Search results for "Nonlinear system"
showing 10 items of 1446 documents
Longterm damped dynamics of the extensible suspension bridge
2010
This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k^2. For a general external source f, we prove the existence of bounded absorbing sets.When f is timeindependent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.
A Nonlinear Nonviscous Hydrodynamical Model for Change Transport Derived from Kinetic Theory
2002
In the paper, methods of Extended Thermodynamics are used to derive nonlinear closure relations for hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. For the sake of simplicity only the case of single parabolic band approximation is studied. In this work the velocity v i is not considered as a small parameter; therefore, the models obtained can be useful when one wishes to study phenomena in a neighborhood of a stationary non-equilibrium process.
Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation
2004
In this paper we, to our knowledge, for the first time obtain the rate equations for Zeeman coherences in the broad line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations straightforward. We compare our approach with the perturbation theory approach as given previously and show that our approach is more flexible in analyzing various experiments. Meanwhile we also show the validity …
Interface states in polariton topological insulators
2019
We address linear and nonlinear topological interface states in polariton condensates excited at the interface of the honeycomb and Lieb arrays of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. Such interface states appear only in total energy gaps of the composite structure when parameters of the honeycomb and Lieb arrays are selected such that some topological gaps in the spectrum of one of the arrays overlap with topological or nontopological gaps in the spectrum of the other array. This is in contrast to conventional edge states at the interface of periodic topological and uniform trivial insulators, whose behavior is dete…
Contour detection based on nonlinear discrete diffusion in a cellular nonlinear network
2001
International audience; A contour detection based on a diffusive cellular nonlinear network is proposed. It is shown that there exists a particular nonlinear function for which, numerically, the obtained contour is satisfactory. Furthermore, this nonlinear function can be achieved using analog components.
Diffusion effects in a nonlinear electrical lattice
1998
International audience; We consider a nonlinear electrical network modeling the generalized Nagumo equation. Focusing on the particular case where the initial load of the lattice consists in the superimposition of a coherent information weakly varying in space and a perturbation of small amplitude, we show that the perturbation can be eliminated quickly, almost without disturbing the information.
Remarks on quadratic Hamiltonians in spaceflight mechanics
2006
A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.
Unified kinetic formulation of incoherent waves propagating in nonlinear media with noninstantaneous response
2010
This article presents a unified kinetic formulation of partially coherent nonlinear optical waves propagating in a noninstantaneous response Kerr medium. We derive a kinetic equation that combines the weak Langmuir turbulence kinetic equation and a Vlasov-like equation within a general framework: It describes the evolution of the spectrum of a random field that exhibits a quasistationary statistics in the presence of a noninstantaneous nonlinear response. The kinetic equation sheds new light on the dynamics of partially coherent nonlinear waves and allows for a qualitative interpretation of the interplay between the noninstantaneous nonlinearity and the nonstationary statistics of the incoh…
Optical rogue waves and localized structures in nonlinear fiber optics
2011
We review our recent work in the field of optical rogue wave physics. Beginning from a brief survey of the well-known instabilities in optical fiber, we trace the links to recent developments in studying the emergence of high contrast localized breather structures in both spontaneous and induced nonlinear instabilities.
Nonlinear dynamics of spatio-temporal waves in multimode fibres
2017
International audience