Covariant wave functions with invariant helicity for massless particles

Considering a wave function for a massless particle, transforming according to an arbitrary irreducible representation (IR) of the homogeneous Lorentz group, we determine the basic conditions for to be an eigenfunction with a specified value of the helicity inall Lorentz frames. The method used is direct and elementary, requiring no knowledge of the IR's of the Poincaré group. It is shown that there existsno invariant helicity state in unitary representations of the Lorentz group, and one such state in any non-unitary representation (with one extra in special cases).     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.     

Itsy Bitsy Topological Field Theory

We construct an elementary, combinatorial kind of topological quantum field theory (TQFT), based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of a TQFT defined by Honda–Kazez–Mati?. This topological field theory stores information in binary format on a surface and has “digital” creation and annihilation operators, giving a toy-model embodiment of “it from bit”.     

Crystal structure of an optically active non-symmetric liquid crystal dimer: cholesteryl 5-[4-(4-n-heptylphenylethynyl)phenoxy]pentanoate

The crystal structure of cholesteryl 5-[4-(4-n-heptylphenylethynyl)phenoxy]- pentanoate (C₅₃H₇₆O₃) was determined by direct methods using single crystal X-ray diffraction data. It crystallises in the triclinic system with space group P1 and Z?=?2. The unit cell parameters are: a?=?10.6791(5), b?=?13.0903(7), c?=?18.6430(9)Å, α?=?94.413(3), β?=?98.222(3), γ?=?112.987(3)°. The final reliability factor was R?=?0.0510 for 7284 observed reflections and the goodness of fit was equal to 1.062. The asymmetric unit cell of the compound was found to contain two symmetry-independent molecules, A and B. In both molecules, the six-membered rings of the cholesterol moiety are conformationally very similar. However, pronounced differences were observed in the conformation of the five-membered ring, which is a half-chair in molecule A and assumes an envelope conformation in molecule B. In both molecules, the phenyl rings are planar. The dihedral angle between the two phenyl rings is 43.4(2) and 42.7(2)° for molecules A and B, respectively. The packing of molecules in the crystalline state was found to be a precursor to the smectic A phase structure. The crystal structure is stabilised by inter-molecular C–H…O and C?H…π interactions.     

Unsymmetrical dimers possessing a cholesteryl ester moiety and a difluoro-substituted biphenyl core: synthesis and mesomorphic behaviour

Some new unsymmetrical dimers consisting of a cholesteryl ester moiety, covalently linked to either a 4′-(1,3-difluoro-4-n-octyloxy) biphenyloxy or a 4′-(2,3-difluoro-4-n-decyloxy) biphenyloxy through odd-even parity paraffinic central spacers, have been synthesized and investigated for their mesomorphic behaviour. Except for one, all the dimers exhibit enantiotropic smectic A, twist grain boundary (TGB) and chiral nematic mesophases. Five of the eight unsymmetrical dimers synthesized show a chiral smectic C (SmC*) phase. Interestingly in some of the compounds the SmC* exists over a wide temperature range including room temperature. Among the eight compounds, a dimer having a C₇ central paraffinic spacer and a C₈ alkoxy terminal chain shows an enantiotropic twist grain boundary with SmC* blocks (TGB_C*) phase. It appears that the variation in the length of the spacer has a remarkable influence on the phase transition temperatures as well as on the mesomorphic behaviour.     

Crystal structure of a liquid crystal non‐symmetric dimer: cholesteryl 4‐[4‐(4‐n‐butylphenylethynyl)phenoxy]butanoate

The crystal structure of cholesteryl 4‐[4‐(4‐n‐butylphenylethynyl)phenoxy]butanoate [phase sequence: Cr 155°C (46.1?J?g^?1) SmA 186.8°C (1.5?J?g^?1) TGB‐N* 204.7 (6?J?g^?1) I] has been solved from single crystal X‐ray diffraction data. The compound crystallizes in the monoclinic space group P2₁ with unit cell parameters: a?=?13.129(2), b?=?9.3904(10), c?=?17.4121(8)?Å, β?=?92.790(7)°, Z?=?2. The structure has been solved by direct methods and refined to R?=?0.0606 for 3?250 observed reflections. The bond distances and angles are in good agreement with the corresponding values for compounds containing phenyl and cholesterol moieties. The phenyl rings A and B are planar. The dihedral angle between the least‐squares planes of the two phenyl rings is 28°. The cholesterol moiety has the usual structure: the C and E rings have chair conformations, and the D and F rings adopt half‐chair conformations. The molecules in the unit cell are arranged in an antiparallel manner. The crystal structure is stabilized by an intermolecular C–H…O contact of 2.989(10)?Å.