Search results for " Nonlinear"
showing 10 items of 1224 documents
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…
Ab initio calculations of SrTiO3, BaTiO3, PbTiO3, CaTiO3, SrZrO3, PbZrO3 and BaZrO3 (001), (011) and (111) surfaces as well as F centers, polarons, K…
2014
In this paper, the review of recent results of calculations of surface relaxations, energetics, and bonding properties for ABO 3 perovskite (001), (011) and (111) surfaces using mostly a hybrid description of exchange and correlation is presented. Both AO and BO 2-terminations of the nonpolar (001) surface and A , BO , and O terminations of the polar (011) surface, as well as B and AO 3-terminations of the polar (111) surface were considered. On the AO -terminated (001) surface, all upper-layer A atoms relax inwards, while all second layer atoms relax outwards. For the BO 2-terminated (001) surface, in most cases, the largest relaxations are on the second-layer metal atoms. For almost all …
Emission of real phonons due to electron’s self-dressing in a covalent crystal
2011
A slow monoelectronic excitation in a covalent crystal at the temperature T=0 is analyzed. The interaction with zero-point longitudinal acoustic phonons leads to the formation of a dressed electronic state at an energy level lower than that of the initial bare state. This aspect of the dressing process is described here by hypothesizing that the excess of energy is released with the emission of real phonons. Specifically, this paper considers the transition probability from the bare monoelectronic state to a dressed state of the electron accompanied by real phonons and a deformation field. The spectrum of the real phonons emitted during the electronic self-dressing is calculated by applying…
Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type
2014
Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.
Bifurcations of cuspidal loops
1997
A cuspidal loop for a planar vector field X consists of a homoclinic orbit through a singular point p, at which X has a nilpotent cusp. This is the simplest non-elementary singular cycle (or graphic) in the sense that its singularities are not elementary (i.e. hyperbolic or semihyperbolic). Cuspidal loops appear persistently in three-parameter families of planar vector fields. The bifurcation diagrams of unfoldings of cuspidal loops are studied here under mild genericity hypotheses: the singular point p is of Bogdanov - Takens type and the derivative of the first return map along the orbit is different from 1. An analytic and geometric method based on the blowing up for unfoldings is propos…
Adaptive control of a seven mode truncation of the Kolmogorov flow with drag
2009
Abstract We study a seven dimensional nonlinear dynamical system obtained by a truncation of the Navier–Stokes equations for a two dimensional incompressible fluid with the addition of a linear term modelling the drag friction. We show the bifurcation sequence leading from laminar steady states to chaotic solutions with increasing Reynolds number. Finally, we design an adaptive control which drives the state of the system to the equilibrium point representing the stationary solution.
Thermal Stability of a DC/DC Converter with Inductor in Partial Saturation
2021
Inductors operated in quasi saturation in dc–dc converters allow reduction of the core size and realization costs; on the other hand, they imply an increase of dissipated power that can jeopardize the thermal stability of the converter. In this article, this issue is studied by a mathematical model able to represent both the inductor nonlinearity and its temperature dependence. The main losses, such as ohmic, skin effect and magnetic, are taken into account in the model. The inductor is characterized by a polynomial curve whose parameters are a function of the temperature. Finally, the whole converter is modeled and simulation results, obtained on a boost converter, are compared with experi…
Polarization-domain-wall complexes in fiber lasers
2013
To study the possible build-up of polarization-domain-walls (PDWs) in fiber laser cavities, an erbium-doped fiber ring laser was used and a wide range of vector polarization dynamics that can be selected at a given pump power, by using the degrees of freedom of two intracavity polarization controllers (PC) was investigated. A simple theoretical model that explains polarization switching in fiber ring lasers featuring a normally dispersive cavity with a typical, moderate, level of birefringence is presented. Such polarization dynamics, based on a special class of polarization-domain-wall structures, agrees qualitatively well with experimental observations. The paper stresses on the complex a…
Hamiltonian tools for the analysis of optical polarization control
2011
Import JabRef; International audience; The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrate…
On the time function of the Dulac map for families of meromorphic vector fields
2003
Given an analytic family of vector fields in Bbb R2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.