Searcharxiv⌕ Search

SEARCH · Searcharxiv

Results for “patt-sol”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33Linked to original sources
arXiv1999

Circular Kinks on the Surface of Granular Material Rotated in a Tilted Spinning Bucket

We find that circular kinks form on the surface of granular material when the axis of rotation is tilted more than the angle of internal friction of the material. Radius of the kinks is measured as a function of the spinning speed and the tilting angle. Stability consideration of the surface results in an explanation that the kink is a boundary between the inner unstable and outer stable regions. A simple cellular automata model also displays kinks at the stability boundary.

cond-mat.stat-mech↗
arXiv1998

Dynamics of axial separation in long rotating drums

We propose a continuum description for the axial separation of granular materials in a long rotating drum. The model, operating with two local variables, concentration difference and the dynamic angle of repose, describes both initial transient traveling wave dynamics and long-term segregation of the binary mixture. Segregation proceeds through ultra-slow logarithmic coarsening.

patt-sol↗
arXiv1998

Solitons on the edge of a two-dimensional electron system

We present a study of the excitations of the edge of a two-dimensional electron droplet in a magnetic field in terms of a contour dynamics formalism. We find that, beyond the usual linear approximation, the non-linear analysis yields soliton solutions which correspond to uniformly rotating shapes. These modes are found from a perturbative treatment of a non-linear eigenvalue problem, and as solutions to a modified Korteweg-de Vries equation resulting from a local induction approximation to the nonlocal contour dynamics. We discuss applications to the edge modes in the quantum Hall effect.

cond-mat.mes-hall↗
arXiv1998

Controlled Dynamics of Interfaces in a Vibrated Granular Layer

We present experimental study of a topological excitation, {\it interface}, in a vertically vibrated layer of granular material. We show that these interfaces, separating regions of granular material oscillation with opposite phases, can be shifted and controlled by a very small amount of an additional subharmonic signal, mixed with the harmonic driving signal. The speed and the direction of interface motion depends sensitively on the phase and the amplitude of the subharmonic driving.

patt-sol↗
arXiv1998

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.

patt-sol↗
arXiv1998

Discreteness-Induced Oscillatory Instabilities of Dark Solitons

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrodinger and generalized Ablowitz-Ladik equations.

patt-sol↗
arXiv1999

Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics

We present results of experiments on the dynamics of Dictyostelium discoideum in a novel set-up which constraints cell motion to a plane. After aggregation, the amoebae collect into round ''pancake" structures in which the cells rotate around the center of the pancake. This vortex state persists for many hours and we have explicitly verified that the motion is not due to rotating waves of cAMP. To provide an alternative mechanism for the self-organization of the Dictyostelium cells, we have developed a new model of the dynamics of self-propelled deformable objects. In this model, we show that cohesive energy between the cells, together with a coupling between the self-generated propulsive force and the cell's configuration produces a self-organized vortex state. The angular velocity profiles of the experiment and of the model are qualitatively similar. The mechanism for self-organization reported here can possibly explain similar vortex states in other biological systems.

patt-sol↗
arXiv1999

Extended parametric resonances in nonlinear Schrodinger systems

We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schrödinger type. It is also conjectured how related models not exactly solvable should behave in the same way. The results have applicability in recent experiments in Bose-Einstein condensation and to classical problems in Nonlinear Optics.

patt-sol↗
arXiv1999

Transitions to Line-Defect Turbulence in Complex Oscillatory Media

The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nucleation, proliferation and erratic motion of synchronization defect lines which separate domains of different oscillation phases. The line defect dynamics is controlled by the competition between diffusion, which reduces line length and curvature, and phase-gradient-induced growth. The onset of each type of defect-line turbulence is identified with a non-equilibrium phase transition characterized by non-trivial critical exponents.

chao-dyn↗
arXiv1999

Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems

Numerical simulations of two dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong correlations along one of the principal axes. Equations that describe the dependence of front motion on the angle illustrate the mechanism leading to stratified chaos.

patt-sol↗
arXiv1999

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.

patt-sol↗
arXiv1999

Stability of multi-hump optical solitons

We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the experimental results reported by M. Mitchell, M. Segev, and D. Christodoulides [Phys. Rev. Lett. v. 80, p. 4657 (1998)].

patt-sol↗
arXiv1998

Faraday waves on a viscoelastic liquid

We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external drive competes with the usual subharmonic Faraday instability. Close to the bicriticality the nonlinear wave interaction gives rise to a variety of novel surface states: Localised patches of hexagons, hexagonal superlattices, coexistence of hexagons and lines. Theoretical stability calculations and qualitative resonance arguments support the experimental observations.

patt-sol↗
arXiv1999

Thermodynamic limit from small lattices of coupled maps

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.

chao-dyn↗
arXiv1999

Braided Rivers and Superconducting Vortex Avalanches

Magnetic vortices intermittently flow through preferred channels when they are forced in or out of a superconductor. We study this behavior using a cellular model, and find that the vortex flow can make braided rivers strikingly similar to aerial photographs of braided fluvial rivers, such as the Brahmaputra. By developing an analysis technique suitable for characterizing a self-affine (multi)fractal, the scaling properties of the braided vortex rivers in the model are compared with those of braided fluvial rivers. We suggest that avalanche dynamics leads to braiding in both cases.

cond-mat.stat-mech↗
arXiv1999

Shock-Like Dynamics of Inelastic Gases

We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity distribution are identical to those of a perfectly inelastic sticky gas, which in turn is described by the inviscid Burgers equation. Asymptotic predictions of this continuum theory, including the t^{-2/3} temperature decay and the development of discontinuities in the velocity profile, are verified numerically for inelastic gases.

cond-mat.stat-mech↗
arXiv1999

Bilateral symmetry breaking in a nonlinear Fabry-Perot cavity exhibiting optical tristability

We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-Perot cylindrical cavity, where three output stable stationary states of the light are possible for a given localized incident field. Two of these states do not preserve the bilateral (i.e. left-right) symmetry of the entire system. These broken-symmetry states are the high-transmission nonlinear modes of the system. We also discuss how to excite these states.

patt-sol↗