Search results for "nonlinear"
showing 10 items of 3684 documents
Diffusion stabilizes cavity solitons in bidirectional lasers
2009
We study the influence of field diffusion on the spatial localized structures (cavity solitons) recently predicted in bidirectional lasers. We find twofold positive role of the diffusion: 1) it increases the stability range of the individual (isolated) solitons; 2) it reduces the long-range interaction between the cavity solitons. Latter allows the independent manipulation (writing and erasing) of individual cavity solitons.
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,…
Traitement d'images avec un système non linéaire
2017
National audience; Cette communication porte sur la présentation d’un outil de traitement d’images s’inspirant des processus de réaction-diffusion.Cet outil s’appuie sur des ́equations différentielles non linéaires et tire plus particulièrement profit des propriétéde multistabilité liées à la non linéarité de ces processus de diffusion. Certaines caractéristiques d’une image peuvent ainsi être extraites.
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.
Elongated push–pull diphenylpolyenes for nonlinear optics: molecular engineering of quadratic and cubic optical nonlinearities via tuning of intramol…
1999
Abstract Push–pull polyenes are of particular interest for nonlinear optics (NLO) as well as model compounds for long-distance intramolecular charge transfer (ICT). In order to tune the ICT phenomenon and control the linear and nonlinear optical properties, we have synthesized and investigated several series of soluble push–pull diphenylpolyenes of increasing length and having various donor (D) and acceptor (A) end groups. Their linear and NLO properties have been studied by performing electro-optical absorption measurements (EOAM) and third-harmonic generation (THG) experiments in solution. Each push–pull molecule exhibits an intense ICT absorption band in the visible characterized by an i…
Organic Materials for Non-Linear Optics: The 2D Approach
1998
Conventional organic molecules for applications in second-order non-linear optics are donor–acceptor substituted π systems that show only one intense charge-transfer (CT) transition. Thus, only a single element of the second-order polarizability tensor, β, is significant in these one-dimensional systems. The advantages and optimization strategies for two new classes of molecules with multiple CT transitions and two-dimensional second-order polarizability are reviewed. These are donor–acceptor substituted π systems that lack a dipole and have a molecular symmetry of C3 or higher, and dipolar molecules of symmetry C2v. A basic introduction to the field is also given.
ChemInform Abstract: Organic Materials for Non-Linear Optics: The 2D Approach
2010
Conventional organic molecules for applications in second-order non-linear optics are donor–acceptor substituted π systems that show only one intense charge-transfer (CT) transition. Thus, only a single element of the second-order polarizability tensor, β, is significant in these one-dimensional systems. The advantages and optimization strategies for two new classes of molecules with multiple CT transitions and two-dimensional second-order polarizability are reviewed. These are donor–acceptor substituted π systems that lack a dipole and have a molecular symmetry of C3 or higher, and dipolar molecules of symmetry C2v. A basic introduction to the field is also given.
Triphenylmethyl and triphenylsilyl based molecular glasses for photonic applications
2015
Triphenylmethyl and triphenylsilyl structural fragments can be used to obtain glass forming, solution processable materials from polar chromophore molecules. Large number of compounds has been synthesized taking advantage of this approach, making it possible to identify some structure-property relations. Regarding the non-linear optical (NLO) properties of the given materials it is evident that triphenylmethyl groups help shielding unwanted NLO efficiency limiting dipolar interactions between polar chromophores in solid films. Chromophore stacking is still observed for compounds with large dipole momentum values. The glass transition temperatures of the compounds increase with the molecular…
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.