Search results for "Nonlinear"
showing 10 items of 3684 documents
Driving slow-light solitons by a controlling laser field
2005
In the framework of the nonlinear Λ-model we investigate propagation of a slow-light soliton in atomic vapours and Bose–Einstein condensates. The velocity of the slow-light soliton is controlled by a time-dependent background field created by a controlling laser. For a fairly arbitrary time dependence of the field we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the location and shape of the spatially localized memory bit imprinted into the medium. We show that the pr…
Poiseuille flow of a Quincke suspension
2014
The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existi…
Fluctuating laser field that induces a blueshift in harmonic generation
1998
The spectrum of a two-level atom in the presence of a multimode laser pulse is calculated. The field is allowed to fluctuate in amplitude or in phase; the emitted spectrum has richer emission lines than in the case of the nonfluctuating field and shows peaks shifted toward the blue with respect to the traditional harmonic peaks. The position of the lines is predicted by the formula ω2n+1=(2n+1)(1+Δ)ωL with Δ being a parameter that can be found numerically. In this way the fluctuations seem to result in an effective increase of the laser frequency.
Turing Patterns in Nonlinear Optics
2000
The phenomenon of pattern formation in nonlinear optical resonators is commonly related to an off-resonance excitation mechanism, where patterns occur due to mismatch between the excitation and resonance frequency. In this paper we show that the patterns in nonlinear optics can also occur due to the interplay between diffractions of coupled field components. The reported mechanism is analogous to that of local activation and lateral inhibition found in reaction-diffusion systems by Turing. We study concretely the degenerate optical parametric oscillators. A local activator-lateral inhibitor mechanism is responsible for generation of Turing patterns in form of hexagons.
Multi-Resolution Analysis and Fractional Quantum Hall Effect: More Results
2009
In a previous paper we have proven that any multi-resolution analysis of $L^2(\R)$ produces, for even values of the inverse filling factor and for a square lattice, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We have also discussed the inverse construction. In this paper we simplify the procedure, clarifying the role of the kq-representation. Moreover, we extend our previous results to the more physically relevant case of a triangular lattice and to odd values of the inverse filling factor. We also comment on other possible shapes of the lattice as well as on the extension to ot…
Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result
2001
In this paper we prove that any multi-resolution analysis of $\Lc^2(\R)$ produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.
A two-dimensional hydrodynamic code for astrophysical flows
1990
We present a two-dimensional hydrodynamic code suited to study astrophysical flows in many different environments. The code solves the hydrodynamic equations in conservative form in the most used coordinate systems and is based on an explicitfully two-dimensional flux corrected transport (FCT) technique, which ensures an accurate description of steep gradient regions and shocks, a relatively ample flexibility to include a variety of physical effects, and a good efficiency for speed on vector or array processors. Extensive testing has allowed an accurate «tuning» of the FCT numerical parameters. This code is among the best FCT codes and performs well in a whole set of demanding strongly nonl…
Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise
2008
We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal respo…
Moment Equations for a Spatially Extended System of Two Competing Species
2005
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…
Four-phase patterns in a forced nonlinear optical oscillator
2009
We present preliminary theoretical and experimental results indicating that a high Fresnel number nonlinear optical oscillator with planar mirrors can display four-phase multistability, eventually leading to four-phase patterns. Such situation is similar to that emerging in extended oscillatory systems forced within a 4:1 resonance and, to the best of our knowledge, has not been predicted nor observed previously in an optical system.