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Pattern Formation and Solitons papers — page 10

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Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices…
S. Flach, C. R. WillisApr 17, 1997
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Compacton Solutions in a Class of Generalized Fifth Order Korteweg-de Vries Equations
We study a class of generalized fifth order Korteweg-de Vries (KdV) equations which are derivable from a Lagrangian L(p,m,n,l) which has variable powers of the first and second derivatives of the…
Fred Cooper, James M. Hyman, Avinash KhareApr 14, 1997
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Instabilities of periodic orbits with spatio-temporal symmetries
Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of…
A. M. Rucklidge, Mary SilberApr 14, 1997
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Liquefaction of a Horizontally Vibrated Granular Bed: Friction, Dilation and Segregation
We present experimental observations of the onset of flow (liquefaction) for horizontally vibrated granular materials. As the acceleration increases above certain value, the top layer of granular…
Sarath G. Tennakoon, R. P. BehringerApr 9, 1997
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Resonances of dynamical checkerboard states in Josephson arrays with self-inductance
We study the dynamics of fully frustrated, underdamped Josephson arrays. Experiments reveal remarkable similarities among the dc current-voltage characteristics of several kinds of square and…
M. Barahona, E. Trias, T. P. Orlando et al.Mar 26, 1997
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Localized and Cellular Patterns in a Vibrated Granular Layer
We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and…
Lev Tsimring, Igor AransonMar 26, 1997
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On the Origin of Traveling Pulses in Bistable Systems
The interaction between a pair of Bloch fronts forming a traveling domain in a bistable medium is studied. A parameter range beyond the nonequilibrium Ising-Bloch bifurcation is found where traveling…
C. Elphick, A. Hagberg, B. A. Malomed et al.Mar 21, 1997
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Spinodal Decomposition in Binary Gases
We carried out three-dimensional simulations, with about 1.4 million particles, of phase segregation in a low density binary fluid mixture, described mesoscopically by energy and momentum conserving…
S. Bastea, J. L. LebowitzMar 19, 1997
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A discrete phi4 system without Peierls-Nabarro barrier
A discrete phi4 system is proposed which preserves the topological lower bound on the kink energy. Existence of static kink solutions saturating this lower bound and occupying any position relative…
J. M. SpeightMar 17, 1997
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Derivation of Amplitude Equations by Renormalization Group Method
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the…
Ken-ichi Matsuba, Kazuhiro NozakiMar 10, 1997
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Nonlinear Dynamics of a Single Ferrofluid-Peak in an Oscillating Magnetic Field
If a magnetic field normal to the surface of a magnetic fluid is increased beyond a critical value a spontaneous deformation of the surface arises (normal field instability). The instability is…
Thomas Mahr, Ingo RehbergMar 7, 1997
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Hexagonal patterns in finite domains
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and…
P. C. MatthewsMar 7, 1997
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Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting…
V. B. Deyirmenjian, Zahir A. Daya, Stephen W. MorrisMar 4, 1997
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Propagation and Structure of Planar Streamer Fronts
Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma.…
Ute Ebert, Wim van Saarloos, Christiane CaroliFeb 21, 1997
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Streamer Propagation as a Pattern Formation Problem: Planar Fronts
Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma.…
Ute Ebert, Wim van Saarloos, Christiane CaroliFeb 21, 1997
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Competition between Spiral-Defect Chaos and Rolls in Rayleigh-Benard Convection
We present experimental results for pattern formation in Rayleigh-Benard convection of a fluid with a Prandtl number, Pr~ 4. We find that the spiral-defect-chaos (SDC) attractor which exists for Pr~1…
Kapil M. S. Bajaj, David S. Cannell, Guenter AhlersFeb 21, 1997
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Transition from Spatiotemporal Chaos to Ideal Straight Rolls in Rayleigh-Benard Convection
For Rayleigh-Benard convection in a square cell with a fluid of Prandtl number one, we report experimental results on the transition between a stationary pattern of ideal straight rolls (ISR) and the…
Reha V. Cakmur, David A. Egolf, Brendan B. Plapp et al.Feb 20, 1997
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Amplitude equations and pattern selection in Faraday waves
We present a systematic nonlinear theory of pattern selection for parametric surface waves (Faraday waves), not restricted to fluids of low viscosity. A standing wave amplitude equation is derived…
Peilong Chen, Jorge VinalsFeb 11, 1997
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Renormalization Group Method and Reductive Perturbation Method
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable…
Ken-ichi Matsuba, Kazuhiro NozakiFeb 2, 1997
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Stability criterion for bright solitary waves of the perturbed cubic-quintic Schroedinger equation
The stability of the bright solitary wave solution to the perturbed cubic-quintic Schroedinger equation is considered. It is shown that in a certain region of parameter space these solutions are…
Todd KapitulaJan 23, 1997
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Order Parameter Equations for Front Transitions: Planar and Circular Fronts
Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup.…
Aric Hagberg, Ehud Meron, I. Rubinstein et al.Jan 23, 1997
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Pattern formation in weakly damped parametric surface waves driven by two frequency components
A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency…
Wenbin Zhang, Jorge VinalsJan 20, 1997
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Predicting Non-linear Cellular Automata Quickly by Decomposing Them into Linear Ones
We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log2 t)…
Cristopher MooreJan 20, 1997
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Travelling waves in electroconvection of the nematic Phase 5: A test of the weak electrolyte model
We investigated travelling waves appearing as the primary pattern-forming instability in the nematic Phase 5 (Merck) in the planar geometry in order to test the recently developed weak electrolyte…
Martin Treiber, Nandor Eber, Agnes Buka et al.Jan 14, 1997
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Synchronization of globally-coupled phase oscillators: singularities and scaling for general couplings
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a…
John David Crawford, K. T. R. DaviesJan 10, 1997
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