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Pattern Formation and Solitons papers — page 18

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On the self-similar solutions of normality equation in two-dimensional case
The integrability in quadratures of normality equation for spatially homogeneous dynamical systems in two-dimensional space is shown. The classical symmetries of this equation are calculated and the…
A. Yu. BoldinJul 25, 1993
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One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations
We study the generalized Korteweg-DeVries equations derivable from the Lagrangian: $ L(l,p) = ∫ ( 12 φx φt - (φx)l l(l-1) + α(φx)p (φxx)2 )…
Avinash Khare, Fred CooperJul 21, 1993
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A quantitative measurement of spatial order in ventricular fibrillation
As an objective measurement of spatial order in ventricular fibrillation (VF), spatial correlation functions and their characteristic lengths were estimated from epicardial electrograms of pigs in…
P. V. Bayly, E. E. Johnson, P. D. Wolf et al.Jul 18, 1993
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Dissipative Boussinesq System of Equations in the Bénard-Marangoni Phenomenon
By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity,…
R. A. Kraenkel, S. M. Kurcbart, J. G. Pereira et al.Jun 28, 1993
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Discrete Breathers and Energy Localization in Nonlinear Lattices
We discuss the process by which energy, initially evenly distributed in a nonlinear lattice, can localize itself into large amplitude excitations. We show that, the standard modulational instability…
T. Dauxois, M. PeyrardJun 25, 1993
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A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation
We present a new class of exact solutions for the so-called Laplacian Growth Equation describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common…
Mark B. Mineev-Weinstein, Silvina Ponce DawsonMay 26, 1993
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Nonequilibrium Phenomena in Liquid Crystals
This paper summarizes a talk presented at the April NATO ASI on Spatiotemporal Chaos in Complex Fluids, in Santa Fe, NM. The paper gives reasons that make complex fluids good material systems for…
John BechhoeferMay 21, 1993
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Phase Transitions In Two-Dimensional Traffic Flow Models
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase…
José A. Cuesta, Froilán C. Martínez, Juan M. Molera et al.May 19, 1993
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Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating…
Aric Hagberg, Ehud MeronMay 19, 1993
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Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection
We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number of approximately 1. We observed a chaotic pattern consisting of many…
Stephen W. Morris, Eberhard Bodenschatz, David S. Cannell et al.May 18, 1993
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Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations
We study the class of generalized Korteweg-DeVries equations derivable from the Lagrangian: $ L(l,p) = ∫ ( 12 x t - (x)l l(l-1) + α(x)p…
Fred Cooper, Harvey Shepard, Pasquale SodanoMay 18, 1993
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Spiral defect chaos in a model of Rayleigh-Benard convection
A numerical solution of a generalized Swift-Hohenberg equation in two dimensions reveals the existence of a spatio-temporal chaotic state comprised of a large number of rotating spirals. This state…
Hao-wen Xi, J. D. Gunton, Jorge VinalsMay 14, 1993
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An integrable shallow water equation with peaked solitons
We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by…
Roberto Camassa, Darryl D. HolmMay 13, 1993
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Pattern formation during Rayleigh-Bénard convection in non-Boussinesq fluids
Motivated by recent experimental studies of Bodenschatz et al. [E. Bodenschatz, J.R. de Bruyn, G. Ahlers and D.S. Cannell, Phys. Rev. Lett. 67, 3078 (1991) ], we present a numerical study of a…
Hao-wen Xi, J. D. Gunton, Jorge VinalsMay 4, 1993
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Solitons and 1/f Noise in Molecular Chains
Davydov's model of solitons in alpha-helix protein chains is shown to display features of self-organized criticality (SOC), i.e., power law behaviour of correlations in space and 1/f-noise, as a…
H. Rosu, E. CanessaApr 20, 1993
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Complex Patterns in a Simple System
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations.…
John E. PearsonApr 17, 1993
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Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward…
Aric Hagberg, Ehud MeronApr 9, 1993
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Multidimensional Dynamical Systems Accepting the Normal Shift
The dynamical systems of the form r= F ( r, r) in Rn accepting the normal shift are considered. The concept of weak normality for them is introduced. The…
A. Yu. Boldin, R. A. SharipovApr 4, 1993
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Threshold-Range Scaling of Excitable Cellular Automata
Each cell of a two-dimensional lattice is painted one of k colors, arranged in a "color wheel." The colors advance (0 to k-1 mod k) either automatically or by contact with at least a…
Robert Fisch, Janko Gravner, David GriffeathApr 2, 1993
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Metastability in the Greenberg-Hastings Model
The Greenberg-Hastings Model (GHM) is a family of multitype cellular automata that emulate excitable media, exhibiting the nucleation and spiral formation characteristic of such complex systems. In…
Robert Fisch, Janko Gravner, David GriffeathMar 23, 1993
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Threshold Growth Dynamics
We study the asymptotic shape of the occupied region for monotone deterministic dynamics in d-dimensional Euclidean space parametrized by a threshold theta, and a Borel set N with positive and finite…
Janko Gravner, David GriffeathMar 23, 1993
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Solitons and Long Josephson Junctions
Magnetic flux quanta, of value h/2e, in long Josephson junctions behave as (quasi) solitons. Fluxon dynamical states are well described by a perturbed sine-Gordon equation model, with boundary…
R. D. ParmentierMar 23, 1993
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Asymptotic Behavior of Excitable Cellular Automata
We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating…
Richard Durrett, David GriffeathMar 22, 1993
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Localized States in Discrete Nonlinear Schrödinger Equations
A new 1-D discrete nonlinear Schrödinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The…
David Cai, A. R. Bishop, Niels Grønbech-JensenMar 14, 1993
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Rotating Rayleigh-Bénard Convection: Aspect Ratio Dependence of the Initial Bifurcations
The initial bifurcations in rotating Rayleigh-Bénard convection are studied in the range of dimensionless rotation rate 0 < Ω< 2150 for an aspect-ratio-2.5 cylindrical cell. We used simultaneous…
Li Ning, Robert E. EckeMar 11, 1993
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