Search results for "Pattern formation"
showing 10 items of 408 documents
Spectral long-range interaction of temporal incoherent solitons.
2014
We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.
Impact of self-steepening on incoherent dispersive spectral shocks and collapse-like spectral singularities
2014
International audience; Incoherent dispersive shock waves and collapselike singularities have been recently predicted to occur in the spectral evolution of an incoherent optical wave that propagates in a noninstantaneous nonlinear medium. Here we extend this work by considering the generalized nonlinear Schrödinger equation. We show that self-steepening significantly affects these incoherent spectral singularities: (i) It leads to a delay in the development of incoherent dispersive shocks, and (ii) it arrests the incoherent collapse singularity. Furthermore, we show that the spectral collapselike behavior can be exploited to achieve a significant enhancement (by two orders of magnitudes) of…
Compact-like pulse signals in a new nonlinear electrical transmission line
2013
International audience; A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers' equations. This equation admits compact pulse solutions and shares some symmetry properties with the Rosenau-Hyman K(2,2) equation. An exact discrete compactly- supported signal voltage is found for the network and the dissipative effects on the pulse motion analytically studied. Numerical simulations confirm the validity of analytical results and the robustness of these …
Pattern dynamics in a nonlinear electrical lattice
2003
International audience; In this paper, we present experiments using a nonlinear electrical line, modeling the FitzHugh-Nagumo equation, without recovery term. Different patterns are studied according to the para meters of this medium and initial conditions. We then propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, two kinds,of binarization-one depending on an amplitude threshold, the other on an energetical threshold-and nonlinear filtering allowing noise removal can be obtained in the same medium.
Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
2017
International audience; We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the 'energy' parameter E. We show that as |E| -> infinity, NV behaves, as expected, similarly to its formal limit, the Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when |E| is not very large, more varied scenarios are possible, in particular, blow-ups are observed. The mechanism of the blow-up is studied.
Other 2N− 2 parameters solutions of the NLS equation and 2N+ 1 highest amplitude of the modulus of theNth order AP breather
2015
In this paper, we construct new deformations of the Akhmediev-Peregrine (AP) breather of order N (or APN breather) with real parameters. Other families of quasirational solutions of the nonlinear Schrodinger (NLS) equation are obtained. We evaluate the highest amplitude of the modulus of the AP breather of order N; we give the proof that the highest amplitude of the APN breather is equal to . We get new formulas for the solutions of the NLS equation, which are different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We simultaneously get triangular configurations and isolated rings. Moreover,…
Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions
2011
We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schr\"odinger equations.
The angle of repose of spherical grains in granular Hele-Shaw cells: A molecular dynamics study
2007
We report the results of three dimensional molecular dynamic simulations on the angle of repose of a sandpile formed by pouring mono-sized cohesionless spherical grains into a granular Hele-Shaw cell. In particular, we are interested to investigate the effects of those variables which may impact significantly on pattern formation of granular mixtures in Hele-Shaw cells. The results indicate that the frictional forces influence remarkably the formation of pile on the grain level. Furthermore, We see that increasing grain insertion rate decreases slightly the angle of repose. We also find that in accordance with experimental results, the cell thickness is another significant factor and the an…
From deterministic cellular automata to coupled map lattices
2016
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit $\kappa \to 0$ of a continuous parameter $\kappa$. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when $\kappa$ is finite and nonvanishing. In the limit $\kappa \to \infty$ all RDCAs are shown to ex…
Dynamics of Pattern Formation in Biomimetic Systems
2008
This paper is an attempt to conceptualize pattern formation in self-organizing systems and, in particular, to understand how structures, oscillations or waves arise in a steady and homogenous environment, a phenomenon called symmetry breaking. The route followed to develop these ideas was to couple chemical oscillations produced by Belousov-Zhabotinsky reaction with confined reaction environments, the latter being an essential requirement for any process of Life. Special focus was placed on systems showing organic or lipidic compartments, which represent more reliable biomimetic matrices.