Search results for "Nonlinear"
showing 10 items of 3684 documents
The mKdV equation and multi-parameters rational solutions
2021
Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .
Observateur et contrôle optimal : améliorer l'efficacité de la conduite automobile avec Kalman et Pontryagin
2010
The PhD presents a combined approach to improving individual car efficiency. An optimal observer, the Extended Kalman Filter, is used to create an efficiency model for the car. Particular attention was paid to handling the asynchronous and redundant nature of the measurement data. A low-cost sensor suite developed to measure data is described. This sensor suite was installed on multiple vehicles to good success. It employsan accelerometer, gps, fuel injector timer, and Vss input to measure all the data necessary to reconstruct the car's state. This observer and sensor suite can be used as the base for any study which requires car efficiency maps, allowing research to proceed without manufac…
Nouveaux systèmes de contrôle de la polarisation de la lumière par effets non lineaires dans les fibres optiques
2013
This thesis deals with the work the development of an all-optical device for the control of the polarization state of light. Actually, this feature of light remains so far an uncontrolled variable, which can degrade the performances of all-optical systems. Based on nonlinear interaction between two counterpropagating waves inside an optical fiber, this device called polarization attractor allows to control the polarization state of light without polarization dependent losses.In a first part, we carry out extensive studies of the polarization attractor properties leading to the control and the regeneration of the polarization state of the 10-Gb/s NRZ and RZ telecommunication signals. Then, t…
Nonlinear resonances and some of their applications to information processing
2021
The study of resonance phenomena in nonlinear dynamical systems has drawn considerable attention for years. The most studied nonlinear resonance is undoubtedly the famous stochastic resonance, which consists of perturbing a nonlinear system with an appropriate amount of noise to enhance the detection of a subthreshold input signal. Since the introduction of stochastic resonance in the context of climate dynamics, it was later observed that a deterministic high frequency perturbation can replace noise leading to vibrational resonance. Even if this latter resonance was investigated in many areas of science for more than two decades now, it is still receiving attentions. It is the subject of t…
Fiber-based light source for biomedical applications
2013
This manuscript presents the work done concerning the development of a light source used for biomedical imaging and more particularly for coherent Raman scattering imaging. In fact an efficient broadcasting of these ones is hampered by the need of two synchronized and wavelength shifted pulses. As so, the handiness and frequency conversion capabilities of nonlinear fiber optics are used to circumvent this technological lock. First of all, an easy wavelength tunable source is set by the use of the self-shifting in optical frequency of a soliton. A study of the main fiber parameters lead to shifts of 320 to more than 500 nm which allows interesting molecular resonances imaging (≈ 1000-4000 cm…
Effet du couplage non linéaire dans un système de sine-Gordon modifié
2016
National audience; Cette Communication porte sur une étude numérique visant à montrer les conditions d'existence du phénomène de supratransmission dans un milieu gouverné par l'équation de sine-gordon à couplage mixte: le couplage linéaire pur étant associé à un couplage non linéaire. Nous montrons également l'effet de la variation du coefficient du couplage non linéaire sur l'amplitude de seuil du signal excitateur nécessaire pour déclencher le phénomène de supratransmission dans le milieu, en maintenant constant le coefficient du couplage linéaire pur.
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
Harmonic Balance Method and Stability of Discontinuous Systems
2019
The development of the theory of discontinuous dynamical systems and differential inclusions was not only due to research in the field of abstract mathematics but also a result of studies of particular problems in mechanics. One of first methods, used for the analysis of dynamics in discontinuous mechanical systems, was the harmonic balance method developed in the thirties of the 20th century. In our work the results of analysis obtained by the method of harmonic balance, which is an approximate method, are compared with the results obtained by rigorous mathematical methods and numerical simulation. peerReviewed
Nonlinear optical properties of diaromatic stilbene, butadiene and thiophene derivatives
2021
Series of highly polar stilbene (1a–e), diphenylbutadiene (2a–c) and phenylethenylthiophene (3a–c) derivatives were prepared via Horner–Wadsworth–Emmons method with a view to produce new and efficient materials for second harmonic generation (SHG) in the solid-state. The single-crystal X-ray structures of compounds 1–3 reveal extensive polymorphism and a peculiar photodimerization of the 2-chloro-3,4-dimethoxy-4′-nitrostilbene derivative 1a to afford two polymorphs of tetra-aryl cyclobutane 4. The stilbene congeners 2-chloro-3,4-dimethoxy-4′-nitrostilbene (1a·non-centro), 5-bromo-2-hydroxy-3-nitro-4′-nitrostilbene (1b) and 4-dimethylamino-4′-nitrostilbene (1e), as well as 4′-fluoro-4′′-nitr…
Parabolic equations with nonlinear singularities
2011
Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…