Stagnation flow on a cylinder with partial slip--an exact solution of the Navier-Stokes equations

The stagnation slip flow on an axially moving cylinder is studied.The Navier–Stokes and energy equations reduce to nonlinearordinary differential equations under a similarity transform.For large slip, the flow field decays exponentially into potentialflow. The heat transfer can be expressed as an incomplete gammafunction. In general, the heat transfer increases with slip,Prandtl number and Reynolds number.     

Numerical study on performance of disk MHD generator using frozen inert gas plasma

In an magnetohydrodynamic (MHD) generator using a frozen inert gas plasma (FIP), the availability of a frozen argon plasma, the influence of plasma uniformity at the generator inlet on the performance, and the feasibility of a large-scale generator are numerically examined by /spl gamma/-/spl theta/ two-dimensional simulation. The FIP is produced by pre-ionizing inert gas without an alkali metal seed at the generator inlet, then the ionization degree of the plasma is kept almost constant in the whole of the channel because of considerable slow recombination of the inert gas just like frozen reaction plasma. It is found that not only helium, but also argon frozen plasma MHD generation is realized, although highly accurate control of inlet ionization degree is necessary for argon. It is important to reduce the nonuniformity of plasma properties at the generator inlet in order to raise the maximum enthalpy extraction ratio. Even for the large-scale generator with 1000-MW thermal input, the ionization degree is kept almost constant in the whole of the channel and the high performance is obtainable. This result is extremely attractive for the FIP MHD generator.     

Nonlinear magneto-optical diffraction by two-dimensional magnetic superstructures

Nonlinear (at the second-harmonic frequency of the incident light) optical reflection by two-dimensional magnetic superstructures is theoretically studied. A square lattice of magnetic dots and a hexagonal lattice of magnetic bubbles (cylindrical magnetic domains) are considered. Because the periods of these structures are comparable with the wavelengths of the fundamental and the second-harmonic radiation, it would be possible to observe diffraction at the second-harmonic frequency. A polarization analysis of nonlinearly diffracted radiation is performed and the numbers of observable diffraction orders for the above structures are estimated. Received: 10 January 2002 / Published online: 11 June 2002     

Fluorides of ruthenium and chromium: Theoretical studies

The electronic and structural characteristics of CrF₅, CrF₄, RuF₅ and RuF₄ were studied. Ab initio (SCF-CI) calculations were performed with different structures and spin states for each complex. The favored conformation always corresponds to the highest multiplicity: doublet for CrF₅ in D_3h, triplet for CrF₄ in T_d, quadruplet for RuF₅ in C_4v and quintuplet for RuF₄ in D_4h symmetry.     

Transport of gases in aromatic polyesters: Correlation with WAXD studies

Polymer packing density can be conveniently measured by either density-based measurements (direct or estimated free volume) or wide-angle X-ray diffraction (WAXD) spectra. Previously reported diffusivity and permeability values for various polyarylates and polyimides are examined on the basis of the packing density measured by these different techniques. It is shown that in these rigid glassy polymers, the mean intersegmental distance, the d-spacing, obtained from WAXD provides a better measure of the effect of polymer packing on diffusivity than either direct density measurements or estimated free volumes. It has been possible to correlate previously reported diffusivity and sorption data for various polyarylates and polycarbonate on the basis of the WAXD investigation, using the d-spacing and the amorphous peak width, respectively. The effect of polyarylate structure on d-spacing has been studied. A series of polyarylates have been synthesized with different substituents on the bridge carbon. In this series the d-spacing remains constant while the carbonyl group density and the glass transition temperatures are varied. However, small substituents on the aromatic ring cause significant changes in the d-spacing. These results can be used to tailor polyarylates with desired intersegmental distances and chain flexibility.     

Study of the reciprocal space image of the biaxial nematic phase in the plane of the amphiphilic bilayer

High resolution synchrotron X-ray measurements have been performed on the uniaxial and biaxial phases of the lyotropic mixture potassuim laurate, decanol and water. An elegant magnetic orientational procedure allows us to obtain the cut of the reciprocal space image of the biaxial phase at the plane perpendicular to the amphiphilic bilayer. The analysis of densitometric profiles of the diffracted bands indicate an anisotropic micellar correlation in the plane of the amphiphilic bilayer. It is suggested that an anisotropic distribution of decanol and potassium laurate in this plane could be responsible for this effect.     

Mesomorphic properties of orthopalladated complexes of laterally substituted azobenzene derivatives, 2-alkoxycarbonyl-4-(4-ethoxyphenylazo)phenyl 4-methoxybenzoates

Homologous series of 2-alkoxycarbonyl-4-(4-ethoxyphenylazo)phenyl 4-methoxybenzoates (L) and their orthopalladated μ-chloro dimers (Pd₂Cl₂L₂) have been synthesized and their thermotropic phase transition behaviour has been characterized. The ligands, L, are three-ring nematogens with their central rings substituted in the 2-position by n-alkyl chains of varied length. The thermal stability of the nematic phases decreases rapidly with increasing side chain length and then levels off as the series is ascended. In every case the mesomorphic phase appears only over a small temperature range (less than 20° C). The orthopalladated species also proved to be nematogenic. Melting and clearing points rise on the average by 87° C and 126° C, respectively, and thus the temperature ranges of the nematic phases are enlarged considerably upon metallation. In relation to the observed stabilization of the nematic phases, particularly of higher homologues, a lath-like molecular structure, in which the side chains of the ligands fill up the clefts of the core part, has been deduced for a Pd2Cl2L2 homologue from its solution ¹H-NMR spectrum.     

Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.