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Pattern Formation and Solitons papers

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Pulse Shepherding and Multi-Channel Soliton Transmission in Bit-Parallel-Wavelength Optical Fiber Links
We study bit-parallel-wavelength (BPW) pulse transmission in multi-channel single-mode optical fiber links for high-performance computer networks. We develop a theory of the pulse shepherding effect…
Yuri S. Kivshar, Elena A. OstrovskayaAug 16, 2000
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A Particle Model of Rolling Grain Ripples Under Waves
A simple model is presented for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave. An equation of motion is derived for the individual…
K. H. AndersenMay 2, 2000
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Two-color multistep cascading and parametric soliton-induced waveguides
We introduce the concept of two-color multistep cascading for vectorial parametric wave mixing in optical media with quadratic (second-order or chi-2) nonlinear response. We demonstrate that the…
Yuri S. Kivshar, Andrey A. Sukhorukov, Solomon M. SaltielJan 21, 2000
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Pattern formation in inclined layer convection
We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number σ≈ 1. We observed a number of new nonlinear, mostly…
Karen E. Daniels, Eberhard BodenschatzDec 21, 1999
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On the Properties of Two Pulses Propagating Simultaneously in Different Dispersion Regimes in a Nonlinear Planar Waveguide
Properties of two pulses propagating simultaneously in different dispersion regimes, anomalous and normal, in a Kerr-type planar waveguide are studied in the framework of the nonlinear Schroedinger…
Monika E. PietrzykDec 21, 1999
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Formation and Pinch-off of Viscous Droplets in the Absence of Surface Tension: an Exact Result
Within a class of exact time-dependent non-singular N-logarithmic solutions (Mineev-Weinstein and Dawson, Phys. Rev. E 50, R24 (1994); Dawson and Mineev-Weinstein, Phys. Rev. E 57, 3063 (1998)), we…
Mark Mineev-Weinstein, Gary D. Doolen, John E. Pearson et al.Dec 18, 1999
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Dipole-Mode Vector Solitons
We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. These solitons, which appear as a consequence of the vector nature of the…
Juan J. Garcia-Ripoll, Victor M. Perez-Garcia, Elena A. Ostrovskaya et al.Dec 15, 1999
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1/f noise in spatially extended systems with order-disorder phase transitions
Noise power spectra in spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations…
Kestutis StaliunasDec 15, 1999
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Defect Chaos of Oscillating Hexagons in Rotating Convection
Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven…
Blas Echebarria, Hermann RieckeDec 7, 1999
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Vector solitons in (2+1) dimensions
We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of…
Johan N. Malmberg, Andreas H. Carlsson, Dan Anderson et al.Dec 1, 1999
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Kink dynamics in a novel discrete sine-Gordon system
A spatially-discrete sine-Gordon system with some novel features is described. There is a topological or Bogomol'nyi lower bound on the energy of a kink, and an explicit static kink which…
J. M. Speight, R. S. WardNov 25, 1999
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Time resolved pattern evolution in a large aperture laser
We have measured quasi-instantaneous transverse patterns in a broad aperture laser. Non-ordered patterns yielding to boundary determined regular structures in progressive time-integrated recording…
F. Encinas-Sanz, I. Leyva, J. M. GuerraNov 22, 1999
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Origin of Multikinks in Dispersive Nonlinear Systems
We develop the first analytical theory of multikinks for strongly dispersive nonlinear systems, considering the examples of the weakly discrete sine-Gordon model and the generalized…
Alan Champneys, Yuri S. KivsharNov 19, 1999
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Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio
Rayleigh-Bénard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions.…
B. Huke, M. Lücke, P. Büchel et al.Nov 16, 1999
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Surface tension-driven convection patterns in two liquid layers
Two superposed liquid layers display a variety of convective phenomena that are inaccessible in the traditional system where the upper layer is a gas. We consider several pairs of immiscible liquids.…
Anne Juel, John M. Burgess, W. D. McCormick et al.Nov 16, 1999
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Development and geometry of isotropic and directional shrinkage crack patterns
We have studied shrinkage crack patterns which form when a thin layer of an alumina/water slurry dries. Both isotropic and directional drying were studied. The dynamics of the pattern formation…
Kelly A. Shorlin, John R. de Bruyn, Malcolm Graham et al.Nov 15, 1999
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Instanton solutions in the problem of wrinkled flame front dynamics
The statistics of wrinkling flame front is invetigated by the quantum filed theory methods. We dwell on the WKB approximation in the functional integral which is analogous to the Wyld functional…
Dmitri Volchenkov, Ricardo LimaNov 2, 1999
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Crossover from a square to a hexagonal pattern in Faraday surface waves
We report on surface wave pattern formation in a Faraday experiment operated at a very shallow filling level, where modes with a subharmonic and harmonic time dependence interact. Associated with…
C. Wagner, H. W. Mueller, K. KnorrNov 2, 1999
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Solitons in anharmonic chains with ultra-long-range interatomic interactions
We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened…
Serge F. Mingaleev, Yuri B. Gaididei, Franz G. MertensOct 19, 1999
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Cross-Newell equations for hexagons and triangles
The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in flux-divergence form. Specific examples of complex governing equations that…
Rebecca B. HoyleOct 16, 1999
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Dynamics of a Single Peak of the Rosensweig Instability in a Magnetic Fluid
To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear…
Adrian Lange, Heinz Langer, Andreas EngelOct 5, 1999
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Planform selection in two-layer Benard-Marangoni convection
Benard-Marangoni convection in a system of two superimposed liquids is investigated theoretically. Extending previous studies the complete hydrodynamics of both layers is treated and buoyancy is…
A. Engel, J. B. SwiftOct 5, 1999
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Discrete stochastic modeling of calcium channel dynamics
We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the…
Markus Baer, Martin Falcke, Herbert Levine et al.Oct 4, 1999
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Linear and nonlinear waveguides induced by optical vortex solitons
We study, numerically and analytically, linear and nonlinear waveguides induced by optical vortex solitons in a Kerr medium. Both fundamental and first-order guided modes are analyzed, as well as the…
Andreas H. Carlsson, Johan N. Malmberg, Dan Anderson et al.Sep 30, 1999
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Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic Electroconvection
We present the first quantitative verification of an amplitude description for systems with (nearly) spontaneously broken isotropy, in particular for the recently discovered abnormal-roll states. We…
Axel G. Rossberg, Nandor Eber, Agnes Buka et al.Sep 29, 1999
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