Coriolis term

It is important to note that Eq. (34) becomes independent of the Coriolis term because the symmetrical components of P and ytl cancel it identically. 

This decomposition suggests the strategy for parallel computing. In the simplest implementation, we distribute the job over processors, where Nk is the number of K values in our problem. Each processor is labeled by an index, k = 0,1,..., Nk — 1, associated with a particular value of K. We distribute the wave packet vector, v, over the processors such that processor k contains v( , k) and is responsible for everything related to its propagation, in particular, for computing the action of on v( , fe). Except for the work associated with the Coriolis terms, all of the computation is done locally on each processor, proceeds independently, and involves no communication. 

With this distribution, each size of the job on each processor is less than or equal to the size of a 7 = 0 calculation. However, the computation of the Coriolis terms involves communication between processor k and processors k 1. In fact, processor k will send q ,k) to each of its neighboring processors and will receive both q , fe 1) and q , fe + 1) from its neighbors. (Processor 0... 

The vibration-rotation hamiltonian of a polyatomic molecule is more complicated than that of a diatomic molecule, both because of the increased number of co-ordinates, and because of the presence of Coriolis terms which are absent from the diatomic hamiltonian. These differences lead to many more terms in the formulae for a and x values obtained from the contact transformation, and they also lead to various kinds of vibrational and rotational resonance situations in which two or more vibrational levels are separated by so small an energy that interaction terms in the hamiltonian between these levels cannot easily be handled by perturbation theory. It is then necessary to obtain an effective hamiltonian over these two or more vibrational levels, and to use special techniques to relate the coefficients in this hamiltonian to the observed spectrum. 

As mentioned above, the terms which are responsible for the coupling of the 25+1 n state to the 25+1 states are the spin-orbit coupling and the rotational electronic Coriolis term. Thus in the second-order perturbation expression in equation (7.43), the perturbation term is... 

The dynamics across this linearized relative TS is exactly comparable to the dynamics across the linearized usual TS. Like the usual TS, a relative TS defines two regions in phase space an outer region and an inner region with > 0 and < 0, for the Hamiltonian equation, Eq. (49)]. However, the full dynamics may be qualitatively different, precisely because of the relative nature of the equilibrium and the occurrence of Coriolis terms in the relative frame. 

The MRS closures will attract most interest for use wherever MTE methods fail. For example, in flows with rotation the Coriolis terms enter the Rij equations, but drop out in the equation for Ru — q Therefore, an MRS method probably will be essential for including rotation effects, which are of considerable importance in many practical engineering and geophysical problems. Other effects that have not yet been adequately modeled and for which MRS methods may offer some hope include additive drag reduction, ultrahigh Reynolds numbers, separation, roughness, lateral and transverse curvature, and strong thermal processes that affect the hydrodynamic motions. 

The first two terms are pure rotational terms, the third a pure vibrational term, and the last a Coriolis term. The partitioning of the energy between the pure rotational terms and the Coriolis term depends on the choice of the rotating axis system used to describe the problem18-22. ... 

On the other hand, for a polyatomic molecule, no well-defined average distance exists. For example, for the general polyatomic molecule, the experimental Igy value is given by an average of I corrected for Coriolis terms [21] ... 

For polyatomic molecules the physical significance of the effective moment of inertia is complicated by the presence of Coriolis terms. Thus one has the relation ... 

Since the Coriolis term is small, in the first approximation we may decide to neglect it. Also, when assuming small vibrational amplitudes which is a reasonable approximation in most cases, we may replace r by the corresponding equilibrium positions in the rotational term of Eq. (6.35) x fa) Ma([Pg.293]

---