Search results for "Nonlinear"
showing 10 items of 3684 documents
Broadband telecom to mid-infrared supercontinuum generation in a dispersion-engineered silicon germanium waveguide.
2015
We demonstrate broadband supercontinuum generation (SCG) in a dispersion-engineered silicon-germanium waveguide. The 3 cm long waveguide is pumped by femtosecond pulses at 2.4 μm, and the generated supercontinuum extends from 1.45 to 2.79 μm (at the −30 dB point). The broadening is mainly driven by the generation of a dispersive wave in the 1.5–1.8 μm region and soliton fission. The SCG was modeled numerically, and excellent agreement with the experimental results was obtained.
<title>Second harmonic generation in selenium thin films</title>
2008
Results of second harmonic (SH) generation in amorphous and crystalline selenium films induced by titanium-sapphire femtosecond laser (wavelength λ - 800-1000 nm) are presented. It is found that the highest intensity of SH is provided by fundamental wave at wavelength 1000 nm and it reaches maximum in approximately 100 sec. The intensity of transmitted SH depends on film thickness while that of reflected does not.
<title>Second harmonic generation in selenium-metal structures</title>
2008
The article examines the processes of second harmonic generation (SHG) when selenium-metal (Cu) film structures are illuminated by femtosecond radiation (180 fs, 80 MHz) at wavelength 800 - 1000 nm. Selenium-copper structures were obtained by successive thermal evaporation of selenium and copper onto the glass substrate in vacuum. Microanalysis of the film composition was performed to determine amount of copper in thin films. The as-evaporated selenium-copper structures were crystallised by annealing in inert atmosphere at temperature 85°C. Just evaporated as well as annealed thin films were explored. The experiment was performed by confocal microscope [1] where the femtosecond radiation fr…
ON THE BOUSSINESQ HIERARCHY
2002
A new sequence of nonlinear evolution systems satisfying the zero curvature property is constructed, by using the invariant singularity analysis. All these systems are completely integrable and a pseudo-potential (linearization) is explicitly determined for each of them. The second system of the sequence is the Broer-Kaup system, which, as is well known, corresponds to the higher order Boussinesq approximation in describing shallow water waves.
Cross-diffusion driven instability for a nonlinear reaction-diffusion system
2008
In this work we investigate the possibility of the pattern formation for a system of two coupled reaction-diffusion equations. The nonlinear diffusion terms has been introduced to describe the tendency of two competing species to diffuse faster (than predicted by the usual linear diffusion) toward lower densities areas. The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The system is supplemented with the initial conditions and no-flux boundary conditions. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show h…
Well-posedness of Prandtl equations with non-compatible data
2013
In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.
Well-posedness of a nonlinear evolution equation arising in growing cell population
2011
We prove that a nonlinear evolution equation which comes from a model of an age-structured cell population endowed with general reproduction laws is well-posed. Copyright © 2011 John Wiley & Sons, Ltd.
On the classification of type D space–times
2002
We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-exi…
Nonlinear evolution of cosmological inhomogeneities
2008
The nonlinear evolution of a cosmologically significant fluid is studied up to shell crossing. The magnetic part of the Weyl tensor, the pressure and the vorticity vanish. A suitable spatial grid is chosen. The relativistic Ellis equations are particularized on the world lines defined by the nodes of the grid and, then, the resulting equations are numerically solved. The integrations are performed in suitable Lagrangian inertial coordinates, in which the differential equations become ordinary. After the integration, a method to change from Lagrangian to Eulerian coordinates is applied. This approach has been outlined with the essential aim of studying the evolution of large scale cosmologic…
Relations between multi-resolution analysis and quantum mechanics
2005
We discuss a procedure to construct multiresolution analyses (MRA) of L2 (R) starting from a given seed function h (s) which should satisfy some conditions. Our method, originally related to the quantum mechanical Hamiltonian of the fractional quantum Hall effect, is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA. © 2005 American Institute of Physics.