Search results for "Linear system"
showing 10 items of 1558 documents
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…
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.
Spatial soliton formation in photonic crystal fibers
2003
We demonstrate the existence of spatial soliton solutions in photonic crystal fibers (PCF's). These guided localized nonlinear waves appear as a result of the balance between the linear and nonlinear diffraction properties of the inhomogeneous photonic crystal cladding. The spatial soliton is realized self-consistently as the fundamental mode of the effective fiber defined simultaneously by the PCF linear and the self-induced nonlinear refractive indices. It is also shown that the photonic crystal cladding is able to stabilize these solutions, which would be unstable otherwise if the medium was entirely homogeneous.
Dark spatial solitary waves in a cubic-quintic-septimal nonlinear medium
2017
We consider the evolution of light beams in nonlinear media exhibiting nonlinearities up to the seventh order wherein the beam propagation is governed by the cubic-quintic-septimal nonlinear Schr\"odinger equation. An exact analytic solution that describes dark solitary wave propagation is obtained, based on a special ansatz. Unlike the well-known $\text{tanh}$-profile dark soliton in Kerr media, the present one has a functional form given in terms of ``${\text{sech}}^{2/3}$''. The requirements concerning the optical material parameters for the existence of this localized structure are discussed. This propagating solitary wave exists due to a balance among diffraction, cubic, quintic, and s…
Pattern formation in clouds via Turing instabilities
2020
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare. From many scientific disciplines the occurrence of patterns in non-equilibrium systems due to Turing instabilities is known, i.e. unstable modes grow and form spatial structures. In this study we investigate a generic cloud model for the possibility of Turing instabilities. For this purpose, the model is extended by diffusion terms. We can show that for some cloud models, i.e special cases of the generic model, no Turing instabilities are possible. However,…
Well-posed nonlinear problems in integrated circuits modeling
1991
In this paper we study the problem (E) + (BC) + (IC) (see below) which represents a model for integrated circuits. We assume that the distributed parametersr(x) andc(x) are nonconstant, dielectric leakages depend on thex-coordinate as well as the voltage level, while the interconnecting multiport is nonlinear and possibly multivalued.
Batch fermentation process: Modelling and direct sensitivity analysis
2009
Based on a nonlinear model, this article realizes an investigation of dynamic behaviour of a batch fermentation process using direct sensitivity analysis (DSA). The used nonlinear mathematical model has a good qualitative and quantitative description of the alcoholic fermentation process. This model has been discussed and validated by authors in other studies. The DSA of dynamic model was used to calculate the matrix of the sensitivity functions in order to determine the influence of the small deviations of initial state, control inputs, and parameters from the ideal nominal values on the state trajectory and system output in time. Process optimization and advanced control strategies can be…
(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms
2018
We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian ($$p>2$$) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric $$(p-1)$$-linear term which is resonant as $$x \rightarrow - \infty $$, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.
Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator
2020
Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.
Positive solutions for singular (p, 2)-equations
2019
We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.