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Pattern Formation and Solitons papers — page 14

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Two Scale Model for Aggregation and Etching
We propose a dual scale drift-diffusion model for interfacial growth and etching processes. The two scales are: (i) a depletion layer width surrounding the aggregate and (ii) a drift length.The…
George C. John, Vijay A. SinghDec 4, 1995
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The Speed of Fronts of the Reaction Diffusion Equation
We study the speed of propagation of fronts for the scalar reaction-diffusion equation ut = uxx + f(u)\, with f(0) = f(1) = 0. We give a new integral variational principle for the speed of…
R. D. Benguria, M. C. DepassierNov 29, 1995
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Noise and dynamical pattern selection
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is…
Douglas A. KurtzeNov 27, 1995
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Existence and Stability of Steady Fronts in Bistable CML
We prove the existence and we study the stability of the kink-like fixed points in a simple Coupled Map Lattice for which the local dynamics has two stable fixed points. The condition for the…
B. FernandezNov 7, 1995
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Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability
Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show…
Laurent Daudet, Valerie Ego, Sebastien Manneville et al.Oct 26, 1995
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Steady and Oscillatory Side-Band Instabilities in Marangoni Convection with Deformable Interface
The stability of Marangoni roll convection in a liquid-gas system with deformable interface is studied in the case when there is a nonlinear interaction between two modes of Marangoni instability:…
A. A. Golovin, A. A. Nepomnyashchy, L. M. Pismen et al.Oct 23, 1995
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Attracting Manifold for a Viscous Topology Transition
An analytical method is developed describing the approach to a finite-time singularity associated with collapse of a narrow fluid layer in an unstable Hele-Shaw flow. Under the separation of time…
Raymond E. Goldstein, Adriana I. Pesci, Michael J. ShelleyOct 20, 1995
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Stability of periodic arrays of vortices
The stability of periodic arrays of Mallier-Maslowe or Kelvin-Stuart vortices is discussed. We derive with the energy-Casimir stability method the nonlinear stability of this solution in the inviscid…
Thierry Dauxois, Stephan Fauve, Laurette TuckermanOct 16, 1995
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Pattern selection of cracks in directionally drying fracture
We study pattern selection of cracks in directionally drying fractures by analyzing the experimental systems recently devised by C. Allain and L. Limat. [Phys. Rev. Lett. 74, 2981 (1995).]…
Teruhisa S. Komatsu, Shin-ichi SasaOct 11, 1995
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Synchronisation in Coupled Sine Circle Maps
We study the spatially synchronized and temporally periodic solutions of a 1-d lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and…
Nandini Chatterjee, Neelima GupteOct 5, 1995
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Stability Results for Steady, Spatially--Periodic Planforms
We consider the symmetry-breaking steady state bifurcation of a spatially-uniform equilibrium solution of E(2)-equivariant PDEs. We restrict the space of solutions to those that are doubly-periodic…
B. Dionne, M. Silber, A. C. SkeldonSep 26, 1995
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The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a…
R. A. Kraenkel, M. A. Manna, J. C. Montero et al.Sep 25, 1995
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Reductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each…
R. A. Kraenkel, M. A. Manna, J. C. Montero et al.Sep 25, 1995
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Tangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization
We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new…
Sergej FlachSep 25, 1995
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Controlling domain patterns far from equilibrium
A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations.…
A. Hagberg, E. Meron, I. Rubinstein et al.Aug 29, 1995
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A Geometrical Formulation of the Renormalization Group Method for Global Analysis II: Partial Differential Equations
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations…
Teiji KunihiroAug 22, 1995
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Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy
We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the…
R. A. Kraenkel, M. A. Manna, J. C. Montero et al.Jul 31, 1995
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Front Stability in Mean Field Models of Diffusion Limited Growth
We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of…
Douglas Ridgway, Herb Levine, Yuhai TuJul 18, 1995
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Hexagons, Kinks and Disorder in Oscillated Granular Layers
Experiments on vertically oscillated granular layers in an evacuated container reveal a sequence of well-defined pattern bifurcations as the container acceleration is increased. Period doublings of…
Francisco Melo, Paul Umbanhowar, Harry L. SwinneyJul 17, 1995
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Onset of Surface-Tension-Driven Benard Convection
Experiments with shadowgraph visualization reveal a subcritical transition to a hexagonal convection pattern in thin liquid layers that have a free upper surface and are heated from below. The…
Michael F. Schatz, Stephen J. VanHook, William D. McCormick et al.Jul 7, 1995
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Long-Wavelength Instability in Surface-Tension-Driven Benard Convection
Laboratory studies reveal a deformational instability that leads to a drained region (dry spot) in an initially flat liquid layer (with a free upper surface) heated uniformly from below. This…
Stephen J. Vanhook, Michael F. Schatz, William D. McCormick et al.Jul 7, 1995
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Cancer Detection via Determination of Fractal Cell Dimension
We utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from…
Wolfgang Bauer, Charles D. MackenzieJul 6, 1995
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A Kink Soliton Characterizing Traffic Congestion
We study traffic congestion by analyzing a one dimensional traffic flow model. Developing an asymptotic method to investigate the long time behavior near a critical point, we derive the modified…
Teruhisa S. Komatsu, Shin-ichi SasaJun 26, 1995
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Two-phase binary fluids and immiscible fluids described by an order parameter
A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a…
Morton E. Gurtin, Debra Polignone, Jorge VinalsJun 19, 1995
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Domain Coarsening in Systems Far from Equilibrium
The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling…
M. C. Cross, D. I. MeironMay 26, 1995
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