Kinematic coupling

Consider now the equality Hoj> n Jm=8j>j. Thus, in this model, preparing the system in the ground state of the Coulomb Hamiltonian, no time evolution can be expected if we do not switch on the kinematic couplings. We take a simple case where the electron-phonon coupling is on. The matrix elements of H in this base set look like ... 

It should be emphasized that the high yOH/yOD ratio is not the result of kinematic coupling since the yOH and yOD modes are rather pure. 

Kinematic coupling is supposed to be nil and reduced masses are written as ... 

Here is the momentum conjugate to 5, is the momentum conjugate to is a kinematic coupling of the kth orthogonal vibration to the... 

A qualitatively appealing feature of the RPH is that the kinematic coupling between motion along the reaction coordinate and the vibrational modes is made explicit in the matrix elements. From the early work of Polanyi and co-workers on collinear triatomic reactions, we know that from the position of the saddle point relative to the corner in the reaction path, qualitative conclusions can be drawn about the effect of the energy distribution in the reactants on the rate and about the distribution of energy in the products [20, 22]. The Bj appear to contain quite analogous and quite detailed information about curvature effects for polyatomic systems, identifying which modes should couple to (and... 

In terms of the RPH (for 7 = 0) of Eq. (4.14), the simplest approximation to tunneling assumes that the process is vibrationally adiabatic that is, the 37V - 7 orthogonal vibrational modes have constant quantum numbers. Even then, several levels of further simplification have been considered [76,114,115,143]. First, we might ignore all kinematic coupling elements, including Tunneling is then one-dimensional and subject to the effective Hamiltonian,... 

An appealing way to view the complications caused by the kinematic coupling elements is presented in Fig. 12. The IRP path is shown on a... 

During the first normal-coordinate studies of ferrocene, the authors treated the Cp rings as separate entities [50] therefore, the effect of the changing reduced mass was not introduced in this treatment. The revision of the normal-coordinate analysis of ferrocene by Brunvoll and co-workers, based on the treatment of the ferrocene complex as a whole, has demonstrated that similar kinematic coupling effects play a significant role in the normal vibrational frequencies for ferrocene as well [43c]. This study also concluded that the differences between the frequencies of ferrocene and those of the free Cp- ring are... 

Figure 8.3 shows, for PC, that there is a substantial difference between the yield stress in compression and that in tension. As discussed in Chapter 7, for metallic glasses, and as outlined here in Section 8.6.1, this difference is a consequence of the quite considerable activation dilatation, e, kinematically coupled to the transformation shear strain. It arises from the transitory expansion of the transformation volume Qf of the ST due to the internal random rearrangement of molecular segments occuring during the relaxation event. 

The best approximation to CC is called coupled states or and involves neglecting the kinematic couplings between the different projection quantum states. This approximation greatly reduces computer time so that reactions involving all the H3 isotopes as well as a few other atom-diatom reactions are feasible. Tests of accuracy of the most recent versions of CS indicate that errors of 25% or smaller in cross sections or rate constants compared to CC are to be expected for H + H2 close to threshold. More accurate CS approximations have also been studied, but computational effort has generally made such methods prohibitively expensive to use. Recently, an approach which combines simplicity with physical accuracy has been proposed but not yet tested. 

In the telerobotic system the master side is operated by the human operator and the master movements are replicated on the slave side. If the slave is xmder position control and if the master and slave kinematics are similar, the kinematic coupling between master and slave is achieved with a straightforward mapping transformation, once a perfect coupling is achieved. 

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