Naphthyl azomesogens with lateral chloro groups

A homologous series of azomesogens, 2″-[4-(4′-n-alkoxybenzoyloxy)-2-chlorophenylazo] naphthalenes, with lateral chloro groups was synthesised. All the homologues synthesized exhibit enantiotropic nematic mesophase. The mesomorphic properties of the present series are compared with other structurally related series to evaluate the effect of lateral chloro group and its position on mesomorphism This paper was presented at the 10th National Conference on Liquid Crystals held at Bangalore, India during 9–11 October 2003.     

A proof of Howard’s conjecture in homogeneous parallel shear flows

A rigorous mathematical proof of Howard's conjecture which states that the growth rate of an arbitrary unstable wave must approach zero, as the wave length decreases to zero, in the linear instability of nonviscous homogeneous parallel shear flows, is presented here for the first time under the restriction of the boundedness of the second derivative of the basic velocity field with respect to the vertical coordinate in the concerned flow domain.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Floc breakage in agitated suspensions: Theory and data processing strategy

Flow visualization of chemical flocs in a simple extensional flow field reveals two distinct mechanisms for their breakage: splitting into a relatively small number of daughter fragments whose sizes are comparable to the parent flocs, along with continual disintegration by erosion to produce extremely fine particles from the extremities of the parent floc along the axis of extension. In turbulent flow, these two mechanisms still occur, although the kinematics of flow are more complex. This work presents a formulation of the population balance equation that governs the floc size distribution in turbulent flow, incorporating both the splitting and erosion mechanisms discussed above. Experiments were conducted in which floc size distributions of dilute suspensions are measured by a combination of techniques, including computerized optical scanning of photographs and pulse height analysis of signals from a light blockage transducer. The experimentally determined size distributions are then fit to those computed from the population balance equation, using constrained nonlinear least squares. This yields best values of certain coefficients that appear in the governing equation, providing a strategy to obtain a data base to promote deeper theoretical analysis. The method is demonstrated by analyzing data for kaolin-Fe(OH)₃ flocs in aqueous suspensions.     

Mixed-ligand and binuclear complexes of oxovanadium(IV)

Summary Mixed ligand complexes of the type [VOLA]ClO₄ where L=5-bromosalicylaldehyde (L) or 5-nitrosalicylaldehyde (L) and A=2, 2-dipyridyl (A) or 1, 10-phenanthroline (A) have been prepared. Treatment of the mononuclear complexes, [VOLA]ClO₄, withp-phenylenediamine (ppd) orm-phenylenediamine (mpd) yielded homobinuclear [VOLA-NC₆H₄N-LAVO](ClO₄)₂, complexes, which were characterised by elemental analyses, spectra, magnetic susceptibility and molar conductance measurements.     

Radiationless transitions in trivalent lanthanide ions embedded in solids

Radiationless transitions in lanthanide ions embedded in glassy and crystalline hosts have been briefly reviewed. The correlations of multiphonon relaxation rates with energy gaps, vibrational frequencies, temperatures and electronic symmetries have been discussed. The essence of various theories, such as Nth order methods, non-adiabatic Hamiltonian method, dynamic coupling model has also been presented.