Search results for "Linear system"
showing 10 items of 1558 documents
Nonlinear response of superparamagnets with finite damping: an analytical approach
2004
The strongly damping-dependent nonlinear dynamical response of classical superparamagnets is investigated by means of an analytical approach. Using rigorous balance equations for the spin occupation numbers a simple approximate expression is derived for the nonlinear susceptibility. The results are in good agreement with those obtained from the exact (continued-fraction) solution of the Fokker-Planck equation. The formula obtained could be of assistance in the modelling of the experimental data and the determination of the damping coefficient in superparamagnets.
Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion
2016
In this paper the Turing pattern formation mechanism of a two components reaction-diffusion system modeling the Schnakenberg chemical reaction is considered. In Ref. (Madzavamuse et al., J Math Biol 70(4):709–743, 2015) it was shown how the presence of linear cross-diffusion terms favors the destabilization of the constant steady state. We perform the weakly nonlinear multiple scales analysis to derive the equations for the amplitude of the Turing patterns and to show how the cross-diffusion coefficients influence the occurrence of super-critical or sub-critical bifurcations. We present a numerical exploration of far from equilibrium regimes and prove the existence of multistable stationary…
Noise effects on gap wave propagation in a nonlinear discrete LC transmission line
2007
International audience; We report here the results of numerical investigation of noise effects on the propagation in a nonlinear waveguide modeled by a discrete electrical line. Considering a periodic signal of frequency exceeding the natural cutoff frequency of this system, we show that noise can be used to trigger soliton generation in the medium. Besides the classical stochastic resonance signature exhibited by each oscillator of the network, our simulation results reveal in particular that the signal-to-noise ratio remains almost constant in the whole network for an appropriate amount of noise. This interesting feature insures for the generated solitons a quality preserved propagation a…
Parametric solitons in nonlinear photonic crystals
2007
We present theoretical and experimental investigations on the soliton dynamics associated to multiple second harmonic generation resonances in two-dimensional nonlinear photonic crystals, highlighting a wealth of new possibilities for soliton management in such structures.
Velocity locking of incoherent nonlinear wave packets
2006
We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.
Hot electrons and nonlinear optical nanoantennas
2017
The large field enhancement generated at the surface of a resonant plasmonic nanoparticle, or optical antennas, is the key mechanism that eventually led to the development of nonlinear plasmonics [1-2]. While the resonance may boost the nonlinear yield of an adjacent structure or surrounding medium, it was soon realized that optical antennas possess nonlinear coefficients comparable or exceeding those of standard nonlinear optical materials [3]. We discuss here two nonlinear optical processes — incoherent multi-photon luminescence (MPL) and coherent second-harmonic generation (SHG) — emitted from gold rod optical antennas upon local illumination with a tightly focused femtosecond near-infra…
Dynamics of surface enrichment: A theory based on the Kawasaki spin-exchange model in the presence of a wall
1991
A mean-field theory is developed for the description of the dynamics of surface enrichment in binary mixtures, where one component is favored by an impenetrable wall. Assuming a direct exchange (Kawasaki-type) model of interdiffusion, a layerwise molecular-field approximation is formulated in the framework of a lattice model. Also the corresponding continuum theory is considered, paying particular attention to the proper derivation of boundary conditions for the differential equation at the hard wall. As an application, we consider the explicit solutions of the derived equations in the case where nonlinear effects can be neglected, studying the approach of an initially flat (homogeneous) co…
Simulation of surface-controlled phase separation in slit pores: Diffusive Ginzburg-Landau kinetics versus Molecular Dynamics
2008
The phase separation kinetics of binary fluids in constrained geometry is a challenge for computer simulation, since nontrivial structure formation occurs extending from the atomic scale up to mesoscopic scales, and a very large range of time needs to be considered. One line of attack to this problem is to try nevertheless standard Molecular Dynamics (MD), another approach is to coarse-grain the model to apply a time-dependent nonlinear Ginzburg–Landau equation that is numerically integrated. For a symmetric binary mixture confined between two parallel walls that prefer one species, both approaches are applied and compared to each other. There occurs a nontrivial interplay between the forma…
Variational theory of soliplasmon resonances
2013
We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational ansatz is based on the existence of solutions exhibiting differentiated and spatially resolvable localized soliton and SPP components. These states, referred to as soliplasmons, can be physically understood as bound states of a soliton and a SPP. Their respective dispersion relations permit the existence of a resonant interaction between them, as pointed out in Ref.[1]. The existence of soliplasmon states and their interesting nonlinear resonant behavior has …
Soliton-plasmon resonances as Maxwell nonlinear bound states
2012
We demonstrate that soliplasmons (soliton–plasmon bound states) appear naturally as eigenmodes of nonlinear Maxwell’s equations for a metal/Kerr interface. Conservative stability analysis is performed by means of finite element numerical modeling of the time-independent nonlinear Maxwell equations. Dynamical features are in agreement with the presented nonlinear oscillator model.