Translational motion description

A complete description of the translational motion-internal motion coupling and its effects is, in principle, contained in eqs. (11-29), (11-30), and (11-31). Unfortunately, even for the simplified form of hypothetical molecular spectrum studied by Rice, McLaughlin, and Jortner, it has not yet been possible to perform the indicated quadratures. Even without actual calculation, our previous analysis of the theory of radiationless processes suffices to define the following general properties of the photo-dissociative act ... 

Classical Path. Another approach to scattering calculations uses a quantum-mechanical description of the internal states, but classical mechanics for the translational motion. This "classical path" method has been popular in line-shape calculations (37,38). It is almost always feasible to carry out such calculations in the perturbation approximation for the internal states (37). Only recently have practical methods been developed to perform non-perturbative calculations in this approach (39). 

In solution things are more complex. The reaction partners are no longer free in their translational motion as they are in the gas phase they have to move in a condensed medium, and their motion is governed by other physical phenomena which for economy of exposition we shall not consider in detail. It is sufficient to recall that the physical models for the most important terms, Brownian motions, diffusion forces, are expressed in their basic form using a continuum description of the medium. 

It ought to be stressed that the above description of relaxation does not account for the velocity of translational motion of a separate particle. That is justified in the case where the spectral intensity of the exciting laser light is constant within the range of the Doppler contour of the optical transition, and the molecules can thus absorb light irrespective... 

Inertia A descriptive term for that property of a body which resists change in its motion. Two kinds of changes of motion are recognized changes in translational motion, and changes in rotational motion. 

The process by which something moves from c ie position to another is referred to as motion that is, a chang-ii position involvii Hme, velocity and acceleration. Motions can be classified as linear or translational (motion aloi a stra ht line), rotational (motion about some axis), or curvilinear (a combination of linear and rotational). A detailed description of all aspects of motion is called kinematics and is a hjndamental part of mechanics. 

At ultra-low temperatures, where we expect quantum dynamics to govern the translational motion of atoms, this magnetic potential should be included in some sort of Schroedinger equation for the translational motion. However, this inclusion is not trivial, since even the simplest description of such an atom must also include its internal angular-momentum degrees of freedom. For example, the wave function of an atom with angular momentum A obeys the following equation ... 

For dispersed multiphase flows a Lagrangian description of the dispersed phase are advantageous in many practical situations. In this concept the individual particles are treated as rigid spheres (i.e., neglecting particle deformation and internal flows) being so small that they can be considered as point centers of mass in space. The translational motion of the particle is governed by the Lagrangian form of Newton s second law [103, 148, 120, 38] ... 

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... 

Rabitz s use of a multiple-time-scale representation of the collision dynamics is somewhat different. The separation of timescales in this theory is based on the rate of phase accumulation, since in the semiclassical limit this is related to the time needed for transfer of a quantum of ener r. When the interactions are such as to generate rapid-phase accumulation, as in the description of deflected translational motion, classical mechanics is appropriate, and when the interactions generate slow-phase accumulation, as in vibrational depopulation, quantum mechanics must be used. The effect of interactions on rotational motion spans the range of behavior between these two limits. The stochastic assumption introduced by Rabitz asserts that large and rapidly varying phases permit use of a random phase approximation. Reduction of the equations of motion to a useful form requires further approximations the reader is referred to the original paper for full discussion of these. The theory described has some very interest-... 

Mesophases are intermediate phases between rigid, fully ordered crystals and the mobile melt, as explained in the introductory discussion of phases in Sect. 2.5, and summarized in Figs. 2.103 and 2.107. The quantitative analysis of melting in Sect. 5.4 shows that with a suitable molecular stracture, three types of disorder and motion can be introduced on fusion (1) positional disorder and translational motion, (2) orientational disorder and motion, and (3) conformational disorder and motion [43]. In case not all the possible disorders and motions for a given molecule are achieved, an intermediate phase, a mesophase results. These mesophases are the topic of this section. Both structure and motion must be characterized for a full description of mesophases. 

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