Search results for "Linear"

Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion

2012

In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively. When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a travelin…

Propagation failure in discrete bistable reaction-diffusion systems: Theory and experiments

2001

International audience; Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.

Elastic waves in random-fibre networks

1997

The propagation of the first displacement maximum of a semi-infinite wavetrain in a two-dimensional random-fibre network is analysed. Model calculations and numerical simulations are used for demonstrating that two qualitatively different wavefront velocities appear in the network. A transient wave, which travels fast and whose amplitude decreases exponentially, dominates the short-time behaviour when the bending stiffness of the fibres is small and the driving frequency is high. This mode can be described by a one-dimensional model. The transient-wave mode propagates even if the bending stiffness of the fibres vanishes, in which case the normal sound velocity is zero. The usual, and slower…

Pseudodifferential operators of Beurling type and the wave front set

2008

AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.

Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth

2015

We focus on the morphochemical reaction–diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerica…

A pilot study on the differences in wavefront aberrations between two ethnic groups of young generally myopic subjects

2008

A comparative population-based cross-sectional study design was used to examine the prevalence of wavefront patterns in two different ethnic groups, and the relationship of these patterns with ocular biometrics and gender. The Shin–Nippon SRW5000 open field autorefractor, the Wavefront Analysis Supported Customized Ablation (WASCA) wavefront analyser and the IOLMaster were used to determine wavefront aberrations, mean spherical equivalent (SE) refractive error and axial length (AL). Seventy-four eyes from 74 young healthy subjects (44 British Asians, 30 Caucasians; 36 men, 38 women; mean age 22.51 ± 3.89 years) with mean SE averaging )1.90 ± 2.76 D (range )10.88 to +2.19 D) were examined. R…

Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion

2013

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…

Broadband telecom to mid-infrared supercontinuum generation in a dispersion-engineered silicon germanium waveguide.

2015

We demonstrate broadband supercontinuum generation (SCG) in a dispersion-engineered silicon-germanium waveguide. The 3 cm long waveguide is pumped by femtosecond pulses at 2.4 μm, and the generated supercontinuum extends from 1.45 to 2.79 μm (at the −30  dB point). The broadening is mainly driven by the generation of a dispersive wave in the 1.5–1.8 μm region and soliton fission. The SCG was modeled numerically, and excellent agreement with the experimental results was obtained.

FDTD signal extrapolation using a finite impulse response neural network model

1999

<title>Second harmonic generation in selenium thin films</title>

2008

Results of second harmonic (SH) generation in amorphous and crystalline selenium films induced by titanium-sapphire femtosecond laser (wavelength λ - 800-1000 nm) are presented. It is found that the highest intensity of SH is provided by fundamental wave at wavelength 1000 nm and it reaches maximum in approximately 100 sec. The intensity of transmitted SH depends on film thickness while that of reflected does not.