Search results for "Linear system"
showing 10 items of 1558 documents
Modular Schrödinger equation and dynamical duality.
2008
We discuss quite surprising properties of the one-parameter family of modular (Auberson and Sabatier (1994)) nonlinear Schr\"{o}dinger equations. We develop a unified theoretical framework for this family. Special attention is paid to the emergent \it dual \rm time evolution scenarios which, albeit running in the \it real time \rm parameter of the pertinent nonlinear equation, in each considered case, may be mapped among each other by means of an "imaginary time" transformation (more seriously, an analytic continuation in time procedure).
Improving on numerical simulations of nonlinear CMB anisotropies
2015
An Adaptative-Particle-Particle-Particle-Mesh code (HYDRA) plus a ray-tracing procedure was used in [1] to perform an exhaustive analysis of the weak lensing anisotropy. Other nonlinear Cosmic Microwave Background anisotropies, such as the Rees-Sciamaand the Sunyaev-Zel.dovicheffects are also being studied by using the same tools. Here we present some advances in our study of these nonlinear anisotropies. The primary advance is due to the use of better simulations with greater particle densities and appropriate softening, although other parameters have also been adjusted to get better estimates. Thus, we improve on a previous paper [2] where the Rees-Sciamaeffect was studied with Particle-M…
The relaxation-time limit in the quantum hydrodynamic equations for semiconductors
2006
Abstract The relaxation-time limit from the quantum hydrodynamic model to the quantum drift–diffusion equations in R 3 is shown for solutions which are small perturbations of the steady state. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density including the quantum Bohm potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. The relaxation-time limit is performed both in the stationary and the transient model. The main assumptions are…
Chiral excitations of magnetic droplet solitons driven by their own inertia
2019
The inertial effects of magnetic solitons play a crucial role in their dynamics and stability. Yet governing their inertial effects is a challenge for their use in real devices. Here, we show how to control the inertial effects of magnetic droplet solitons. Magnetic droplets are strongly nonlinear and localized autosolitons than can form in current-driven nanocontacts. Droplets can be considered as dynamical particles with an effective mass. We show that the dynamical droplet bears a second excitation under its own inertia. These excitations comprise a chiral profile, and appear when the droplet resists the force induced by the Oersted field of the current injected into the nanocontact. We …
Analog simulation of neural information propagation using an electrical FitzHugh-Nagumo lattice
2004
International audience; A nonlinear electrical lattice modelling neural information propagation is presented. It is shown that our system is an analog simulator of the FitzHugh-Nagumo equations, and hence supports pulse propagation with the appropriate properties.
Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrodinger equations
2006
International audience; A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable N-coupled nonlinear Schrodinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which nonsingular soliton propagation can occur. The multisoliton …
Resonant Kelvin-Helmholtz modes in sheared relativistic flows
2007
Qualitatively new aspects of the (linear and non-linear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz factors up to 20; specific internal energies $\approx 60c^2$). As a distinct feature of our work, we have combined the analytical linear approach with high-resolution relativistic hydrodynamical simulations, which has allowed us i) to identify, in the linear regime, resonant modes specific to the relativistic shear layer ii) to confirm the result of the linear analysis with numerical simulations and, iii) more interestingly, to follow the instability develo…
Kerr effect as a tool for the investigation of dynamic heterogeneities
2006
We propose a dynamic Kerr effect experiment for the distinction between dynamic heterogeneous and homogeneous relaxation in glassy systems. The possibility of this distinction is due to the inherent nonlinearity of the Kerr effect signal. We model the slow reorientational molecular motion in supercooled liquids in terms of non-inertial rotational diffusion. The Kerr effect response, consisting of two terms, is calculated for heterogeneous and for homogeneous variants of the stochastic model. It turns out that the experiment is able to distinguish between the two scenarios. We furthermore show that exchange between relatively 'slow' and 'fast' environments does not affect the possibility of …
Vectorial Kerr-cavity solitons.
2000
It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CS’s). A parametrically driven Ginzburg–Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CS’s is numerically investigated.
Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror
2016
Abstract In this work we study statistically the internal structure of noiselike pulses generated by a passively mode-locked fiber laser. For this purpose, we use a technique that allows estimating the distribution of the amplitudes of the sub-pulses in the bunch. The technique takes advantage of the fast response of the optical Kerr effect in a fiber nonlinear optical loop mirror (NOLM). It requires the measurement of the energy transfer characteristic of the pulses through the NOLM, and the numerical resolution of a system of nonlinear algebraic equations. The results yield a strongly asymmetric distribution, with a high-amplitude tail that is compatible with the existence of extreme-inte…