\sim γ^{5/2}$, as $γ\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim γ^{2}$ is predicted.

patt-sol↗
arXiv1996

Numerical Simulation of Three-Dimensional Dendritic Growth

Dendritic crystal growth in a pure undercooled melt is simulated quantitatively in three dimensions using a phase-field approach. The full non-axisymmetric morphology of the steady-state dendrite tip and $σ^*$ are determined as a function of anisotropy for a crystal with a cubic symmetry. Results are compared to experiment and used to critically test solvability theory.

patt-sol↗
arXiv1997

Streamer Propagation as a Pattern Formation Problem: Planar Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations.

patt-sol↗
arXiv1996

Velocity Selection for Propagating Fronts in Superconductors

Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a unique speed which is controlled by the amount of magnetic flux trapped in the front. For small flux the speed can be determined from the linear marginal stability hypothesis, while for large flux the speed may be calculated using matched asymptotic expansions. At a special point the order parameter and vector potential are dual, leading to an exact solution which is used as the starting point for a perturbative analysis.

cond-mat↗
arXiv1996

Links, Knots and Knotted Labyrinths in Bistable Systems

The existence of stable links and knots is demonstrated in three-dimensional, bistable, chemical media. The reaction-diffusion medium segregates into regions of high and low concentration separated by sharp interfaces. The interfaces repel at short distances so that domains with various topologies are possible depending on the initial conditions and system parameters. Front instabilities can give rise to knotted labyrinthine patterns. A lattice-gas model whose mean-field limit is the FitzHugh-Nagumo equation is described and implemented to carry out the simulations.

patt-sol↗
arXiv1996

The Dynamics of Curved Fronts: Beyond Geometry

We derive a new set of kinematic equations for front motion in two-dimensional bistable media. The equations generalize the geometric approach by complementing the equation for the front curvature with an order parameter equation associated with a nonequilibrium Ising-Bloch bifurcation. The resulting equations capture the core structure of spiral waves and spontaneous spiral-wave nucleation.

patt-sol↗
arXiv1997

Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices

Discrete breathers are time-periodic, spatially localized solutions of equations of motion for classical degrees of freedom interacting on a lattice. They come in one-parameter families. We report on studies of energy properties of breather families in one-, two- and three-dimensional lattices. We show that breather energies have a positive lower bound if the lattice dimension of a given nonlinear lattice is greater than or equal to a certain critical value. These findings could be important for the experimental detection of discrete breathers.

patt-sol↗
arXiv1997

Dynamical transitions in correlated driven diffusion in a periodic potential

The diffusion of a two-dimensional array of particles driven by a constant force in the presence of a periodic external potential exhibits a hierarchy of dynamical phase transitions when the driving force is varied. This behavior can be explained by a simple phenomenological approach which reduces the system of strongly interacting particles to weakly interacting quasi-particles (kinks). The richness of the strongly coupled system is however not lost because, contrary to a single-Brownian particle, the array shows an hysteretic behavior even at non-zero temperature. The present investigation can be viewed as a first step toward understanding nanotribology.

cond-mat.stat-mech↗