Search results for "Pattern formation"
showing 10 items of 408 documents
Spatiotemporal Complexity in Step-Index Multimode Fibers
2016
We study supercontinuum generation in step-index fibers with a varying number of modes. We observe new spatiotemporal effects, including evidence of multimode spectral incoherent solitons, and a universal transition to spatiotemporal complexity.
Analog simulation of neural information propagation using an electrical FitzHugh-Nagumo lattice
2004
International audience; A nonlinear electrical lattice modelling neural information propagation is presented. It is shown that our system is an analog simulator of the FitzHugh-Nagumo equations, and hence supports pulse propagation with the appropriate properties.
Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrodinger equations
2006
International audience; A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable N-coupled nonlinear Schrodinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which nonsingular soliton propagation can occur. The multisoliton …
Observation of collapse arrest in pure kerr media sustained by a parametric interaction
2013
We demonstrate a parametric interaction based on four wave mixing that can arrest the collapse and stabilize solitary propagation in a pure Kerr material by controlling the wavelength of the interacting beams.
Switching Dynamics of Dark Solitons in Kerr Microresonators
2019
Dissipative Kerr solitons (DKS) are localized structures in optical resonators that arise from a double balance between dispersion and Kerr effect, and linear loss and parametric gain [1]. The periodic nature of DKS corresponds to frequency combs. DKS can be generated in high-Q microresonators for diverse applications, from coherent communications to precision frequency synthesis [1]. Most studies of DKS have focused on microresonator cavities operating in the anomalous dispersion regime, where the waveforms correspond to bright soliton pulses. Coherent microresonator combs can also be formed in the normal dispersion regime [2]. The time-domain waveform corresponds to a localized dark-pulse…
Vectorial Kerr-cavity solitons.
2000
It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CS’s). A parametrically driven Ginzburg–Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CS’s is numerically investigated.
Microscopic approach to the kinetics of pattern formation of charged molecules on surfaces.
2010
A microscopic formalism based on computing many-particle densities is applied to the analysis of the diffusion-controlled kinetics of pattern formation in oppositely charged molecules on surfaces or adsorbed at interfaces with competing long-range Coulomb and short-range Lennard-Jones interactions. Particular attention is paid to the proper molecular treatment of energetic interactions driving pattern formation in inhomogeneous systems. The reverse Monte Carlo method is used to visualize the spatial molecular distribution based on the calculated radial distribution functions (joint correlation functions). We show the formation of charge domains for certain combinations of temperature and dy…
Long-range effects on the periodic deformable sine-Gordon chains
1999
The model of long-range interatomic interactions is found to reveal a number of new features, closely connected with the substrate potential shape parameter s. The phase trajectories, as well as an analytical analysis, provide information on a disintegration of solitons upon reaching some critical values of the lattice parameters. An implicit form for two classes of these topological solitons (kink) is calculated exactly.
Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation
2007
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…
Cellular automaton for chimera states
2016
A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority (voting) rule. This suggests the universality of chimera-like behavior from a new point of view: Already simple CA rules based on the majority rule exhibit this behavior. After a short transient, we find chimera states for arbitrary initial conditions, the system spontaneously splitting into stable domains separated by static boundaries, ones synchronously oscillating and the others incoherent. When the coupling range is local, nontrivial coherent struct…