Nonlinearity, cubic

Shearer, M., and Y. Y ang, 1993, The Riemann problem for a p-system of conservation laws of mixed type with cubic nonlinearity, Proc.Roy.Soc. Edinburgh A. ... 

The effect of metal replacement has not been established with certainty. Direct comparison of ferrocene complexes with analogous ruthenocene complexes is only possible for the parent compounds, with ruthenocene having a slightly larger cubic nonlinearity.1819 This result needs to be treated cautiously, as the technique employed (OPL) is susceptible to thermal contributions (see earlier) and the low nonlinearities of the complexes induce substantial errors. The differing fundamental frequencies employed... 

Very few calculations of cubic nonlinearities have been carried out. Table XV contains computationally derived static y values for ferrocene and some ferrocenyl derivatives. 

The basic molecular properties that give rise to high values of the hyperpolarizabihties, such as P and 7, are reasonably well understood in organic solids. For quadratic molecular effects, conjugation and intramolecular charge transfer are important. Cubic-nonlinearity-related effects are enhanced in one-dimensional conjugated structures, but no charge-transfer-induced asymmetry is required. 

Mackay, T.G., Lakhtakia A.. Weiglhofer, W.S. Homogeneisation of isotropic, cubically nonlinear, composite mediums by the strong-permittivity-fluctuation theory third-order considerations. Opt. Commun. 204. 219-228 (2002)... 

The amplitude equations (65) cannot describe the nonlinear stabilization of a growing surface structure and cannot provide conditions for the formation of stable, spatially regular structures near the instability threshold. In order to obtain such conditions higher order (usually cubic) nonlinear terms in the amplitude equations need to be taken into account. However, in the presenee of the resonant quadratic interaction, the addition of cubic terms in the amplitude equations near the instability threshold is asymptotically rigorous only if the quadratic interaction coefficient is small, o e, which restricts the validity of... 

The simplest possible autocatalytic reaction is the quadratic autocatalysis of Eq. [76]. We now consider the next simplest case, in which a cubic nonlinearity appears in the rate law ... 

F. Kajzar, J. Messier, Cubic Nonlinear Optical Effects in Conjugated Polymers. Polym. J. 1987,19, 275-284. 

Keywords Cubic nonlinearity. Molecular switches, Nonlinear absorption. Nonlinear refraction... 

Switching the cubic nonlinearity of ruthenium alkynyl complexes by a protmi-ation/deprotonation sequence (via a vinylidene complex) was demraistrated by fs Z-scan studies at 800 nm several years ago [41]. Recently, protic and electrochemical switching were demonstrated in the ruthenium alkynyl cruciform complex 11 for which distinct linear optical and NLO behavior were noted for the vinylidene complex and the Ru(II) and Ru(III) alkynyl complexes [42]. Because the oxidation/ reduction and protonation/deprotonation procedures are independent, this system corresponds to switching by orthogonal stimuli. 

Fig. 1. Examples of restoring forces Frestore as functions of for (A) a linear restoring force, (B) a restoring force with a quadratic nonlinear term, and (C) a restoring force with a cubic nonlinear term.

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