Rayleigh scattering induced by static bends of layers in a smectic A liquid crystal

We observe the anisotropy and the polarization properties of the Rayleigh scattered light for a planar smectic A texture of butoxyl benziledene-p-n anilino-acetophenone (BBAA). This scattering is attributed to static bends of the smectic layers, with wave vectors parallel to the smectic planes. This effect gives a simple method to measure the ratio of the extraordinary to the ordinary indices: n_e/n₀ = 1.18 at 89°C.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Convective mass transfer in helical pipes: effect of curvature and torsion

A 3D numerical analysis of the flow and mass transfer in helical pipes is presented. The interpretation of the flow patterns and their impact on mass transfer is shown to require a non-orthogonal pseudo-stream function based visualization. The strong coupling between torsion and curvature effects, and the resulting secondary flow regimes are well characterized by a parameter combining both the Dean (Dn) and Germano numbers (Gn). For membrane separation applications, helical modules combining high curvature with low torsion would alleviate concentration polarization and yield appreciable flux improvement.     

Light scattering studies of crossover to a liquid crystal tricritical point

We have used light scattering to study nematic elastic constantsK ₂ andK ₃ in the alkyl-cyanobiphenyl (n CB) system. As the average alkyl chain lengthn increases, the temperature range of the nematic phase decreases and the system approaches a tricritical point. Our data are analyzed to determine the parallel and perpendicular correlation lengths and critical exponents for smectic short-range order. We find a continuous decrease in the critical exponentsv andv as the tricritical point, which occurs at 9.1 CB, is approached. There is also a significant decrease in the magnitude of the parallel correlation length at a fixed reduced temperature.