Search results for "Nonlinear"
showing 10 items of 3684 documents
Analysis of the sensitivity to the systematic error in least-squares regression models
2004
An algorithm that calculates the sensitivity to the systematic error of the fitted parameters of a least-squares regression model, with respect to the known parameters, is developed. The algorithm can be applied to mechanistic and empirical models, obtained by linear and non-linear regression, including principal component and partial least-squares. It can be useful in identifying those parameters or calibration regions that can influence other parameters and the response mostly, and thus, whose accuracy should be particularly procured. Other applications are the weighing of experimental points and the comparison of different models and regression methods in terms of its ability of amplifyi…
Enhanced nonlinear optical properties and thermal stability of donor-acceptor substituted oligothiophenes
1997
Abstract Linear and nonlinear optical properties of a series of novel donor-acceptor substituted α-oligothiophenes were investigated by means of electrooptical absorption measurements (EOAM) and electric field induced second harmonic generation (EFISH). The second-order polarizabilities β(−2ω; ω, ω) were related to dipole changes Δμ ag and transition dipoles μ ag associated with low-lying charge-transfer (CT) excitations by using the perturbational two-level approximation. Systematic variation of the donor and acceptor groups led to compounds with exceptional nonlinearity and thermal stability. Too strong donor/acceptor pairs, however, yielded structures in the charge-resonance (CR) limit w…
Nonlinear optical spectra of conjugated polymers: Effect of long-range coulomb interactions
1993
Abstract Nonlinear optical spectra of conjugated polymers are theoretically studied in the Su-Schrieffer-Heeger model supplemented by long-range Coulomb interactions. Excitonic correlation for electron-hole excitations in explicitly taken into account by a standard method. Nonlinear susceptibilities χ (3) are calculated numerically with a standard sum-over-states method for finite chains (up to 1000 sites). Using moderate interaction strength, our calculations can reproduce many distinct features observed in the linear and nonlinear spectra (two-photon absorption, third-harmonic generation, and electroabsorption) of polydiacetylenes and some other polymers. Especially, a hump in the spectru…
Large Quadratic Hyperpolarizabilities with Donor–Acceptor Polyenes Exhibiting Optimum Bond Length Alternation: Correlation Between Structure and Hype…
1997
Donor-acceptor polyenes of various lengths, and that combine aro- matic electron-donating moieties with powerful heterocyclic electron-withdraw- ing terminal groups, have been synthe- sized and characterized as efficient non- linear optical (NLO) chromophores. Their linear and nonlinear optical proper- ties have been investigated, and variations in these properties have been related to ground-state polarization (dipole p) and structure. In particular, unprecedented quadratic hyperpolarizabilities (p) have been achieved (up to p(0) =I500 x 10-30esu) by reduction of the bond- length alternation (BLA) in the polyenic chain. In each series of homologous com-
Up-conversion processes in NaLaF4:Er3+
2009
abstract Structural and spectroscopic investigation of NaLaF 4 :Er 3+ material at different doping concentrations ispresented. X-ray diffraction patterns, up-conversion luminescence spectra and decay curves for 2 H 9/2 ? 4 I 15/2 , 4 S 3/2 ? 4 I 15/2 and 4 F 9/2 ? 4 I 15/2 optical transitions in the material are shown and possibleexcitation routes are discussed. Raman spectrum for the undoped material is presented and the effectivephonon energy of the material is estimated. Based on the obtained results application of rare-earth dopedNaLaF 4 in the field of up-conversion phosphors is evaluated. 2009 Elsevier B.V. All rights reserved. 1. IntroductionFor many years rare-earth (RE) doped materi…
Donor-acceptor substituted polyenes : orientation in mono- and multilayers
1992
Large molecules containing different chemical units whose interactions within the molecule result in new macroscopically observable effects, have become increasingly important.The organization of molecules of this type in ordered structures leads to functional molecular materials.Their use in molecular electronics requires that the units exhibit specific electronic properties. Recently, we reported on the intramolecular energy transfer through terminally substituted conjugated polyenes. An intramolecular electron transfer within donor-acceptor substituted polyenes can be achieved by introducing suitable terminal groups.
Chiral anomalies in even and odd dimensions
1985
Odd dimensional Yang-Mills theories with an extra ‘topological mass” term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.
Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion …
2013
A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for th…
Hidden and self-excited attractors in radiophysical and biophysical models
2017
One of the central tasks of investigation of dynamical systems is the problem of analysis of the steady (limiting) behavior of the system after the completion of transient processes, i.e., the problem of localization and analysis of attractors (bounded sets of states of the system to which the system tends after transient processes from close initial states). Transition of the system with initial conditions from the vicinity of stationary state to an attractor corresponds to the case of a self-excited attractor. However, there exist attractors of another type: hidden attractors are attractors with the basin of attraction which does not have intersection with a small neighborhoods of any equ…
Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems
2011
The method of harmonic linearization, numerical methods, and the applied bifurcation the- ory together discover new opportunities for analysis of oscillations of control systems. In the present survey analytical-numerical algorithms for hidden oscillation localization are discussed. Examples of hidden attrac- tor localization in Chua's circuit and counterexamples construction to Aizerman's conjecture and Kalman's conjecture are considered.