Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, by R.B. Bird, S.V. Bronnikov, C.F. Curtiss, S.Y. Frenkel, N.

By R.B. Bird, S.V. Bronnikov, C.F. Curtiss, S.Y. Frenkel, N. Hiramatsu, K. Matsushige, H. Okabe, V.I. Vettegren

This article examines advances in polymer technological know-how, overlaying the parts of statistical mechanics, deformation and ultrasonic spectroscopy.

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Additional info for Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science)

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The same thing can be done for the terms involving (F(e)'iBi) and (F~)~Bi) in the last term. '~_,. = (EaEsE~F~(d)~,ajB~) requires special treatment. First, integrals over the delta functions 6(r aJ - r a) and 6(p pj - pa) are inserted inside the angular brackets (cf. Sect. 5) and then use is made of Eq. 6): F~. • 6(r - r:)J(p "~ - p:) ~Ju F,. 4) When this is inserted into the previous equation, we finally get the equation for the time evolution of the distribution function in the one-molecule phase space: Integration over all momenta p~, and use of the definitions in Eq.

F. B. Bird v(r, t)E~m~ F iVy(r, Q~, t)dQ ~ + 0 - ½v(r, t)VV: Evm~ fR~R:W~(r, O ~, t ) d Q ~ + ... 11) In each series, the first term is the dominant contribution, and it is this zeroth-order contribution that is featured in Table 1 and used in Sect. t. The first-order contribution (containing V) is used in Sect. 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 (DPL, Equation of Motion and the Stress Tensor Sect.

Eq. 3-1 of Ref. [i1]). 3 The I n t r a m o l e c u l a r Contribution to the H e a t - F l u x Vector Next we turn to the source term Q(®) given in Eq. 8), which accounts for all intra- and intermolecular forces; with the help of Eq. 3) this can be written as follows: 6 pJu from 1st ( . - ) term in Eq. 8) - ½ (~ Z • 17(*)~"'k)f(r:'- r ) ) ykq from 2nd ( . . ) term in Eq. 8) 6The last line of Eq. 16 can also be written in such a way that the difference of two delta functions appears: 6(~ ~- r) - 6(r~j - r).

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