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At least 343 records · Page 19Linked to original sources

arXiv1997

Breaking the symmetry in bimodal frequency distributions of globally coupled oscillators

The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical simulations support the results based of bifurcation theory and high-frequency calculations. In the latter case, the order parameter is a linear superposition of parameters corresponding to rotating and counterrotating phases.

patt-sol↗

arXiv1997

Surface tension and dynamics of fingering patterns

We study the minimal class of exact solutions of the Saffman-Taylor problem with zero surface tension, which contains the physical fixed points of the regularized (non-zero surface tension) problem. New fixed points are found and the basin of attraction of the Saffman-Taylor finger is determined within that class. Specific features of the physics of finger competition are identified and quantitatively defined, which are absent in the zero surface tension case. This has dramatic consequences for the long-time asymptotics, revealing a fundamental role of surface tension in the dynamics of the problem. A multifinger extension of microscopic solvability theory is proposed to elucidate the interplay between finger widths, screening and surface tension.

patt-sol↗

arXiv1998

Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems

A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view, the two phases are characterized by two distinct single-particle motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous diffusion is observed up to a time $τ$ that increases linearly with $N$. Therefore, the finite particle number acts like a white noise source for the system, inhibiting anomalous transport at longer times.

cond-mat.stat-mech↗

arXiv1998

Phase chaos in the anisotropic complex Ginzburg-Landau Equation

Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.

patt-sol↗

arXiv1998

Front Propagation: Precursors, Cutoffs and Structural Stability

We discuss the problem of fronts propagating into metastable and unstable states. We examine the time development of the leading edge, discovering a precursor which in the metastable case propagates out ahead of the front at a velocity more than double that of the front and establishes the characteristic exponential behavior of the steady-state leading edge. We also study the dependence of the velocity on the imposition of a cutoff in the reaction term. These studies shed new light on the problem of velocity selection in the case of propagation into an unstable state. We also examine how discreteness in a particle simulation acts as an effective cutoff in this case.

patt-sol↗

arXiv1998

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $Ω$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $ε^{1/2}$ at small $ε$ ($ε\equiv Ω/Ω_c - 1$) and agrees well with calculations based on the equations of motion over a wide $ε$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $ε$ the boundary-mediated band-width is linear in $ε$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.

patt-sol↗

arXiv1998

Turing Instability in a Boundary-fed System

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.

patt-sol↗

arXiv1998

Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems

We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures. This behavior originates from the competition between the scroll curvature and unstable core dynamics. We show that the obtained instability persists even beyond the meander core instability of two-dimensional spiral wave.

patt-sol↗

arXiv1998

Analysis of Optimal Velocity Model with Explicit Delay

We analyze Optimal Velocity Model (OVM) with explicit delay. The properties of congestion and the delay time of car motion are investigated by analytical and numerical methods. It is shown that the small explicit delay time has almost no effects. In the case of the large explicit delay time, a new phase of congestion pattern of OVM seems to appear.

patt-sol↗

arXiv1998

Rayleigh-Bénard convection in a homeotropically aligned nematic liquid crystal

We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference $ΔT$ and the applied vertical magnetic field $H$ and compare them with theoretical calculations. The experiments cover the field range $8 \alt h \equiv H/ H_{F} \alt 80$ ($H_F =$ is the Fréedericksz field). For $h$ less than a codimension-two field $h_{ct} \simeq 46$ the bifurcation is subcritical and oscillatory, with travelling- and standing-wave transients. Beyond $h_{ct}$ the bifurcation is stationary and subcritical until a tricritical field $h_t= 57.2$ is reached, beyond which it is supercritical. The bifurcation sequence as a function of $h$ found in the experiment confirms the qualitative aspects of the theoretical predictions. However, the value of $h_{ct}$ is about 10% higher than the predicted value and the results for $k_c$ are systematically below the theory by about 2% at small $h$ and by as much as 7% near $h_{ct}$. At $h_{ct}$, $k_c$ is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field $h_t^{th} = 51$ is somewhat below the experimental one. The fully developed flow above $R_c$ for $h < h_{ct}$ is chaotic. For $h_{ct} < h < h_t$ the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below $R_c$, i.e. the bifurcation is hysteretic. Above the tricritical field $h_t$, we find a bifurcation to a time independent pattern which within our resolution is non-hysteretic.

