Ring collision events

These ring collision events are now a familiar part of the kinetic theory description of dynamic processes in simple dense fluids. A brief comparison of the theory for the velocity autocorrelation function with that for the chemically reacting fluid will help motivate our description. Recent developments in the theory of the velocity autocorrelation function have arisen out of an attempt to understand the slow t power law decay observed by Alder and Wainwright in a computer simulation of a dense hard-sphere fluid. This work also showed that the translational motion of a small hard sphere in a fluid of similar hard spheres has a significant collective (hydro-dynamic) component. On the theoretical side, this type of behavior was discussed from the kinetic theory point of view in terms of the ring collision events described above and provided a microscopic basis for the introduction of collective effects. In addition, it was shown that mode... 

Fig. 56. Simple binary collision events in liquids, (a) Patti of two particles, 1 and 2, undergoing a single collision only, (b) Three particles undergoing two binary collisions, (c) Three particles undergoing three binary collisions where the second collision of particles 1 and 2 is correlated with the first collision between these particles this is the simplest ring graph. After R ibois and De Leener [490].

The R operators are repeated ring operators and account for the correlated collision events discussed above. The R (l z) operator describes sequences of correlated elastic collisions of the solute molecule A with the... 

The repeated ring operator in (7.21b) is a new operator that appears in the theory on account of the reactive collision events. It has a form analogous to that of... 

The structure of this repeated ring operator is much richer than that of the repeated ring operators discussed earlier. The various classes of collision events can be examined by expanding the (T bs propagator in powers of %Bs- Consider, for instance, the one-ring term... 

Fig. 24. Some of the four successive binary collision events taking place among four particles (four-body ring events) that are responsible for the divergence of the four-body collision operator.

How do moons and rings form The solid bodies around the giant planets formed as a consequence of the assembly of the giant planets, but stochastic events such as large collisions may have played crucial roles. For example, we do not know whether the massive Saturnian rings are as old as Saturn itself. 

Before carbonaceous chondrites arrive on the Eartli, tire carbon-bearing materials in tliem may imdergo shock events in at least tire following tliree stages die fonnation of parent bodies by accretion of interstellar medimn particles, the break-up of the parent bodies by their mutual collisions, and die fall of meteorites on the Earth traversing the atmosphere. Through these shock events, primitive carbonaceous materials diat had been present in the interstellar medium would become more complex compounds and they would be detected in meteorites. Shock reacdons may have promoted the secondaiy production of heavier and more complicated PAHs such as the insoluble polymers of muldple benzene rings detected in meteorites. 

We discussed the structure of the repeated ring operator in Section VII.D and pointed out that it contains a variety of dynamic events such as a series of correlated collisions identical to those that appear in the singlet theory via the operators and R. These operators represent the correlated collisions of a single solute molecule with the solvent and serve to renormalize the single-particle motion. Other events in R represent the coupling of the motion of the two solute molecules. In view of this, it is convenient to introduce the propagator for independent motion of the pair... 

In the other constrained simulations (constraint respectively at 2.75, 3.0, 3.5, 3.75, 3.9 A) the formation of this kind of defects has been observed in the whole simulation times, and defects transform each other in a very short time ( 100 fs). However for such values of the constraint, the reacting O atom was still bound to the framework. The reactive event occurred only when the constraint was set to an NO distance of 4.0 A. After few fs, the oxygen previously trapped in the framework defects, left the four ring region and diffused in the adjacent cage colliding with the second NOj. Such collision first led to the transient species [N02---02] , that appeared in the unconstrained nitrite sodalite -I- O2 simulation. Then, such species reached rapid equilibrium with the separated NOj and O2 compounds. 

The dynamical events that lead to the secular growth of the collision integrals are usually referred to in the literature as the ring events, in accordance with a description that can be given for them in terms of ring graphs. Statements (a)-(c) are based on phase space estimates of the type discussed here. Only in the case that the molecules are hard spheres or... 

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