Search results for "Linea"
showing 10 items of 7724 documents
Pseudo-force method for a stochastic analysis of nonlinear systems
1996
Nonlinear systems, driven by external white noise input processes and handled by means of pseudo-force theory, are transformed through simple coordinate transformation to quasi-linear systems. By means of Itô stochastic differential calculus for parametric processes, a finite hierarchy for the moment equations of these systems can be exactly obtained. Applications of this procedure to the first-order differential equation with cubic nonlinearity and to the Duffing oscillator show the versatility of the proposed method. The accuracy of the proposed procedure improves by making use of the classical equivalent linearization technique.
An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations
2020
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.
On critical behaviour in generalized Kadomtsev-Petviashvili equations
2016
International audience; An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev–Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the disp…
Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms
2018
Abstract We consider differential systems in R N driven by a nonlinear nonhomogeneous second order differential operator, a maximal monotone term and a multivalued perturbation F ( t , u , u ′ ) . For periodic systems we prove the existence of extremal trajectories, that is solutions of the system in which F ( t , u , u ′ ) is replaced by ext F ( t , u , u ′ ) (= the extreme points of F ( t , u , u ′ ) ). For Dirichlet systems we show that the extremal trajectories approximate the solutions of the “convex” problem in the C 1 ( T , R N ) -norm (strong relaxation).
Thermodynamic approach of supercontinuum generation
2009
International audience; This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i. e., the state of maximum n…
<title>Photoinduced anisotropy and holographic recording in amorphous chalcogenides</title>
2001
The effect of photoinduced anisotropy and its application to vector hologram recording is reviewed focusing on amorphous chalcogenides. Vector holographic grating recording in amorphous As-S-Se(a-As-S-Se) films is experimentally studied and analyzed in comparison with scalar recording. It is holographically established that a linearly polarized 632.8 nm light produces photoinduced anisotropy and the chalcogen related D+, D- center reorientation and generation mechanism is proposed. It is used to explain the observed peculiarities of vector recording in comparison with scalar recording based on photoinduced structural changes: much lower diffraction efficiency (4 X 10-3% versus 4%), much lar…
Diffractive optics for spectral tuning of second harmonic and supercontinuum generated in nonlinear crystals
2011
It is shown that diffractive lenses can tune the spectrum of femtosecond pulses after nonlinear optical processes. We focus on spectra of second-order pulses generated in birefringent crystals and supercontinuum in sapphire crystals. The tunability is achieved by changing the relative distance between the nonlinear crystal and the diffractive lens.
Behaviour of the non-linear optical material KTiOPO4in the temperature range 293-973 K studied by x-ray diffractometry at high resolution: alkaline d…
1999
The crystal structure of potassium titanyl phosphate, KTiOPO4 (space group Pna21), has been refined at room temperature, at 673 K, and at 973 K, by using accurate single-crystal x-ray diffraction techniques at high resolution (dmin = 0.35 A). The data show a large amount of anharmonic motion of the potassium ions, increasing with temperature. To describe this motion, two models are developed: a normal refinement including potassium anharmonic thermal displacement parameters, which describes the average motion of the alkaline sites, and another model in which the potassium sites are split within the harmonic approximation and the displacements of the potassium ions versus temperature are des…
Third-harmonic light polarization control in magnetically resonant silicon metasurfaces
2021
Nonlinear metasurfaces have become prominent tools for controlling and engineering light at the nanoscale. Usually, the polarization of the total generated third harmonic is studied. However, diffraction orders may present different polarizations. Here, we design an high quality factor silicon metasurface for third harmonic generation and perform back focal plane imaging of the diffraction orders, which present a rich variety of polarization states. Our results demonstrate the possibility of tailoring the polarization of the generated nonlinear diffraction orders paving the way to a higher degree of wavefront control.
Subwavelength Bessel beams in wire media
2013
Recent progress is emerging on nondiffracting subwavelength fields propagating in complex plasmonic nanostructures. In this paper, we present a thorough discussion on diffraction-free localized solutions of Maxwell’s equations in a periodic structure composed of nanowires. This self-focusing mechanism differs from others previously reported, which lie on regimes with ultraflat spatial dispersion. By means of the Maxwell–Garnett model, we provide a general analytical expression of the electromagnetic fields that can propagate along the direction of the cylinder’s axis, keeping its transverse waveform unaltered. Numerical simulations based on the finite element method support our analytical a…