Nonlinear-like effect

In addition, we investigated a nonlinear-like effect (NLE), activity, temperature dependence, and kinetics of hydroxy[2.2]paracyclophane ketimine ligands with the 1,2-addition reaction of diethylzinc to cyclohexylcarbaldehyde. A linear correlation between the enantiomeric excess of AHPC ketimine ligands bearing a phenylethyl side group and the product was observed with 0.5 mol% of catalyst loading. When the catalyst loading of (Sp,S)/(Rp,R)-4a was increased to 4 mol%, a precipitate of the inactive heterochiral species was formed and resulted in a positive nonlinear like effect (Fig.2.1.3.6), while a linear behavior is observed with 5b (Fig. 2.1.3.7). The enantiomeric ratio was found to have linear temperature dependence. [16]... 

Such a behavior of the total field is observed provided that the beam power is smaller than a definite value P which depends on the waveguide width (for a = 1.8pm, P 8). The spatial dynamics of a light beam with P > Pi is more complicated because nonlinear self-effects in radiation field increase so that the formation of soliton-like light beams propagating in the waveguide cladding is observed. 

Out of the large range of possible nonlinear optical effects, chemists are likely to encounter only a limited number of measurement techniques. These include both second- and third-order NLO characterization methods. A brief listing of the different types of measurements, the nonlinear susceptibility involved and the related molecular nonlinear polarizabilities is given here. 

The most pronounced evidence of the critical-like behavior in these compounds can be found by using the nonlinear dielectric effect (NDE). NDE is coupled via the 4-point correlation to multimolecular heterogeneities -fluctuations. It was shown in refs. that ... 

To summarize, we have demonstrated the possibility of strong resonance hybridization of ID Frenkel and Wannier-Mott excitons in parallel organic and semiconductor wires. Like the 2D case, the new states possess the properties of both types of excitons. They have a relatively large size (along the wires) like Wannier-Mott excitons, but they also have a large transition dipole moment which is typical for Frenkel excitons. Thus, one may expect the same as for 2D structures (see Fig. 13.1b) the strong nonlinear optical effects in such structures. 

To obtain initial estimates, an Emax model was fit to the data set in a na ive-pooled manner, which does not take into account the within-subject correlations and assumes each observation comes from a unique individual. The final estimates from this nonlinear model, 84% maximal inhibition and 0.6 ng/mL as the IC50, were used as the initial values in the nonlinear mixed effects model. The additive variance component and between-subject variability (BSV) on Emax was modeled using an additive error models with initial values equal to 10%. BSV in IC50 was modeled using an exponential error model with an initial estimate of 10%. The model minimized successfully with R-matrix singularity and an objective function value (OFV) of 648.217. The standard deviation (square root of the variance component) associated with IC50 was 6.66E-5 ng/mL and was the likely source of the... 

The study of the perception of compounds present in odor mixtures is also fraught with the sorts of nonlinear "contextual effects" with which vision and auditory scientists are all too familiar. At present, most studies use human subjects to examine the way that odor compounds affect perception in complex mixtures such studies show that perceived odor similarity between two complex blends is likely to be mediated both by the types of compounds found in the mixtures and the relative... 

These analyses and associated experiments demonstrate that fracture mechanics can be used to provide information and insight into the value of the failure load, the locus of likely crack growth, and the path along which the crack will then grow. Where analytical analyses of stress, strain, and energy release rates are difficult or impossible, modern numerical methods can be very useful. In the opinion of the authors, the utility of these combined tools has hardly been exploited. The inclusion of nonlinear, nonelastic effects in the analyses is feasible is such materials are carefully characterized and/or properties become available. 

Coherent interactions can also give rise to new nonlinear optical effects. These are listed in Table XV, along with some of their characteristics and the conditions under which they are likely to occur. 

For Sq elastomers, a mechanical field should cause orientation effects toward uniform alignment of the phase structure. Additionally, the piezoelectric behavior is expected to be similar to the piezoelectricity of solid-state material because the network structure prevents flow. The electro-mechanical behavior of smectic C networks was already addressed by Brand in 1989 [8]. In agreement with the monoclinic symmetry of these systems, he derived ten piezoconstants for the S networks. Furthermore, rotatoelectric effects are predicted. Due to the noncentrosymmetric character of the untwisted phase, further nonlinear optical effects like frequency doubling occur. 

In this particular case, the experimenter would not be likely to use the first design, from realization that the factors could (and probably do) interact. Thus, while the design of Example 1 would increase understanding of the process somewhat, it would leave critical questions about interactions unanswered. Example 2 might be chosen as a quick and easy way to sort out the possible catalyst types and get a good idea of how linear or nonlinear the effects of the numerical factors might be. It would still be a flawed design, because of the certainty that important interactions exist and would remain undetected. 

Nonlinear Raman effects Raman-like processes occurring at high photon densities, in which second- and higher-order terms in the expression for the induced... 

The metric term Eq. (2.8) is important for all cases in which the manifold M has non-zero curvature and is thus nonlinear, e.g. in the cases of Time-Dependent Hartree-Fock (TDHF) and Time-Dependent Multi-Configurational Self-Consistent Field (TDMCSCF) c culations. In such situations the metric tensor varies from point to point and has a nontrivial effect on the time evolution. It plays the role of a time-dependent force (somewhat like the location-dependent gravitational force which arises in general relativity from the curvature of space-time). In the case of flat i.e. linear manifolds, as are found in Time-Dependent Configuration Interaction (TDCI) calculations, the metric is constant and does not have a significant effect on the dynamics. 

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