Boundary edge

It was demonstrated by Sundman (1985) and later by Ansara et al. (1988) that an order-disorder transformation could be modelled by setting specific restrictions on the parameters of a two>sublattice phase. One of the first phases to be considered was an A B-ordered compoimd. In such circumstances the sublattice formula A, B)j(A, B) can be applied and the possible relationships between site fiactions and mole fiactions are given in Figure 5.6. The dashed lines denoted xb = 0.25, 0.5 and 0.75 show variations in order of the phase while the composition is maintained constant. When these lines cross the diagonal joining AjA and B3B the phase has disordered completely as Vb Vb As the lines go toward the boundary edge the phase orders and, at the side and comers of the composition square, there is complete ordering of A and B on the sublattices. 

If M is a finite non-closed map, then we can add some faces along the boundary edges and obtain a closed map. So, finite non-closed maps are obtained by removing some feces of closed ones. 

Theorem 6.2.3 For any r, there exists isohedral (r, 4)-polycycle with exactly one boundary edge on each r-gon. 

Any internal edge of a polycycle P belongs to exactly two r-gons, while any boundary edge belongs to only one r-gon. Therefore, the following equality holds ... 

HLZ96] P. Hansen, C. Lebatteux, and M. Zheng, The boundary-edges code for polyhexes, Journal of Molecular Structure (Theochem) 363 (1996) 237—247. 

The formation of a new glide layer due to the motion of the internal boundary edge under stress may occur for o < o in a thermally activated way. In [6.29] the expression has been derived for the boundary-edge velocity, vs ... 

Continuity is selected between surfaces across their common boundaries. This default continuity between the network based surfaces and with the surfaces from which the curves on surfaces, isoparametric curves, and boundary curves are extracted as curve network elements is enforced by the surface creation procedure. Moreover, local continuity can be defined across individual curves. Continuity at a boundary curve is dependent on other curvature definitions along the surfaces connected by it. In Figure 7-46, continuity G1 is specified for boundary edge eh,. This continuity can be achieved only if the continuity across pairs of curves from the two surfaces (ehy-eh ) incident along this curve is at least G2. At the same time, this condition would be good for continuity G2 across eh,. 

The overall shape and character of the surface complex defined by network curves is tailored and modified by sculpt curves because some shapes are difficult to control by curves in a curve network. In Figure 7-47, two surfaces (Sj and S2) are created by using a curve network. Boundary edge ebi, bounds a single surface, while interior edge eh,- bounds two surfaces. The ffect of sculpt curve is usually defined by its level as large, medium, etc., instead of a numerical value. 

The shapes of the surfaces within a network are modified by the shape of the actually mapped sculpt curve. At the same time, surfaces must interpolate the curve network. This interpolation can be restricted to the extent of modification by the sculpt curve. The sculpt curve can take control when the network surface is made free from one or more of its construction curves. For example, when the sculpt curve extends across an interior boundary edge. 

Boundary edges of left reservoir (L) Bulk concentratirai Bulk concentration 0... 

Boundary edges of right restavoir (R) Bulk concentration Bulk concentration 1... 

Figure 8. Oscillogram of the current decay at the moment of collision of a thick step on the face boundary edge. Time axis 20 msec div, current axis 10" A div. ...

Within the flow channel, a parabolic flow profile is created because of the laminar flow of the liquid. As a result, the stream moves slower closer to the boundary edges than it does at the center of the channel flow. When a perpendicular force field, in this case, fluid cross-flow, is applied to the flowing, laminar stream, the analytes are driven toward the boundary layer of the channel. 

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