patt-sol↗

arXiv1998

The Dynamics of Granular Segregation Patterns in a Long Drum Mixer

We have studied the early time evolution of granular segregation patterns in a horizontal rotating cylinder partially filled with a sand/salt mixture. The growth of concentration fluctuations starting from premixed initial conditions was analyzed using Fourier techniques. In one mixture, we observed generally merging dynamics in the segregated bands up to the onset of saturation. At the threshold of saturation, we found a spectrum of wavelengths with a broad peak. The peak position was nearly independent of the tube rotation rate. The overall growth rate of Fourier modes had a maximum at a particular value of the angular rotation frequency. In a slightly different mixture, we observed transient traveling waves when the larger grains were in the majority. We measured the wave speed as a function of several parameters using presegregated initial conditions to launch waves of various wavelengths.

patt-sol↗

arXiv1998

Velocity correlations in granular materials

A system of inelastic hard disks in a thin pipe capped by hot walls is studied with the aim of investigating velocity correlations between particles. Two effects lead to such correlations: inelastic collisions help to build localized correlations, while momentum conservation and diffusion produce long ranged correlations. In the quasi-elastic limit, the velocity correlation is weak, but it is still important since it is of the same order as the deviation from uniformity. For system with stronger inelasticity, the pipe contains a clump of particles in highly correlated motion. A theory with empirical parameters is developed. This theory is composed of equations similar to the usual hydrodynamic laws of conservation of particles, energy, and momentum. Numerical results show that the theory describes the dynamics satisfactorily in the quasi-elastic limit, however only qualitatively for stronger inelasticity.

patt-sol↗

arXiv1998

A Potential of Interaction between Two- and Three-Dimensional Solitons

A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full Hamiltonian of the system (_without_ assuming that the ``tail'' of each soliton is not affected by its interaction with the other soliton, and, in fact,_without_ knowing the exact form of the solution for an isolated soliton - the latter problem is circumvented by reducing a bulk integral to a surface one). The result is obtained in an explicit form that does not contain an artificially introduced radius of the overlapping region. The potential applies to spatial and spatiotemporal solitons in nonlinear optics, where it may help to solve various dynamical problems: collisions, formation of bound states (BS's), etc. In particular, an orbiting BS of two solitons is always unstable. In the presence of weak dissipation and gain, the effective potential can also be derived, giving rise to bound states similar to those recently studied in 1D models.

patt-sol↗

arXiv1998

$π$-kinks in strongly ac driven sine-Gordon systems

We demonstrate that $π$-kinks exist in non-parametrically ac driven sine-Gordon systems if the ac drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are two stable and two unstable equilibria in the sine-Gordon phase. The pairwise symmetry of these equilibria implies the existence of a one-parameter family of $π$-kink solutions in the reduced system. In the dissipative case of the ac driven sine-Gordon systems, corresponding to Josephson junctions, the velocity is selected by the balance between the perturbations. The results are derived from a perturbation analysis and verified by direct numerical simulations.

patt-sol↗

arXiv1998

Dynamics of Wetting Fronts in Porous Media

We propose a new phenomenological approach for describing the dynamics of wetting front propagation in porous media. Unlike traditional models, the proposed approach is based on dynamic nature of the relation between capillary pressure and medium saturation. We choose a modified phase-field model of solidification as a particular case of such dynamic relation. We show that in the traveling wave regime the results obtained from our approach reproduce those derived from the standard model of flow in porous media. In more general case, the proposed approach reveals the dependence of front dynamics upon the flow regime.

patt-sol↗

arXiv1999

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.

cond-mat.stat-mech↗

arXiv1999

Traveling wave solutions in the Burridge-Knopoff model

The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the form of the self-sustained shock waves traveling with constant speed which depends only on the amount of the accumulated stress in front of the wave. For a wide class of initial conditions the behavior of the system is determined by these shock waves and the dynamics of the system can be expressed in terms of their motion. The solutions in the form of the periodic wave trains and sources of counter-propagating waves are analyzed. It is argued that depending on the initial conditions the system will either tend to synchronize or exhibit chaotic spatiotemporal behavior.

patt-sol↗

arXiv1998

Numerical Bifurcation Diagram for the Two-Dimensional Boundary-fed CDIMA System

We present numerical solution of the chlorine dioxide-iodine-malonic acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from non-symmetry breaking structures along boundary feed gradients to transverse symmetry breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make connection with earlier results and discuss prospects for future work.

patt-sol↗