Search results for "nonlinear"
showing 10 items of 3684 documents
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…
Ab initio calculations of SrTiO3, BaTiO3, PbTiO3, CaTiO3, SrZrO3, PbZrO3 and BaZrO3 (001), (011) and (111) surfaces as well as F centers, polarons, K…
2014
In this paper, the review of recent results of calculations of surface relaxations, energetics, and bonding properties for ABO 3 perovskite (001), (011) and (111) surfaces using mostly a hybrid description of exchange and correlation is presented. Both AO and BO 2-terminations of the nonpolar (001) surface and A , BO , and O terminations of the polar (011) surface, as well as B and AO 3-terminations of the polar (111) surface were considered. On the AO -terminated (001) surface, all upper-layer A atoms relax inwards, while all second layer atoms relax outwards. For the BO 2-terminated (001) surface, in most cases, the largest relaxations are on the second-layer metal atoms. For almost all …
Strategies for structure solution and refinement of small organic molecules from electron diffraction data and limitations of the simulation approach
1999
In recent years, a series of non-linear optically active bis(benzylidene) ketones have been synthesized and investigated by electron crystallography. In most cases, structure refinement was possible by combining electron diffraction analysis and quantum-mechanical calculations with maximum-entropy methods. However, when the torsional angles between the phenyl rings and the C=C double bonds are strongly affected by the crystal field, this method fails because packing-energy calculations are not sufficiently sensitive. This problem can be solved by refining the approximate model with SHELXL, if the data set is sufficiently accurate and the model close to the correct structure. Here it is show…
Structure determination to calculate nonlinear optical coefficients in a class of organic material
1999
A class of molecules with intramolecular two-dimensional charge transfer upon excitation has been synthesized. It is expected that these materials should be prospective candidates for nonlinear optical (NLO) applications such as second harmonic (SHG) generation. In order to optimize the macroscopic NLO properties of the compounds, it is necessary to relate their first hyperpolarizability tensors at a molecular level to those at a crystal bulk level. This requires a complete structure determination and refinement. However, the growth of sufficiently large single crystals, which are needed for structural analysis and refinement by x-ray methods, is a time-consuming and sometimes impossible ta…
Emission of real phonons due to electron’s self-dressing in a covalent crystal
2011
A slow monoelectronic excitation in a covalent crystal at the temperature T=0 is analyzed. The interaction with zero-point longitudinal acoustic phonons leads to the formation of a dressed electronic state at an energy level lower than that of the initial bare state. This aspect of the dressing process is described here by hypothesizing that the excess of energy is released with the emission of real phonons. Specifically, this paper considers the transition probability from the bare monoelectronic state to a dressed state of the electron accompanied by real phonons and a deformation field. The spectrum of the real phonons emitted during the electronic self-dressing is calculated by applying…
Quadratic Nonlinear Behaviour of Various Langmuir-Blodgett Molecules
1989
The Langmuir-Blodgett (L-B) technique is well known as a method of building-up ordered arrays of organic molecules, and especially as a means of imposing a noncentrosymmetric structure from molecules that crystallize in a centrosymmetric space group(1–3). L-B films for use in quadratic nonlinear optics can be ordered in a statistically noncentrosymmetric lattice. The method involves the compression of a mono-layer of the organic molecule, spread on top of a water surface, into a two-dimensional solid, followed by the repeated dipping of the substrate to be coated into and out of the subphase. Monolayers may be deposited onto the substrate both on immersion and withdrawal, resulting in a cen…
Relationship between microscopic and macroscopic structures of organic thin films for SHG
1993
The experiments described in this paper were undertaken in order to obtain information about the relationship between the structure and non-linear optical properties (second-harmonic generation) of organic thin films. For this purpose, two closely related dyes, diones and tetrones, were compared, both of which are shown to have large hyperpolarisabilities. Their microscopic properties are investigated by conformational analysis and electron diffraction. It could be shown that detailed knowledge about the structure and the adjacent neighbour packing can be obtained from conformational analysis and electron diffraction in order to understand the non-linear optical properties of the two dyes.
Storage of information in lithium niobate single crystals
2011
Reported studies of recording information were made with a number of LiNbO 3 compositions: stoichiometric and congruent single crystals. The present study shows that recording is possible in pure LiNbO 3 single crystals and in single crystals containing inactive cation dopants. Recording in stoichiometric crystals is likely possible because of a considerable amount of electrons localised in shallow traps. Absence of recorded information in pure congruent crystals were observed.
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
2012
International audience; The nonlinear Schro¨dinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important serie…
Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type
2014
Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.