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Pattern Formation and Solitons papers — page 13

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Breathing Spots in a Reaction-Diffusion System
A quasi-2-dimensional stationary spot in a disk-shaped chemical reactor is observed to bifurcate to an oscillating spot when a control parameter is increased beyond a critical value. Further increase…
D. Haim, G. Li, Q. Ouyang et al.May 17, 1996
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A Variational Principle for Eigenvalue Problems of 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. We give a…
R. D. Benguria, M. C. DepassierMay 9, 1996
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A Simple Model for Faraday Waves
We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle waveform rather than by…
John Bechhoefer, Brad JohnsonMay 9, 1996
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The Newell-Whitehead-Segel Equation for Traveling Waves
An equation to describe nearly one-dimensional traveling-waves patterns is put forward. This is a dispersive generalization of the classical Newell-Whitehead-Segel (NWS) equation. Transverse…
Boris MalomedMay 7, 1996
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Non-Monotonic Dispersion of Surface Waves in Magnetic Fluids
The dispersion relation of surface waves of a magnetic fluid in a magnetic field is studied experimentally. We verify the theoretically predicted existence of a non-monotonic dispersion relation. In…
Thomas Mahr, Ingo Rehberg, Alexander GroismanMay 1, 1996
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Twisted and Nontwisted Bifurcations Induced by Diffusion
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the…
Xiao-Biao LinApr 15, 1996
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Solitonic-exchange mechanism of surface~diffusion
We study surface diffusion in the framework of a generalized Frenkel-Kontorova model with a nonconvex transverse degree of freedom. The model describes a lattice of atoms with a given concentration…
Oleg M. Braun, Thierry Dauxois, Michel PeyrardApr 12, 1996
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Mobility and diffusivity in a generalized Frenkel-Kontorova model
Molecular dynamics simulations are used to investigate the atomic mobility and diffusivity of a generalized Frenkel-Kontorova model which takes into account anharmonic (exponential) interaction of…
Oleg M. Braun, Thierry~Dauxois, Maxim V. Paliy et al.Apr 12, 1996
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Shadowing matching errors for wave-front-like solutions
Consider a singularly perturbed system εut=ε2 uxx + f(u,x,ε), u∈ Rn,x∈ R,t≥ 0. Assume that the system has a sequence of regular and internal layers occurring…
Xiao-Biao LinApr 11, 1996
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Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves
Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms…
Wenbin Zhang, Jorge VinalsMar 19, 1996
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Systematic derivation of a rotationally covariant extension of the 2-dimensional Newell-Whitehead-Segel equation
An extension of the Newell-Whitehead-Segel amplitude equation covariant under abritrary rotations is derived systematically by the renormalization group method.
Robert GrahamMar 14, 1996
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Critical phenomena employed in hydrodynamic problems: A case study of Rayleigh-Benard convection
By virtue of Rayleigh-Benard convection, we illustrate the advantages of combining a hydrodynamic pattern forming instability with a thermodynamic critical point. This has already lead to many novel…
Michel Assenheimer, Victor SteinbergMar 11, 1996
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Convective Fingering of an Autocatalytic Reaction Front
We report experimental observations of the convection-driven fingering instability of an iodate-arsenous acid chemical reaction front. The front propagated upward in a vertical slab; the thickness of…
Michael R. Carey, Stephen W. Morris, Paul KolodnerMar 9, 1996
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General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
An asymptotic method for finding instabilities of arbitrary d-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2-…
C. B. Muratov, V. V. OsipovMar 6, 1996
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Numerical Proof of Self-Similarity in Burgers' Turbulence
We study the statistical properties of solutions to Burgers' equation, vt + vvx = νvxx, for large times, when the initial velocity and its potential are stationary Gaussian processes. The…
Erik Aurell, Sergey N. Gurbatov, Sergey I. SimdyankinFeb 23, 1996
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Stability of Travelling Waves for a Damped Hyperbolic Equation
We consider a nonlinear damped hyperbolic equation in n, 1 n 4, depending on a positive parameter ε. If we set ε=0, this equation reduces to the well-known…
Th. Gallay, G. RaugelFeb 22, 1996
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Core Dynamics of Multi-Armed Spirals in Rayleigh-Benard Convection
We report experimental observations of the core dynamics of multi-armed, rotating spirals in Rayleigh-Benard convection for a fluid with Prandtl number near one. In addition to the large-scale…
Brendan B. Plapp, Eberhard BodenschatzFeb 14, 1996
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Hydrodynamics of Monolayer Domains at the Air-Water Interface
Molecules at the air-water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through…
David K. Lubensky, Raymond E. GoldsteinFeb 13, 1996
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Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations
We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear…
A. Amengual, D. Walgraef, M. San Miguel et al.Feb 6, 1996
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Coarse-grained description of thermo-capillary flow
A mesoscopic or coarse-grained approach is presented to study thermo-capillary induced flows. An order parameter representation of a two-phase binary fluid is used in which the interfacial region…
David Jasnow, Jorge VinalsJan 29, 1996
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Local and Global Existence of Multiple Waves Near Formal Approximations
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a Spatial Shadowing lemma to construct exact solutions near the formal…
Xiao-Biao LinJan 26, 1996
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Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?
Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a non-monotonic dispersion relation. The effect of a parametric driving on such waves is studied within suitable coupled…
David Raitt, Hermann RieckeJan 19, 1996
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On the Interaction of Extreme-Low-Frequency Radiation with Living Matter's Coherent Spiral States
Conventional physics cannot explain bioeffects caused by ELF fields [1]. A (double) resonance interaction of ELF radiation with the highly sub-thermal coherent motion of spiral waves in living matter…
K. ZioutasJan 5, 1996
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Early stages of ramified growth in quasi-two-dimensional electrochemical deposition
I have measured the early stages of the growth of branched metal aggregates formed by electrochemical deposition in very thin layers. The growth rate of spatial Fourier modes is described…
John R. de BruynDec 22, 1995
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Absolutely stable solitons in two-component active systems
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one…
Boris Malomed, Herbert WinfulDec 18, 1995
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