Harmonic simple, relaxation time

Z is proportional to the gas pressure, and, since Z1>0, the collision number for energy transfer, is constant for a particular transition, the actual value of fi is inversely proportional to the pressure. For convenience relaxation times are usually referred to a pressure of 1 atm. Equation (1) is an approximation, and requires modification to take into account the reversibility between quantum states 0 and 1. For example, the correct equation for vibrational relaxation of a simple harmonic oscillator of fundamental frequency, v, is... 

The dynamics of a coil in a low-molecular weight melt can be described well by an ingeniously simple model, the Rouse model [18]. This model represents a polymer chain as a set of beads cormected by harmonic springs (compare Fig. 2b). The beads move as (tethered) Brownian particles subject to random forces and to frictional forces proportional to their velocity exerted from their environment (see Section I.F). For a linear polymer chain the Rouse model predicts that the longest relaxation time (time needed for... 

Let us now imagine that the function p(0,axial symmetry with respect to the z-axis, as, e.g., in Fig. 4.1(6), and that it is created by pulsed excitation at t = 0. In this case its expansion over multipoles includes transversal polarization moments pq (these are complex quantities) where Q 0. If the precession frequency uj< is much larger than the relaxation rate, then the components pQ will depend on time, in the time scale wj,1, following (4.9), according to the simple harmonic law ... 

No general rules can be given for the frequency dependence of G and G". because these depend on the nature of the system, which may relax according to several processes, each with its own time scale. However, for the case of only one relaxation process and a harmonic oscillation the mathematics becomes rather simple. The phase angle (p can be introduced as before (Lapp. 8 and sec. II.4.8a). This angle measures the extent to which the strain lags behind the applied strain or the stress is ahead of the strain. An illustration will be given in fig. 3.41. In this case G can be written as... 

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