Split multiple-collision

Mixer 61 [M 61] Multiple-collisions Split-and-recombine Micro Mixer... 

A typical problem of interest at Los Alamos is the solution of the infrared multiple photon excitation dynamics of sulfur hexafluoride. This very problem has been quite popular in the literature in the past few years. (7) The solution of this problem is modeled by a molecular Hamiltonian which explicitly treats the asymmetric stretch ladder of the molecule coupled implicitly to the other molecular degrees of freedom. (See Fig. 12.) We consider the the first seven vibrational states of the mode of SF (6v ) the octahedral symmetry of the SF molecule makes these vibrational levels degenerate, and coupling between vibrational and rotational motion splits these degeneracies slightly. Furthermore, there is a rotational manifold of states associated with each vibrational level. Even to describe the zeroth-order level states of this molecule is itself a fairly complicated problem. Now if we were to include collisions in our model of multiple photon excitation of SF, e wou d have to solve a matrix Bloch equation with a minimum of 84 x 84 elements. Clearly such a problem is beyond our current abilities, so in fact we neglect collisional effects in order to stay with a Schrodinger picture of the excitation dynamics. 

In this equation, I is the unit tensor, is the pseudo-Fourier fluctuating kinetic energy flux, and y is the dissipation rate of granular energy due to inelastic particle-particle collisions. In the KTGF, coUisions are assumed binary and quasi-instantaneous and do not take long-term and multiple particle contact into account (which is the case in the dense part of the fluidized bed). To correct for this shortcoming, the solids phase viscosity Ps and the solids phase pressure are split up into a kinetic part and a frictional part. 

It is useful to consider the angular momentum dependence of the results. In Fig. 3(a), the / dependence of the CRP is shown up to collision energies of 4 kcal/mol. The resonance positions do not show a large /-dependence, but it is obvious that as the / is increased the multiplicity of the resonance features increases. This is emphasized in Fig. 3(b) where we show an expanded view of the 2.5 to 3 kcal/mol region. It is seen that each base resonance splits into /+1 peaks. Since the increase in the total angular momentum allows for the increase in the number of helicity states, i.e. /> k and /> k, it is reasonable to infer that a single /=0 level splits into a J+1 member multiplet of helicity states as / increases. (We presume that the k and — k states are nearly degenerate.)... 

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