Spiral independent spirals

The spiral die, commonly used to extrude tubular blown films, eliminates weld line effects and produces a thermally and geometrically homogeneous extrudate. The polymer melt in a spiral die flows through several feed ports into independent spiral channels wrapped around the circumference of the mandrel. This type of die is schematically depicted in Fig. 3.18. 

Many complex structures can be formed with various Mo and V oxoanions and organic cations. The crystalline compound [Me2NH2]K4VioOio(H20)2(OH)2(P04)7-4H20 contains a remarkable inorganic double helix consisting of two intertwined but independent spirals of linked O and V atoms [106]. 

When the mutual separation of screw dislocations is larger than 9pJ2 (with pc the radius of critical 2D nuclei), independent spirals appear at first and after some turns, and the spirals demonstrate a parallel nonintersecting step system. 

Densmore, A. Xu, D. X. Janz, S. Waldron, P. Mischki, T. Lopinski, G. Delage, A. Lapointe, J. Cheben, P. Lamontagne, B. Schmid, J. H, Spiral path high sensitivity silicon photonic wire molecular sensor with temperature independent response, Opt. Lett. 2008, 6, 596 598... 

Briefly, astronomers have two basic methods for estimating distance scales for spiral galaxies that are independent of the observation of special standard candles such as supernovae. 

This represents a set of p spirals, one on each sublattice v, having respective phases 0 . It is the only configuration derivable from equation 145 that has, to within rotations of the plane of the spins, Sly independent of n. With this equation, the strong constraints of equation 134 become p equations in the p unknowns 0. . . 0P ... 

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