Mechanics

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

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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, masking the parts of statistical mechanics, deformation and ultrasonic spectroscopy.

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

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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). This quantity can then be expanded in a Taylor series, according to the procedure used by Irving and Kirkwood [6]. This method also yields Eqs.

5) To get the (statistically averaged) equations of motion for the beads, we multiply Eq. 5) by p~i and integrate over all the momenta of molecule ~. This gives, when use is made of Eqs. 1): mat~ d EEi'~]Y Tat = - mvX. 1) Next we replace the double bracket in the first term on the right side by [[(i-~,- u ~ ) ( ~ - u~)J]at, and add appropriate compensating terms; here and elsewhere we use the notation u~i(r~, t) = [[f~J]at for the average velocity of bead v. Then Eq. 1) becomes: rn, ~ uvW~ + m~E u at o a~u~u~W~ ct =--m:X.

5) by p~i and integrate over all the momenta of molecule ~. This gives, when use is made of Eqs. 1): mat~ d EEi'~]Y Tat = - mvX. 1) Next we replace the double bracket in the first term on the right side by [[(i-~,- u ~ ) ( ~ - u~)J]at, and add appropriate compensating terms; here and elsewhere we use the notation u~i(r~, t) = [[f~J]at for the average velocity of bead v. Then Eq. 1) becomes: rn, ~ uvW~ + m~E u at o a~u~u~W~ ct =--m:X. (~r~. 2) Statistical Mechanicsof Transport Phenomena 47 The terms on the left side can be differentiated by parts, and Eq.

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