# Statistical mechanics, deformation, ultrasonic spectroscopy by R Byron Bird; et al

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By R Byron Bird; et al

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Example text

18) in which S is the unit tensor, and the temperature T is a function of r and i. We note also that [[(rî - uf)*(r? 19) In Sect. 14 we will need the double-bracket quantity that appears in Eq. 8): am - *)« - *)]]" = am - om -

This cannot, however, be done until something is inserted for the double-bracket 56 C F Curtiss and R B Bird quantities indicating momentum-space averages. Up to now there is not sufficient information about the phase-space distribution function fx to allow for the calculation of these double-bracket quantities [16,19]. We therefore freely make use of the friction coefficient empricism in Eqs. 7): When Eqs. 10) are combined, we get- uf(rf i ) - v ( r ? 1) Here, we have assumed that the temperature is a linear function of position (see Eq.

2, and the second-order contribution (containing VV) is used in Sect. 3. The complete expression in Eq. 10) is used in Appendix B 7 The Hydrodynamic Equation of Motion and the Stress Tensor (DPL, Sect. 2b) From continuum mechanics arguments [11,12] the equation of motion for a fluid mixture is known to be:4 -py= _ [ v * p w ] - [ V . The stress tensor is defined so that [n • it] dS is the force transmitted across the element of surface dS from the negative to the positive side of dS. We now have to find a vector function B such that is the momentum flux py at position r and time t.