Search results for "Linear"
showing 10 items of 7165 documents
Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential
2022
Abstract This work extends to higher-order interactions the results of Ref. Nguetcho (2021), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic-quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel-Kontorova model, is …
Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class
2014
Abstract The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…
On the correlation between phase-locking modes and Vibrational Resonance in a neuronal model
2018
International audience; We numerically and experimentally investigate the underlying mechanism leading to multiple resonances in the FitzHugh-Nagumo model driven by a bichromatic excitation. Using a FitzHugh-Nagumo circuit, we first analyze the number of spikes triggered by the system in response to a single sinusoidal wave forcing. We build an encoding diagram where different phase-locking modes are identified according to the amplitude and frequency of the sinusoidal excitation. Next, we consider the bichromatic driving which consists in a low frequency sinusoidal wave perturbed by an additive high frequency signal. Beside the classical Vibrational Resonance phenomenon, we show in real ex…
Efficient finite difference formulation of a geometrically nonlinear beam element
2021
The article is focused on a two-dimensional geometrically nonlinear formulation of a Bernoulli beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element lev…
Nonlinear radiation imprisonment in magneto-optical vapor traps
2008
We analyze nonlinear radiation imprisonment (RI) effects in an optically thick vapor in different temperature regimes. An analytical approach is proposed to treat nonlinear decay problems. Special attention is paid to vapor samples having curvilinear geometries (cylinder, sphere) and being excited by a strong laser pulse. We derive a number of new formulas for different radiative trapping factors as functions of opacity and propose a general approach for RI evaluation allowing us to deal with samples both at room and low, or very low, temperatures, such as those customarily achieved in magneto-optical trap (MOT) experiments. As a result, we predict a "subnatural" decay of radiation escaping…
Quantum Solitons on Quantum Chaos: Coherent Structures, Anyons, and Statistical Mechanics
1991
This paper is concerned with the exact evaluation of functional integrals for the partition function Z (free energy F = -β -1 ln Z, β -1 = temperature) for integrable models like the quantum and classical sine-Gordon (s-G) models in 1+1 dimensions.1–12 These models have wide applications in physics and are generic (and important) in that sense. The classical s-G model in 1+1 dimensions $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi$$ (1) (m > 0 is a “mass”) has soliton (kink, anti-kink and breather) solutions. In Refs 1–12 we have reported a general theory of ‘soliton statistical mechanics’ (soliton SM) in which the particle description can be seen in terms of ‘solitons’ and ‘phonons’. The …
Two-dimensional quantum scattering by non-isotropic interactions localized on a circle, applications to open billiards
2018
Two-dimensional quantum scattering by isotropic and non-isotropic interactions localized on a circle is considered. The expansion of the interaction on the circle in a Fourier series allows us to express basic objects of scattering theory (resolvent, T operator, differential cross length, cross length, and cross length averaged over all orientations of the incident particle), in terms of operations on matrices. For numerical applications, these matrices are truncated to a given order. If the interaction is isotropic, this general formulation reduces to the usual one, and the resonances in the isotropic cases are studied because they allow us to interpret resonances in some non-isotropic cas…
Soliton topology versus discrete symmetry in optical lattices
2005
We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general ``charge rule'' using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing in the case of Bessel lattices allows us to derive also a overall stability rule for the allowed vortex solitons.
Complete characterization of terahertz pulse trains generated from nonlinear processes in optical fibers
2001
The measurement technique of frequency-resolved optical gating (FROG) is used to characterize the intensity and phase of terahertz pulse trains generated from nonlinear and dispersive interactions in optical fibers. We show that existing FROG retrieval algorithms are easily adapted to allow the retrieval of periodic pulse characteristics and, using synthetic pulse trains generated from numerical simulations, we demonstrate how FROG can differentiate between periodic pulse trains with fundamentally different intensity and phase characteristics, yet qualitatively similar autocorrelation functions and spectra. Experimental results are presented for the FROG characterization of a 0.3-THz sinuso…
Generation of vector dark-soliton trains by induced modulational instability in a highly birefringent fiber
1999
International audience; We present a set of experimental observations that demonstrate the generation of vector trains of dark-soliton pulses in the orthogonal axes of a highly birefringent optical fiber. We generated dark-soliton trains with terahertz repetition rate in the normal group-velocity dispersion regime by inducing a polarization modulational instability by mixing two intense, orthogonal continuous laser beams. Numerical solutions of the propagation equations were used to optimize the emission of vector dark pulses at the fiber output.