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Pattern Formation and Solitons papers — page 8

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Wavy film flows down an inclined plane. Part I: Perturbation theory and general evolution equation for the film thickness
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be…
Alexander L. Frenkel, Keshavamurthy IndireshkumarDec 15, 1997
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The dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: instability, stretching, entanglement, and helices
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 shown that a straight vortex…
I. S. Aranson, A. R. Bishop, L. KramerDec 9, 1997
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Amplitude equations and pattern selection in Faraday waves
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion…
Peilong Chen, Jorge VinalsDec 8, 1997
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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…
R. Faller, L. KramerDec 4, 1997
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Adiabatic reduction near a bifurcation in stochastically modulated systems
We re-examine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary…
Francois Drolet, Jorge VinalsDec 3, 1997
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Propagation failure of traveling waves in a discrete bistable medium
Propagation failure (pinning) of traveling waves is studied in a discrete scalar reaction-diffusion equation with a piecewise linear, bistable reaction function. The critical points of the pinning…
Gabor FathNov 20, 1997
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Introduction to Extended Electrodynamics
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main…
Stoil DonevNov 14, 1997
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Mutator Dynamics on a Smooth Evolutionary Landscape
We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion…
David A. Kessler, Herbert LevineNov 2, 1997
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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…
Zahir A. Daya, V. B. Deyirmenjian, Stephen W. Morris et al.Oct 9, 1997
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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…
Mary Silber, Michael R. E. ProctorOct 8, 1997
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Extended Electrodynamics: III. Free Photons and (3+1)-Soliton- like Vacuum Solutions
This paper aims to give explicitly all non-linear vacuum solutions to our non-linear field equations, and to define in a coordinate free manner the important subclass of non-linear solutions, which…
S. Donev, M. TashkovaOct 6, 1997
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Propagation Failure in Excitable Media
We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that…
Aric Hagberg, Ehud MeronOct 3, 1997
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Extended Electrodynamics: II. Properties and invariant characteristics of the non-linear vacuum solutions
This paper aims to consider the general properties of the non-linear solutions to the vacuum equations of Extended Electrodynamics. The *-invariance and the conformal invariance of the equations are…
S. Donev, M. TashkovaOct 3, 1997
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Extended Electrodynamics I. Basic Notions, Principles and Equations
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in…
S. Donev, M. TashkovaOct 2, 1997
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Spiral Motion in a Noisy Complex Ginzburg-Landau Equation
The response of spiral waves to external perturbations in a stable regime of the two-dimensional complex Ginzburg-Landau equation (CGLE) is investigated. It is shown that the spiral core has a finite…
Igor Aranson, Hugues Chate, Lei Han TangSep 25, 1997
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Kinematic Equations for Front Motion and Spiral-Wave Nucleation
We present a new set of kinematic equations for front motion in bistable media. The equations extend earlier kinematic approaches by coupling the front curvature with the order parameter associated…
Aric Hagberg, Ehud MeronSep 23, 1997
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Uses of Envelopes for Global and Asymptotic Analysis; geometrical meaning of renormalization group equation
We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of…
Teiji KunihiroSep 20, 1997
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Localized moving breathers in a 2-D hexagonal lattice
We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2-D hexagonal non-linear lattice. The lattice is…
J. L. Marín, J. C. Eilbeck, F. M. RussellSep 17, 1997
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Complexation of Wavenumbers in Solitons
It is shown that, by letting wavenumbers and frequencies complex in Hirota's bilinear method, new classes of exact solutions of soliton equations can be obtained systematically. They include not…
M. UmekiSep 3, 1997
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Amplitude equations for coupled electrostatic waves in the limit of weak instability
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude…
John David Crawford, Edgar KnoblochAug 21, 1997
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Spatio-temporal dynamics of coupled array of Murali-Lakshmanan-Chua circuits
The circuit recently proposed by Murali, Lakshmanan and Chua (MLC) is one of the simplest non-autonomous nonlinear electronic circuits which shows a variety of dynamical phenomena including various…
P. Muruganandam, K. Murali, M. LakshmananAug 20, 1997
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Nature of Roll to Spiral-Defect-Chaos Transition
We investigate the nature of the parallel-roll to spiral-defect-chaos (SDC) transition in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We carry out extensive,…
Xiao-jun Li, Hao-wen Xi, J. D. GuntonAug 12, 1997
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Noise sustained pattern growth: Bulk versus boundary effects
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at…
M. Luecke, A. SzpryngerAug 6, 1997
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Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts
Kinematic equations for the motion of slowly propagating, weakly curved fronts in bistable media are derived. The equations generalize earlier derivations where algebraic relations between the normal…
Aric Hagberg, Ehud MeronJul 29, 1997
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Strongly nonlinear convection in binary fluids: Minimal model for extended states using symmetry decomposed modes
Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few-mode-model. It is derived…
St. Hollinger, M. LueckeJul 29, 1997
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