Collisional randomization

In the classical model the inefficiency of purely disorienting elastic collisions can easily be understood if one takes into account the fact that such disorientation is connected with a turn of the angular momentum J by a tangible angle (collisional randomization of 3(0,rotational level, i.e. the collision becomes an inelastic one. 

Quantum-state decay to a continuum or changes in its population via coupling to a thermal bath is known as amplitude noise (AN). It characterizes decoherence processes in many quantum systems, for example, spontaneous emission of photons by excited atoms [35], vibrational and collisional relaxation of trapped ions [36] and the relaxation of current-biased Josephson junctions [37], Another source of decoherence in the same systems is proper dephasing or phase noise (PN) [38], which does not affect the populations of quantum states but randomizes their energies or phases. 

Example 4.1 Determine the collisional heat transfer coefficients under each of the following conditions (1) collisions of a cloud of hot particles with a cold particle (2) collisions of a cloud of cold particles with a hot wall. Assume the particles are in random motion with the average impact velocity of 0.1 m/s. All the particles are spherical and of the same diameter of 100 fim. The particles and wall are made of steel with v = 0.3, E = 2 x 105 MPa, Pp = 7,000 kg/m3, Kp = 30 W/m K, and c = 500 J/kg K. The particle volume fraction is 0.4. 

Thus far we have dealt with the idealized case of isolated molecules that are neither -subject to external collisions nor display spontaneous emission. Further, we have V assumed that the molecule is initially in a pure state (i.e., described by a wave function) and that the externally imposed electric field is coherent, that is, that the " j field is described by a well-defined function of time [e.g., Eq. (1.35)]. Under these. circumstances the molecule is in a pure state before and after laser excitation and S remains so throughout its evolution. However, if the molecule is initially in a mixed4> state (e.g., due to prior collisional relaxation), or if the incident radiation field is notlf fully coherent (e.g., due to random fluctuations of the laser phase or of the laser amplitude), or if collisions cause the loss of quantum phase after excitation, then J phase information is degraded, interference phenomena are muted, and laser controi. is jeopardized. < f... 

The hormone finds the receptor by random, rapid collisions. The location of the receptor in the two-dimensional space of the plasma membrane facilitates collisional encounters. 

Alternatively, the initial preparation process (e.g., collisional excitation, photoexcitation, or chemical activation) may not provide a random initial distribution. Then if the initial decay rate is rapid, i.e., faster than the rate of energy randomization, then its value may depend on the details of the initial... 

This particulate stress represents the kinetic components of granular momentum transfer, and includes both the viscous contribution due to the small-scale random motion of individual particles as well as the macroscopic turbulence contributions due to collective random motions such as eddies and bubbles (Sun, Chen, and Chao, 1990). The complete granular stress should consist of this particulate stress component and a collisional stress component. 

Represented in this way, the interaction between bipyridylium ions and carboxylate ions is strictly analogous to that between pyridinium ions and iodide ion, and photoactivity may result from absorption of a quantum of radiation by the ground state of the charge-transfer pair (intimate or contact-ion pair) or, following absorption, by a contact-pair formed on random collisional encounter. 

The purpose of this chapter is to review the kinetics and mechanisms of photochemical reactions in amorphous polymer solids. The classical view for describing the kinetics of reactions of small molecules in the gas phase or in solution, which involves thermally activated collisions between molecules of approximately equivalent size, can no longer be applied when one or more of the molecules involved is a polymer, which may be thousands of times more massive. Furthermore, the completely random motion of the spherical molecules illustrated in Fig. la, which is characteristic of chemically reactive species in both gas and liquid phase, must be replaced by more coordinated motion when a macromolecule is dissolved or swollen in solvent (Fig. b). Furthermore, a much greater reduction in independent motions must occur when one considers a solid polymer matrix illustrated in Fig. Ic. According to the classical theory of thermal reactions the collisional energy available in the encounter must be suificient to transfer at least one of the reacting species to some excited-state complex from which the reaction products are derived. The random thermal motion thus acts as an energy source to drive chemical reactions. 

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