Search results for "statistical"
showing 10 items of 4960 documents
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…
ideal: an R/Bioconductor package for interactive differential expression analysis
2020
AbstractBackgroundRNA sequencing (RNA-seq) is an ever increasingly popular tool for transcriptome profiling. A key point to make the best use of the available data is to provide software tools that are easy to use but still provide flexibility and transparency in the adopted methods. Despite the availability of many packages focused on detecting differential expression, a method to streamline this type of bioinformatics analysis in a comprehensive, accessible, and reproducible way is lacking.ResultsWe developed the ideal software package, which serves as a web application for interactive and reproducible RNA-seq analysis, while producing a wealth of visualizations to facilitate data interpr…
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…
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…
Enhanced diffraction of light in GaAs microcavities
1995
We theoretically analyze the diffraction of light by gratings that are photogenerated in Fabry–Perot microcavities. The coupled-wave theory of volume gratings is combined with appropriate boundary conditions to yield expressions for the diffraction efficiency. Multiple round trips within the cavity are seen to increase the effective grating thickness and therefore the efficiency. Numerical calculations specific to GaAs microcavities show that the diffraction efficiency can be enhanced by more than 2 orders of magnitude at the resonant wavelengths.
Experimental observation of temporal dispersion gratings in fiber optics
2017
We experimentally demonstrate a temporal analog to the diffraction optical grating in the Fraunhofer formalism. Using amplitude and phase temporal periodic modulations, we show that the accumulation of dispersion in fiber optics induces the development of temporally well-separated sidebands similar to the spatial orders of diffraction that are commonly observed in an optical grating operating in the far field.
Devil’s vortex-lenses
2009
In this paper we present a new kind of vortex lenses in which the radial phase distribution is characterized by the "devil's staircase" function. The focusing properties of these fractal DOEs coined Devil's vortex-lenses are analytically studied and the influence of the topological charge is investigated. It is shown that under monochromatic illumination a vortex devil's lens give rise a focal volume containing a delimited chain of vortices that are axially distributed according to the self-similarity of the lens.
Diffraction management and sub-diffractive solitons in periodically driven Bose–Einstein condensates
2009
Abstract We theoretically investigate the diffraction management in Bose–Einstein condensates (BECs) in one- (1D), two- (2D) and three-dimensional (3D) geometries. The management technique is based on the superposition of harmonic lattices’ potentials moving at a common speed but in different directions, leading to a harmonic spatio-temporal modulation of the potential. In this way a reduction in, and eventually the disappearance of usual diffraction and emergence of fourth-order diffraction are achieved. We show sub-diffractive solitons in such a diffraction managed system and demonstrate their stability in 1D, 2D and 3D. In 2D and 3D cases we investigate diffraction management by lattices…
Diffraction-free propagation of subwavelength light beams in layered media
2010
Self-collimation of tightly localized laser beams demonstrated in periodic media relies on a perfect-matched rephasing of the Fourier constituents of the wavefield induced by a plane isofrequency curve. An alternate way paved for the achievement of such a phase matching condition developed a suitable spatial filtering in order to select those frequencies experiencing the same phase velocity projected over a given orientation. In principle this procedure is valid for complex structured metamaterials. However, a great majority of studies have focused on free-space propagation leading to the well-known Bessel beams. This paper is devoted to the analysis of this sort of nondiffracting beams tra…
Structure of Liquids
2014
An Introduction to the description of the static structure of simple liquids is given. The principle quantity, which describes this structure is the structure factor, which can be measured with neutron and X-ray diffraction. The structure factor is the Fourier transform of the radial pair distribution function, which describes the statistics of the atoms around a given one. Several theories are introduced for calculating this quantities. It is shown that the structure of liquid metals is dominated by their hardcore repulsion. In the low-wavenumber limit the structure factor is related to the compressibility of the liquid. In this limit deviations from the hard-core model become importent, w…