Molecular Interpretation of the Dissipative Terms

The physical interpretation of the terms in the equation is not necessary obvious. The first term on the LHS denotes the rate of accumulation of the kinematic turbulent momentum flux within the control volume. The second term on the LHS denotes the advection of the kinematic turbulent momentum flux by the mean velocity. In other words, the left hand side of the equation constitutes the substantial time derivative of the Reynolds stress tensor v v. The first and second terms on the RHS denote the production of the kinematic turbulent momentum flux by the mean velocity shears. The third term on the RHS denotes the transport of the kinematic momentum flux by turbulent motions (turbulent diffusion). This latter term is unknown and constitutes the well known moment closure problem in turbulence modeling. The fourth and fifth terms on the RHS denote the turbulent transport by the velocity-pressure-gradient correlation terms (pressure diffusion). The sixth term on the RHS denotes the redistribution by the return to isotropy term. In the engineering literature this term is called the pressure-strain correlation, but is nevertheless characterized by its redistributive nature (e.g., [132]). The seventh term on the RHS denotes the molecular diffusion of the turbulent momentum flux. The eighth term on the RHS denotes the viscous dissipation term. This term is often abbreviated by the symbol... 

So far the equilibria between phases have been considered in the light of thermodynamic principles. These, of course, are only a formal embodiment of the statistical laws governing the behaviour of large numbers of particles, and the major results which they predict should be interpretable directly in terms of the molecular-kinetic picture. Though sometimes more difficult to carry through in detail, the molecular interpretations are of considerable interest in themselves. All are variations on the familiar theme that the random motions of the molecules tend by themselves to dissipate matter into the state of rarefied gas, while attractive forces tend to collect it into... 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

Thermal Aging. The use of dissipation factor and dielectric constant to monitor the effects of long-time thermal aging of plastics can involve rather complex changes which occur in dielectric relaxation. The size, shape, and position of the absorption peaks may he useful in interpreting thermal aging of plastics in terms of molecular processes. As for d-c resistance, the a-c properties usually... 

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