Dilation factor distribution

The treatments of Kochendorfer, Porod, and Warren-Averbach identify superposition with the mathematical operation of a convolution. While this is true for translational superposition, for dilational superposition it is a coarse approximation that is only valid for small polydispersity. In the latter case the convolution must be replaced by the Mellin convolution (Eq. (8.85), p. 168) governed by a dilation factor distribution and the structure of the reference crystal, the structure of each observed crystal is generated by affine dilation of the reference crystal (Stribeck [2]). 

In Eq. (10) that gives the toughness in dilatational plasticity the factors C and A are dependent on craze microstructure and will not vary significantly. The stress and temperature dependence of the craze velocity while quite determinate in the interface convolution process of craze matter production will also be quite sensitive to micro-structural detail of phase distribution in block copolymers. The appUed stress = Y ... 

As discussed in this section, the tube-dilation effect, i.e. M J/Me > 1, mainly occurs in the terminal-relaxation region of component two in a binary blend. This effect means that the basic mean-field assumption of the Doi-Edwards theory (Eq. (8.3)) has a dynamic aspect when the molecular-weight distribution of the polymer sample is not narrow. This additional dynamic effect causes the viscoelastic spectrum of a broadly polydisperse sample to be much more complicated to analyze in terms of the tube model, and is the main factor which prevents Eq. (9.19) from being applied... 

Both the above factors promote unequal distribution of dlfiusible ions on either side of biological membranes which in turn would result in establishment of a pH difference and an oanotlc difference between the compartments. Minor pH changes are tolerable for most of the tissues but drastic pH changes may pose problems. Ihe body saves Itself finm the harmful influence of the latter with the help of its buffer tems. But sometimes maintenance of a drastic pH difference is a necessity, as is in the case of stomach. Gastric dilation cannot proceed if the pH is not maintained at a very low level. In this case, the gastric mucosal membrane i up to permit the hydrolysis reaction... 

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