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 components of statistical mechanics, deformation and ultrasonic spectroscopy.
Read or Download Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science) PDF
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Extra resources for Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science)
Note also that the external forces give rise to the terms (v. G) and J in the energy equation. The various contributions to the heat-flux vector are summarized in Tables 1 and 2, along with the analogous contributions to the stress tensor. 9 The Hydrodynamic Angular Momentum Equation [lla] The law of conservation of angular momentum as applied to a system in which there is no intrinsic angular momentum is: 0 Ot [r xpv] = - [ V . v [ r x p v ] ] - [ V . 1) in which T is the external torque per unit volume applied to the fluid, and G is the external force per unit volume (see Eq.
Similarly the quantity C~~ can now be regarded as depending on the r~ (for all/a), and hence the index i on C~~can also be omitted. We next interchange the order of integration in Eq. 5) and perform the integration over all of the x-variables. When use is made of the definition in Eq. 6) When the integrations over all momenta are performed and the definition in Eq. 7) In going from Eq. 3) to this result, essentially all that has been done is to integrate over all the variables except for the coordinates of a single molecule; the integration over the momenta is indicated formally by the double-bracket notation.
F. B. Bird The term q~¢), when dotted into n and multiplied by dS, describes the rate at which work is done on the fluid on the positive side of dS by the fluid on the negative side. The dot product nf 1~(~), with the diffusive velocity [ [/'~ - v] ]" is the rate of doing work associated with the springs in one polymer molecule. The dot product of n with R~,~ indicates that springs that make a small angle with the plane of dS contribute less in the averaging process than springs that make a large angle.