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Pattern Formation and Solitons papers — page 11

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Pattern Formation from Defect Chaos --- A Theory of Chevrons
For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the…
A. G. Rossberg, L. KramerJan 9, 1997
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Diffusive Boundary Layers in the Free-Surface Excitable Medium Spiral
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow…
David A. Kessler, Herbert LevineJan 8, 1997
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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…
S. Flach, K. Kladko, R. S. MacKayJan 6, 1997
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Bistability of Slow and Fast Traveling Waves in Fluid Mixtures
The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common…
St. Hollinger, P. Buechel, M. LueckeJan 3, 1997
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Worm Structure in Modified Swift-Hohenberg Equation for Electroconvection
A theoretical model for studying pattern formation in electroconvection is proposed in the form of a modified Swift-Hohenberg equation. A localized state is found in two dimension, in agreement with…
Yuhai TuJan 2, 1997
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Optical Solitary Waves in the Higher Order Nonlinear Schrodinger Equation
We study solitary wave solutions of the higher order nonlinear Schrodinger equation for the propagation of short light pulses in an optical fiber. Using a scaling transformation we reduce the…
M. Gedalin, T. C. Scott, Y. B. BandDec 25, 1996
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Sources and sinks separating domains of left- and right-traveling waves: Experiment versus amplitude equations
In many pattern forming systems that exhibit traveling waves, sources and sinks occur which separate patches of oppositely traveling waves. We show that simple qualitative features of their dynamics…
Roberto Alvarez, Martin van Hecke, Wim van SaarloosDec 23, 1996
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Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation
In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact…
J. -P. Eckmann, C. E. Wayne, P. WittwerDec 20, 1996
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A Mechanism for Spatio-Temporal Disorder in Bistable Reaction-Diffusion Systems
In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to…
Aric Hagberg, Ehud MeronDec 10, 1996
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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…
Aric Hagberg, Ehud MeronNov 14, 1996
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Vortex Dynamics in Dissipative Systems
We derive the exact equation of motion for a vortex in two- and three- dimensional non-relativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given…
Ola Tornkvist, Elsebeth SchroderNov 5, 1996
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Solvable Optimal Velocity Models and Asymptotic Trajectory
In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the…
K. Nakanishi, K. Itoh, Y. Igarashi et al.Oct 23, 1996
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Solitary vortex couples in viscoelastic Couette flow
We report experimental observation of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex couple ("diwhirl") in Couette flow with highly…
Alexander Groisman, Victor SteinbergOct 22, 1996
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Nonlinear Modulation of Travelling Rolls in Magnetoconvection
Modulational dynamics of oscillatory travelling rolls in magnetoconvection is studied near the onset of a Hopf bifurcation. Using weakly nonlinear analysis, we derive an envelope equation of…
Ken-ichi Matsuba, Kenji Imai, Kazuhiro NozakiOct 8, 1996
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An analytical stability theory for Faraday waves and the observation of the harmonic surface response
We present an analytical stability theory for the onset of the Faraday instability, applying over a wide frequency range between shallow water gravity and deep water capillary waves. For sufficiently…
H. W. Mueller, H. Wittmer, C. Wagner et al.Oct 8, 1996
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Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids
We present the first large scale numerical simulation of three-dimensional Rayleigh-Bénard convection near onset, under free-free boundary conditions for a fluid of Prandtl number σ=0.5. We find…
Hao-wen Xi, Xiao-jun Li, J. D. GuntonOct 7, 1996
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Influence of boundaries on pattern selection in through-flow
The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-Bénard convection. The spatiotemporal structure of convection rolls…
D. Roth, P. Buechel, M. Luecke et al.Sep 30, 1996
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Stationary planar domain walls of a classical spin chain
Domain walls of a discrete model of an anisotropic ferromagnet are studied. They can be described by sequences of two reversible mappings. Competition between the length scale of spatial structures…
Benno RumpfSep 30, 1996
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Influence of through-flow on linear pattern formation properties in binary mixture convection
We investigate how a horizontal plane Poiseuille shear flow changes linear convection properties in binary fluid layers heated from below. The full linear field equations are solved with a shooting…
Ch. Jung, M. Luecke, P. BuechelSep 30, 1996
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Pattern selection as a nonlinear eigenvalue problem
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures…
P. Buechel, M. LueckeSep 30, 1996
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Extended Symbolic Dynamics in Bistable CML: Existence and Stability of Fronts
We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatio-temporal coding, we prove the one-to-one…
R. Coutinho, B. FernandezSep 25, 1996
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A domain wall between single-mode and bimodal states and its transition to dynamical behavior in inhomogeneous systems
We consider domain walls (DW's) between single-mode and bimodal states that occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and complex Ginzburg-Landau (CGL) equations…
M. van Hecke, B. A. MalomedSep 13, 1996
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Convection in rotating annuli: Ginzburg-Landau equations with tunable coefficients
The coefficients of the complex Ginzburg-Landau equations that describe weakly nonlinear convection in a large rotating annulus are calculated for a range of Prandtl numbers σ. For fluids with…
Martin van Hecke, Wim van SaarloosSep 12, 1996
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Structure of Complex-Periodic and Chaotic Media with Spiral Waves
The spatiotemporal structure of reactive media supporting a solitary spiral wave is studied for systems where the local reaction law exhibits a period-doubling cascade to chaos. This structure is…
Andrei Goryachev, Raymond KapralSep 9, 1996
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Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection
Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with m arms in Rayleigh-Benard convection are obtained. Global spirals and parallel…
Xiao-jun Li, Hao-wen Xi, J. D. GuntonAug 28, 1996
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