Search results for "Pattern Formation"
showing 10 items of 408 documents
Inelastic scattering and interactions of three-wave parametric solitons.
2006
We study the interactions of velocity-locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We reveal that the inelastic scattering between three-wave solitons and linear waves may be described in terms of analytical solutions with dynamically varying group velocity, or boomerons. Moreover, we demonstrate the elastic nature of three-wave soliton-soliton collisions and interactions.
From kinks to compactonlike kinks
1998
We show that, in the continuum limit, the generalized \ensuremath{\Phi}-four or double-well model with nonlinear coupling can exhibit compactonlike kink solutions for some specific velocity regimes and when the nonlinear coupling between pendulums is dominant. Our numerical simulations point out that the static compacton is stable and the dynamic compacton is unstable. Our study is extended to other topological systems where compacton solutions can also be found. A nice feature is that a mechanical analog of the double-well system can be constructed in the form of an experimental lattice of coupled pendulums, which, in the strong coupling limit, allows the observation of these entities.
Experimental evidence of X-shaped spatiotemporal coherence of superfluorescence radiation
2006
Considering the parametric generation process in a quadratic nonlinear crystal, we report the experimental observation of optical waves characterized by a X-shaped spatiotemporal coherence, i.e. a coherence skewed along spatiotemporal trajectories.
Dynamics of the labyrinthine patterns at the diffuse phase boundaries
2001
The phase diagram of a magnetic colloid in a Hele-Shaw cell is calculated. As a function of the magnetic field strength, of the concentration and of the layer thickness the magnetic colloid can find itself in a stripe phase, the hexagonal phase or in an unmodulated state. Those results allow to interpret experiments observing the transformation of a labyrinthine pattern into a hexagonal structure. This possibility is confirmed directly by the numerical simulation presented here and showing the transformation of the labyrinthine pattern into the hexagonal structure.
Dark-and-bright rogue waves in long wave-short wave resonance
2014
Nonlinear Photonics, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, in Proceedings Advanced Photonics, Part of Advanced Photonics, Barcelona, Spain, 28-31 July 2014
Self-similarity and scaling of thermal shock fractures
2013
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such process of pattern formation with quasi-static crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest crack. The onset of instability has also been determined from numerical results.
Frenkel-Kontorova model with anharmonic interactions
1986
It is shown that consideration of more realistic interatomic potentials (with limited tensile strength) within the framework of the Frenkel-Kontorova model may lead to a breakdown of the soliton picture in systems with competing periodicities. Closed analytical expressions for the form of a single soliton in an anharmonic chain reveal discontinuities which indicate a disintegration of the entire system beyond some critical values of the misfit, and/or of the height of the periodic substrate potential. The length of anharmonic solitons depends essentially on both the sign and the magnitude of the misfit. The influence of misfit on the pinning-unpinning transition is also investigated.
Symmetry breaking and singularity structure in Bose-Einstein condensates
2012
We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the tra…
Controlled Observation of a Nonequilibrium Ising-Bloch Transition in a Nonlinear Optical Cavity
2004
We describe the controlled observation of the nonequilibrium Ising-Bloch transition in a broad area nonlinear optical cavity, namely, a quasi-1D single longitudinal-mode photorefractive oscilator in a degenerate four-wave mixing configuration. Our experimental technique allows for the controlled injection of the domain walls. We use cavity detuning as control parameter and find that both Ising and Bloch walls can exist for the same detuning values within a certain interval of detunings, i.e., the Ising-Bloch transition is hysteretic in our case. A complex Ginzburg-Landau model is used for supporting the observations.
Optical solitons in erbium doped fibers with higher order effects
2000
Abstract We consider the coupled system of higher order nonlinear Schrodinger equation and Maxwell–Bloch (HNLS–MB) equations, which governs the nonlinear wave propagation in erbium doped optical waveguides in presence of important higher order effects. We present the Lax pair and using Backlund transformation exact soliton solutions are generated.