Second-order current effects

In the "nonrigid symmetric-top rotors" (such as NH ), the second-order Stark effect is observed under normal circumstances. Indeed, field strengths of the order of 1 600 000 [V/m] are required to bring the interaction into the first-order regime in this case [18]. In contrast, very weak interactions suffice to make the mixed-parity states and appropriate for the description of optically active systems. Parity-violating neutral currents have been proposed as the interaction missing from the molecular Hamiltonian [Eq.(1)] that is responsible for the existence of enantiomers [14,19]. At present, this hypothesis is still awaiting experimental verification. 

An even more effective numerical method for calculating the magnetic properties (25), (28), (31), and (34), based on formal annihilation of the paramagnetic contribution to the current density all over the molecular domain (CTOCD-PZ), has been outlined in a series of papers. Extensive numerical tests document the reliability, simplicity, and accuracy of this numerical procedure. To build up the CTCXID-PZ computational scheme it is expedient to define a set of generalized transformation functions theoretical methods which have been examined in detail by Coriani et al. Unlike the DZ procedure, the CTOCD-PZ equations cannot, in general, be solved to obtain closed form expressions. Rather the functions employed to cancel the transverse paramagnetic contribution to current density are evaluated pointwise via conditions imposed on first- and second-order current densities (compare for equations 113 and 115) ... 

Um et al. also examined a transient using their complex model. They saw that in a matter of tens of seconds the current density response reached steady state after a change in potential. However, their model did not include liquid water. The most complex model to examine transients is that of Natarajan and Nguyen. It should be noted that although the model of Bevers et al. has transient equations, they do not report any transient results. Natarajan and Nguyen included liquid saturation effects and water transport in their model. They clearly showed the flooding of the diffusion media and that it takes on the order of a couple of minutes for the profiles to develop. 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

ALTERNATING CURRENT PERTURBATION. SECOND-ORDER RESPONSES 2.4.1 The second-order effects... 

It may be emphasized here that such an elaboration is possible for any small amplitude perturbation technique. It is only necessary to explicitize either the first-order current or the first-order interfacial potential, corresponding to the type of perturbation, to be able to derive expressions for 7q, 1 and AEl. So, the treatment is also useful to estimate the error due to second-order non-linearity in the step methods. However, a separate measurement of the second-order effect can only be done with (sinusoidal) a.c. perturbation. In Table 5, the explicit expressions for SF pertaining to the four methods mentioned in Sect. 2.4.1 are given in such a way that the connection between them is clearly shown. 

Koutecky [57] evaluated Ax = 34.7 and A2 = 100, while Matsuda [58] found = 31.1 and A2 = 294. However, for typical values of D and m, these second-order terms can be neglected. Nevertheless, early in the drop life, the observed currents are lower than those predicted and later on they are higher (possibly due to convection effects). 

As a result of the effects of nonideal structures, second-order effects in parameters, and the numerous approximations made in the derivation of the current-voltage equations, (C.27) and (C.30) can only serve as a qualitative description of the actual device each individual design must be experimentally characterized. For these reasons it is advantageous to operate the FET in the constant drain current mode in which case a suitable feedback circuit supplies the gate voltage of the same magnitude but of the opposite polarity to that produced by the electrochemical part of the device. 

Figure 12(b) shows the local current distribution of first and second order reactions and applied over potentials ° for the coupled anode model without the mass transfer parameter y. The figure also shows the effect of a change in the electrode kinetics, in terms of an increase in the reaction order (with respect to reactant concentration) to 2.0, on the current distribution. Essentially a similar variation in current density distribution is produced, to that of a first order reaction, although the influence of mass transport limitations is more severe in terms of reducing the local current densities. 

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