Search results for "Nonlinear system"
showing 10 items of 1446 documents
Nonlinear energy dissipation in a cellular automaton magnetotail field model
1999
A magnetic field model of the magnetotail current sheet based on cellular automaton (CA) is presented. The present isotropic model is a continuously driven, two-dimensional running CA. The model has a physical interpretation in terms of magnetohydrodynamic (MHD) equations, and features self-organized critical (SOC) behavior with power-law scalings both in durations and sizes of instabilities (avalanches). The model has nonlinear energy dissipation, and shows avalanches with and without an external trigger. Thus the model reproduces some of the statistical features recently observed in the magnetotail.
Spatial Solitons in Nonlinear Photonic Crystal Fibers
2017
This chapter aims to review the most relevant results on solitons in nonlinear solid-core photonic crystal fibers since their introduction about fifteen years ago. These include fundamental solitons and vortices, as well as vector systems of two fundamental, vortex or mixed components. Also other related systems as solitons in double-core photonic crystal fibers will be reviewed. The presentation will describe the mode families as well as their stability properties. The work is intended to be a comprehensive document on the field and provide a fast update to the reader as well as the necessary sources for a further detailed documentation.
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…
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…
A physically based connection between fractional calculus and fractal geometry
2014
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalous dimension of such geometry, as well as to the m…
The melting behaviour of small silicon clusters
1994
Abstract We report an analysis of the melting behaviour of small silicon clusters interacting via a nonlinear interatomic potential with four-body terms. The analysis shows, by means of Monte Carlo and molecular dynamics simulations, that the small silicon clusters undergo, in a vacuum, structural changes from a solid rigid state to a liquid-like state. The melting temperature exhibits a strong variation with cluster size.
Bright and dark optical solitons in fiber media with higher-order effects
2002
We consider N-coupled higher-order nonlinear Schrodinger (N-CHNLS) equations which govern the simultaneous propagation of N optical fields in fiber media with higher-order effects. Bright and dark soliton solutions are derived using Hirota bilinear method for the general cross-coupling ratio between the parameters of self-phase modulation and cross-phase modulation effects. By means of coupled amplitude-phase formulation also, similar kind of dark soliton solutions are obtained. It is found that the parametric conditions for the simultaneous propagation of N dark solitons from both the methods are the same.
Existence results for a nonlinear nonautonomous transmission problem via domain perturbation
2021
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.
Numerical relativistic hydrodynamics: Local characteristic approach.
1991
We extend some recent Ishock capturing methodsR designed to solve nonlinear hyperbolic systems of conservation laws and which avoid the use of artifical viscosity for treating strong discontinuities to a relativistic hydrodynamics system of equations. Some standard shock-tube problems and radial accretion onto a Schwarzschild black hole are used to calibrate our code.
Post-Newtonian constraints onf(R)cosmologies in metric and Palatini formalism
2005
We compute the complete post-Newtonian limit of both the metric and Palatini formulations of $f(R)$ gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian $f(R)$ must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian $f(R)$ must be almost linear in $R$ and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot b…