Other Nonlinear Properties

Certain glass-ceramic materials also exhibit potentially useful electro-optic effects. These include glasses with microcrystaUites of Cd-sulfoselenides, which show a strong nonlinear response to an electric field (9), as well as glass-ceramics based on ferroelectric perovskite crystals such as niobates, titanates, or zkconates (10—12). Such crystals permit electric control of scattering and other optical properties. 

Enclosure also changes the redox properties of a compound, its color, and other physical properties (1,2). On this basis nonlinear optical materials, luminescence markers, controlled light switches, and other high-tech devices might be designed and prepared (15,17,137). 

The simplest description of compoimds of this type is obtained limiting the siun-over-state equations to terms depending only on the properties of the groimd state g and the first excited state e (two-state model) [93]. This is analogous to the two-level model introduced to describe other nonlinear optical properties, for example the nonlinear polarizability pS - co coi,co2) [ 104]. In the case of 2PA, this two-state, or dipolar, contribution to the cross section is, on resonance ... 

In one application (Maitre, 1981), the parallelism of noncoherent optical convolution methods is combined with video techniques in a totally analog application to images. Matsuoka et al (1982) have developed a hybrid optical-video-digital system based on similar principles. Pipeline processors that perform image convolution at high speed are ideal for digital applications. The inherent simplicity of the method adapts it to high-speed implementations by use of other hybrid techniques. It is even possible to devise a transversal filter that has all the desirable nonlinear properties of the method. We describe this filter in the next section. 

The stability and other thermodynamic properties of nonlinear kinetic systems far from thermodynamic equibbrium are commonly accepted to analyze by inspecting the system behavior as functions of some external controlling parameters. Chemical affinity of stepwise processes or those related to it values that characterize the remoteness from the equilibrium point of the system are often chosen as such a controlling parameter of general nature. 

Besides other intriguing properties, such as inherent planar chirality, metallocenes are of interest due to their considerable Lewis basicity. Their direct or conjugative attachment to a polymer chain should enhance the electron density along the main chain and therefore lower the HOMO-LUMO band gap. In addition, organometallic compounds and metallocene-based monomers and polymers represent interesting potential nonlinear optical materials, useful for frequency doubling, modulation, and switching, for three reasons ... 

Second, note marked differences in the slope between the plots in Figure 1. The Arrhenius plots are linear for a solitary water molecule in the organic solvents, whereas the plot for neat liquid water is nonlinear as known for other dynamical properties in water. The Arrhenius activation energies at room temperature are in the sequence,... 

In a similar way it is possible to reduce the SOS expressions defining other nonlinear optical properties. The two-photon transition moment within two-level approximation reads ... 

Thirdly, just like the linear ones, the metal nonlinear properties are affected by electronic confinement. In other words, the intrinsic nonlinear optical susceptibility of a small particle might be different from tire bulk metal one, due to finite size effects as already evoked in Section 2.2.4 for the linear susceptibility. 

Whereas the majority of experimental works has been focused on silica-, glass-or alumina-embedded noble metal nanoparticles, or aqueous colloidal solutions, a few ones have dealt with other kinds of matrices, either amorphous (BaO [177], BaTiOj [164, 167], Bi.()., [178], Nb.O, [179], TiO. [180, 181], ZrO. .. [167]) or crystalline (BaTiOj [164, 182, 183], BiT) [184], LiNbOj [185], SrTiOj [172], ZnO... [186]). A direct comparison of the nonlinear properties from one matrix to another is difficult to carry out, since all other parameters should be kept constant while tuning the wavelength as to match the SPR maximum. 

As already stated for other experimental parameters, two factors may account for the nonlinear optical response dependence on excitation wavelength Local field factor, f, and intrinsic nonlinear properties of the particles, x2 - The interband contribution to x2 expected to vary only for photon energies at least equal to the IB transition threshold, provided the intraband contribution remains negligible. On the other hand, the hot electron contribution, which accounts for the Fermi smearing mechanism, presents spectral variations for photon energies close to the IB transition threshold, since the electron distribution is modified around the Fermi level by the temperature increase subsequent to light absorption (see 3.2.3). The wavelength dependence of x has been already discussed in Section 6. 

The bilinear model, in combination with other physicochemical properties (Eq. (30)) [24,62], was the first mathematical expression to describe nonlinear lipophilicity-activity relationships, precisely and in a flexible manner. Besides pharmacokinetic properties, such as absorption, distribution, elimination, and permeation of the... 

Although a majority of the published ADMET models are based on linear multivariate methods as discussed in Section 16.3.3.1, other nonlinear methods have also been employed. The most commonly used nonlinear method in ADMET modeling is neural networks (NNs). Backpropagation NNs have been used to model absorption, permeation, as well as solubility and toxicological effects. A particular problem for many NNs is the tendency for these networks to overtrain (see further discussions on model validation in Section 16.3.3.4), which needs to be closely monitored to avoid the situation where the derived model becomes an encyclopedia , that is, the model can perfectly explain the variance of the investigated property of the compounds used to derive the model but have quite poor predictive ability with respect to new compounds. 

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