Search results for "Instability"
showing 10 items of 724 documents
Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal
2022
This manuscript tackles the study of vegetation pattern dynamics driven by inertial effects and secondary seed dispersal. To achieve this goal, an hyperbolic extension of the classical parabolic Klausmeier model of vegetation, generally used to predict the formation of banded vegetation along the slopes of semiarid environments, has been here considered together with an additional advective term mimicking the downslope motion of seeds. Linear stability analyses have been carried out to inspect the dependence of the wave instability locus on the model parameters, with particular emphasis on the role played by inertial time and seed advection speed. Moreover, periodic travelling wave solution…
Non-Homogeneous Tension Profile
2013
In this chapter, we will look at the influence of a skewed tension profile on the divergence instability of a travelling, thin elastic plate. The travelling plate is subjected to axial tension at the supports, but the tension distribution along the supports is not uniform. For the nonuniformity, we will use a linear distribution. First, we will perform a dynamic analysis of small time-harmonic vibrations, after which we will concentrate on the divergence instability problem. We will see that a small inhomogeneity in the applied tension may have a large effect on the divergence modes, and that inhomogeneity in the tension profile may significantly decrease the critical velocity of the plate.
From equilibrium to chaos and back : methodological evaluation of research of the majority rule
2000
According to the canonical model situated at the heart of the " economic " - or, as the political scientists prefer to call it, rational-choice - theory of (democratic) politics, whenever the matter to be decided raises, or consists of, at least two distinct issues, it is generally impossible to reach a determinate decision by using the majority rule. This problem, referred to as that of disequilibrium, equilibrium instability, or even"chaos", was first underplayed and then deemed ominous to the point of seriously undermining the development prospects of the whole theory. However, more recently, the concern it was the source o f until the 1980s has given way to a state of renewed confidence…
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…
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…
INSTABILITY OF HAMILTONIAN SYSTEMS IN THE SENSE OF CHIRIKOV AND BIFURCATION IN A NON LINEAR EVOLUTION PROBLEM EMANATING FROM PHYSICS
2004
We prove the existence of a minimal geometrico-dynamical condition to create hyperbolicity in section in the vicinity of a transversal homoclinic partially hyperbolic torus in a near integrable Hamiltonian system with three degrees of freedom. We deduce in this context a generalization of the Easton's theorem of symbolic dynamics. Then we give the optimal estimation of the Arnold diffusion time along a transition chain in the initially hyperbolic Hamiltonian systems with three degrees of freedom with a surrounding chain of hyperbolic periodic orbits .In a second part, we describe geometrically a mechanism of diffusion studied by Chirikov in a near integrable Hamiltonian system with three de…
Intermittency in the homopolar disk-dynamo
2006
We study a modified Bullard dynamo and show that this system is equivalent to a nonlinear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first towards an \lq\lq intermittent\rq\rq state where the absorbing (non-dynamo) state is no more stable but the most probable value of the amplitude of the oscillator is still zero and secondly towards a \lq\lq turbulent\rq\rq (dynamo) state where it is possible to define unambiguously a (non-zero) most probable value around which the amplitude of the oscillator fluctuates. The bifurcation diagram of this system exhibits three regions which are analytically characteri…
Generation of a 160-GHz transform-limited pedestal-free pulse train through multiwave mixing compression of a dual-frequency beat signal.
2002
International audience; We report the experimental generation of a 160-GHz picosecond pulse train at 1550 nm, using multiple four-wave mixing temporal compression of an initial dual-frequency beat signal in the anomalous-dispersion regime of a nonzero dispersion-shifted fiber. Complete intensity and phase characterizations of the pulse train were carried out by means of a frequency-resolved optical gating technique, showing that 1.27-ps transform-limited pedestal-free Gaussian pulses were generated.
Soliton generation and rogue-wave like behavior through fourth order modulation instability
2010
International audience; We numerically study the dynamics of ultra-broadband wavelength converters based on fourth-order scalar modulation instability. We report the spontaneous emergence of solitons and trapped radiation waves as well as L-shaped associated statistical signatures.
Complex rogue wave in the fiber optics
2016
This manuscript presents the generation of complex rogue waves related to nonlinear instabilities occurring through the propagation of light in standard optical fibers. Linear and nonlinear physical phenomena involved are first listed, in particular some of them by analogy with the field of hydrodynamics. The different forms of rogue waves induced by the modulation instability process are then presented. They are also known as "breathers", and they are obtained by solving the nonlinear Schrödinger equation. From these exact solutions, various experimental systems were designed by means of numerical simulations based on two rogue-wave excitation methods. The first one is an exact generation …