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arXiv1997

Synchronization Defects and Broken Symmetry in Spiral Waves

Spiral waves are investigated in oscillatory media exhibiting period-doubling bifurcations. In the period-doubled and chaotic regimes, the rotational symmetry of the spiral wave is broken. The loss of symmetry takes the form of synchronization defect lines where the phase of the local oscillation changes by multiples of 2π. The internal structure and geometry of these synchronization defects is studied and a discussion of the possible types of defect lines is presented.

chao-dyn↗

arXiv1997

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $η\sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.

patt-sol↗

arXiv1998

Continuum-type stability balloon in oscillated granular layers

The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe patterns in a vertically oscillated granular layer. Molecular dynamics simulations show that the mechanism of the skew-varicose instability in granular patterns is similar to that in convection. These results suggest that pattern formation in granular media can be described by continuum models analogous to those used in fluid systems.

patt-sol↗

arXiv1998

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.

patt-sol↗

arXiv1999

Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition

Recently, hysteretic transitions to `synchronized traffic' with high values of both density and traffic flow were observed on German freeways [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. We propose a macroscopic traffic model based on a gas-kinetic approach that can explain this phase transition. The results suggest a general mechanism for the formation of probably the most common form of congested traffic.

cond-mat.stat-mech↗

arXiv1998

Localization of Waves without Bistability: Worms in Nematic Electroconvection

A general localization mechanism for waves in dissipative systems is identified that does not require the bistability of the basic state and the nonlinear plane-wave state. The mechanism explains the two-dimensional localized wave structures (`worms') that recently have been observed in experiments on electroconvection in nematic liquid crystals where the transition to extended waves is supercritical. The mechanism accounts for the propagation direction of the worms and certain aspects of their interaction. The dynamics of the localized waves can be steady or irregular.

patt-sol↗

arXiv1999

Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schröedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.

patt-sol↗

arXiv1998

Standing and Moving Gap Solitons in Resonantly Absorbing Gratings

We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed band within the forbidden gap. This spectrum gives rise, for any Bragg reflectivity, to a vast family of stable gap solitons, both standing and moving, having a unique analytic form, an arbitrary pulse area, and inelastic collision properties. These findings suggest new possibilities of transmission control, noise filtering or ``dynamical cavities'' (self-traps) for both weak and strong signal pulses.

patt-sol↗

arXiv1998

Subharmonic bifurcation cascade of pattern oscillations caused by winding number increasing entrainment

Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable stationary square, roll, and crossroll (CR) structures and the oscillatory competition between rolls and squares are determined numerically as a function of fluid parameters. A novel type of subharmonic bifurcation cascade (SC) where the oscillation period grows in integer steps as $n (2π)/(ω)$ is found and elucidated to be an entrainment process.

patt-sol↗

arXiv1998

Secondary instabilities form a codimension-2 point accompanied by a homoclinic bifurcation

A study of secondary instabilities in ac-driven electroconvection of a planarly aligned nematic liquid crystal is presented. At low frequencies one has a transition from normal rolls to a zig-zag pattern and at high frequencies a direct transition from normal to abnormal rolls. The crossover defines a codimension-2 point. This point is also the origin of a line of homoclinic bifurcations, which enable the transition from zig-zags to abnormal rolls at lower frequencies.

patt-sol↗

arXiv1998

Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection

For Rayleigh-Benard convection of a fluid with Prandtl number σ\approx 1, we report experimental and theoretical results on a pattern selection mechanism for cell-filling, giant, rotating spirals. We show that the pattern selection in a certain limit can be explained quantitatively by a phase-diffusion mechanism. This mechanism for pattern selection is very different from that for spirals in excitable media.

patt-sol↗

arXiv1998

Tunable Pinning of Burst-Waves in Extended Systems with Discrete Sources

We study the dynamics of waves in a system of diffusively coupled discrete nonlinear sources. We show that the system exhibits burst waves which are periodic in a traveling-wave reference frame. We demonstrate that the burst waves are pinned if the diffusive coupling is below a critical value. When the coupling crosses the critical value the system undergoes a depinning instability via a saddle-node bifurcation, and the wave begins to move. We obtain the universal scaling for the mean wave velocity just above threshold.

patt-sol↗

arXiv1998

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.

patt-sol↗

arXiv1998

Parametrically excited surface waves in magnetic fluids: observation of domain structures

Observations of parametrically excited surface waves in a magnetic fluid are presented. Under the influence of a magnetic field these waves have a non--monotonic dispersion relation, which leads to a richer behavior than in ordinary liquids. We report observation of three novel effects, namely: i) domain structures, ii) oscillating defects and iii) relaxational phase oscillations.

patt-sol↗

arXiv1999

``Smoke Rings'' in Ferromagnets

It is shown that bulk ferromagnets support propagating non-linear modes that are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These are circular loops of {\it magnetic} vorticity which travel at constant velocity parallel to their axis of symmetry. The topological structure of the continuum theory has important consequences for the properties of these magnetic vortex rings. One finds that there exists a sequence of magnetic vortex rings that are distinguished by a topological invariant (the Hopf invariant). We present analytical and numerical results for the energies, velocities and structures of propagating magnetic vortex rings in ferromagnetic materials.

cond-mat↗

arXiv1998

Electrostatic Edge Instability of Lipid Membranes

This paper considers the effect of electrostatics on the stability of a charged membrane. We show that at low ionic strength and high surface charge density, repulsion between charges on the membrane renders it unstable to the formation of holes. A free straight edge is unstable to modulations with wavelength longer than the Debye screening length. Hence at low ionic strength, membranes will disintegrate into vesicles. We use these results to interpret stable holes in red blood cell ghosts (Steck et. al., Science 168:255(1970)).

physics.bio-ph↗

arXiv1999

Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves

We present and analyze experimental results on the dynamics of hydrothermal waves occuring in a laterally-heated fluid layer. We argue that the large-scale modulations of the waves are governed by a one-dimensional complex Ginzburg-Landau equation (CGLE). We determine quantitatively all the coefficients of this amplitude equation using the localized amplitude holes observed in the experiment, which we show to be well described as Bekki-Nozaki hole solutions of the CGLE.

patt-sol↗

arXiv1999

Phase Diagram of Traffic States in the Presence of Inhomogeneities

We present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gas-kinetic-based traffic model are in good agreement with empirical findigs. They allow to understand the observed trasitions between free and various kinds of congested traffic, among them localized clusters, stop-and-go waves, and different types of ``synchronized'' traffic. The proposed conditions for the existence of these states suggest that the phase diagram is universal for a class of different microscopic and macroscopic traffic models.

cond-mat.stat-mech↗