Helicoids form

Fig. 13.4.14. The stable manifold of the saddle-focus continued along the homoclinic loop in backward time has a helicoid form.

The screw conveyor is one of the oldest and most versatile conveyor types. It consists of a helicoid flight (helix rolled from flat steel bar) or a sectional flight (individual sections blanked and formed into a helix from flat plate), mounted on a pipe or shaft and turning in a trough. Power to convey must be transmitted through the pipe or shaft and is limited by the allowable size of this member. Screw-conveyor capacities are generally limited to around 4.72 mVmin (10,000 ftvh). 

Organoclay materials with higher-order organization can also be prepared by template-directed methods involving self-assembled supramolecular structures. In this approach, preformed organic architectures in the form of tubes, fibers, hollow shells, gyroids, helicoids, and so on are transferred into hybrid materials exhibiting structural hierarchy, complex form and ordered mesoporosity [47-55]. For example,... 

The first periodic (in one direction only) minimal surface [12] discovered in 1776 was a helicoid The surface was swept out by the horizontal line rotating at the constant rate as it moves at a constant speed up a vertical axis. The next example (periodic in two directions) was discovered in 1830 by Herman Scherk. The first triply periodic minimal surface was discovered by Herman Schwarz in 1865. The P and D Schwarz surfaces are shown in Figs. 2 and 3. The revival of interest in periodic surfaces was due to (a) the observation[13-16] that at suitable thermodynamic conditions, bilayers of lipids in water solutions form triply periodic surfaces and (b) the discovery of new triply periodic minimal... 

Bheda et al. ( ) showed that cellulose triacetate forms a mesophase in dichloroacetic acid. Navard and Haudin (18) examined the thermal behavior of liquid crystalline solutions of CTA in TFA. Navard et al. (23) studied the isotropic to anisotropic transitions of solutions of cellulose triacetate in TFA using differential scanning calorimetry. Navard and Haudin (S2) studied the mesophases of cellulose and cellulose triacetate calorimetrically. Navard et al. (83) report similar studies. Meeten and Navard (97) showed the twist of the cholesteric helicoidal structure of CTA and secondary cellulose in TFA is left-handed. 

Mesophase with a helicoidal superstructure of the director, formed by chiral, calamitic or discotic molecules or by doping a uniaxial nematic host with chiral guest molecules in which the local director n precesses around a single axis. 

Very few structural studies have been concentrated on models of ApG adducts of cisplatin. Conformational analysis of two rotameric forms of the complex m-[Pt(NH3)2(9-MeA-A(7))(9-EtGH-A(7))]2+ has recently been described [40], One of the forms, crystallized as a PI 6 salt, can be characterized as a right-handed helicoidal model for the intrastrand ApG crosslink in double-stranded DNA. The bases in this compound assume a head-to-head orientation (Fig. 6) with the interbase dihedral angles of 81.8° and 87.5°. There are two independent complex cations in the unit cell. The left-... 

Cholesteric mesophases form only from molecules having chiral centers. Since the helicoidal structures of cholesterics are supramolecular, the chiral centers in... 

It is possible to conceive of situations where the chemical linking of molecular components around a template is not as crucial as the formation of defined, non-covalent interactions during templating. This may be exemplified by the polymerisation of a nematic liquid crystalline crosslinker in the presence of a template, a non-polymerisable cholesteric mesogen [23]. The chiral dopant forces the crosslinker to form a cholesteric phase. After polymerisation of the crosslinker, the polymer still exhibits a helicoidal structure which is stable over a wider temperature range than the initial cholesteric phase. It is not reported in this work whether extraction of the chiral mesogen has been attempted or not. 

Following the discovery of the helicoid by Meusnier, sixty years elapsed before additional examples of minimal surfaces were given in explicit form. In 1835 Scherk published five more examples of minimal surfaces [11]. Of these, two are periodic. They are often referred to simply as Scherk s first and second surfaces (Fig. 1.15). ... 

The second type of a-helix/p-sheet domain consists of an open p-sheet which is twisted. The structure of the P-sheet resembles the helicoid, as shown in Fig. 6.4. Here again then the curvature of this surface also corresponds to that of a minimal - or closely related hyperbolic - surface. As the P-sheet is open it can consist of different numbers of P-chains four to ten have been observed(l]. The active site is also in this case at the carboxyl end region, and it is located in a crevice formed when loops from the P-chain to the a-helix have opposite directions (between a set of a-helices on one side of the P-sheet and a set on the other side). 

An interesting recent study of a phospholipid-nucleoside conjugate [30] shows the possibility of spontaneous formation in water of super-helical strands. These structures are of interest with regard to the origin of life, as they can function as templates for polymerisation of nucleic acids. We observe that the helicoid is a zero cur ature surface with the different relevant and seemingly necessary properties also possessed by cubosomes catalytic effects, etc. These helical assemblies are therefore alternatives to cubosomes as candidates of prebiotic assemblies, crucial to the first level of evolution. In any case, two-dimensional hyperbolic forms certainly offer many features essential to the most primitive forms of life. 

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