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Pattern Formation and Solitons papers — page 9

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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.…
F. X. Magdaleno, J. CasademuntJul 25, 1997
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Universal algebraic relaxation of fronts propagating into an unstable state
We analyze ``pulled'' or ``linearly marginally stable'' fronts propagating into unstable states. While ``pushed'' fronts into meta- and unstable states relax exponentially,…
Ute Ebert, Wim van SaarloosJul 16, 1997
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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…
J. A. Acebron, L. L. Bonilla, S. De Leo et al.Jul 11, 1997
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Nonequilibrium phase separation in traffic flows
Traffic jam in an optimal velocity model with the backward reference function is analyzed. An analytic scaling solution is presented near the critical point of the phase separation. The validity of…
H. Hayakawa, K. NakanishiJul 8, 1997
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Optical characterization of chevron texture formation in nematic electroconvection
We characterize the director structures in electroconvection patterns of nematic liquid crystals by means of polarising microscopy. This study was stimulated by a theory put forward by Rossberg et…
H. Amm, R. Stannarius, A. G. RossbergJul 3, 1997
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Phenomenological Theory for Spatiotemporal Chaos in Rayleigh-Benard Convection
We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and…
Xiao-jun Li, Hao-wen Xi, J. D. GuntonJun 18, 1997
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Fingering Instability in a Water-Sand Mixture
The temporal evolution of a water-sand interface driven by gravity is experimentally investigated. By means of a Fourier analysis of the evolving interface the growth rates are determined for the…
A. Lange, M. Schröter, M. A. Scherer et al.Jun 16, 1997
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Weakly nonlinear analysis in spatially extended systems as a formal perturbation scheme
The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation…
Wolfram Just, Frank Matth"aus, Hans Rainer V"olger et al.Jun 16, 1997
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Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions
The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in…
L. L. Bonilla, C. J. Perez Vicente, R. SpiglerJun 16, 1997
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Asymptotic description of transients and synchronized states of globally coupled oscillators
A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to…
J. A. Acebron, L. L. BonillaJun 13, 1997
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Phase Space Derivation of a Variational Principle for One Dimensional 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. A new derivation of a…
R. D. Benguria, M. C. DepassierJun 10, 1997
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Amplitude Equations for Electrostatic Waves: multiple species
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude A(t). In the limit of weak instability, i.e. γ 0+ where γ is the linear growth…
John David Crawford, Anandhan JayaramanJun 10, 1997
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Amplitude Equation for Lattice Maps, a Renormalization Group Approach
We consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps. Under some generic hypothesis we derive an amplitude equation which is the space-time…
P. ColletMay 22, 1997
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Stability of a Nonequilibrium Interface in a Driven Phase Segregating System
We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic…
Claude A. Laberge, Sven SandowMay 20, 1997
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Stretching of vortex lines and generation of vorticity in the three-dimensional complex Ginzburg-Landau Equation
The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is proved that a straight vortex…
Igor Aranson, Alan BishopMay 19, 1997
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Existence and Stability of Propagating Fronts for an Autocatalytic Reaction-Diffusion System
We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B -> 2B) and a cubic (A + 2B -> 3B) autocatalysis.…
Stephane Focant, Thierry GallayMay 16, 1997
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On Envelope Dynamics In 2D Faraday Waves
A weakly nonlinear model for two-dimensional Faraday waves over infinite depth is derived and studied. Sideband instability of monochromatic standing waves as well as non-monochromatic solutions are…
I. Keller, A. Oron, P. Z. Bar-YosephMay 15, 1997
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The branching structure of diffusion-limited aggregates
I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two…
Thomas C. HalseyMay 8, 1997
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Unicellular algal growth: A biomechanical approach to cell wall dynamics
We present a model for unicellular algal growth as motivated by several experiments implicating the importance of calcium ions and ``loosening'' enzymes in morphogenesis. A growing cell at…
Royce Kam, Herbert LevineMay 7, 1997
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Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method
The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding…
T. Kunihiro, J. MatsukidairaMay 7, 1997
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Selection of the Saffman-Taylor Finger Width in the Absence of Surface Tension: an Exact Result
Using our exact time-depending solutions, we solve the Saffman-Taylor finger selection problem in the absence of surface tension by showing that an arbitrary interface in a Hele-Shaw cell evolves to…
Mark Mineev-WeinsteinMay 6, 1997
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A Lubrication Model of Coating Flows over a Curved Substrate in Space
Consider the three-dimensional flow of a viscous Newtonian fluid upon an abitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a…
R. Valery Roy, A. J. Roberts, M. E. SimpsonMay 1, 1997
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Phase Segregation Dynamics In Particle Systems with Long Range Interactions II: Interface motion
We study properties of the solutions of a family of second order integro-differential equations, which describe the large scale dynamics of a class of microscopic phase segregation models with…
G. Giacomin, J. L. LebowitzApr 29, 1997
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Spiral Dynamics in Pattern-Forming Systems: Mean Flow Effects
Mean flow effects are discussed for two different pattern-forming systems: Rayleigh-Benard convection and Faraday instability in viscous fluid. In both systems spirals are observed in certain…
Lev S. TsimringApr 21, 1997
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Onset of oscillatory instabilities under stochastic modulation
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random…
Francois Drolet, Jorge VinalsApr 21, 1997
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