Non-linear study of electrohydrodynamic Rayleigh-Taylor instability in a composite fluid-porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams-Bashforth predictor and Adams-Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.     

Real and complex supersolvable line arrangements in the projective plane

Journal of Algebraic Combinatorics - If we regard a set of s lines in $${\mathbb P}^2$$ over either the reals or the complex numbers as an algebraic plane curve, then it is an open problem to...     

Proton spin relaxation in 2-chloroacrylontirile by double resonance

Nuclear magnetic double resonance experiments were performed on the strongly coupled two-proton system (AB) in 2-chloroacrylontirile to study the spin relaxation processes. The single resonance parameters of the AB spectrum are (operating frequency 100 MHz): |vA - vB|=9.85±0.1 Hz and J _AB=2.8±0.1 Hz. Frequency-sweep double resonance spectra were obtained by irradiating each of the four transitions at different strengths of irradiation in the range 0.015 Hz to 2.35 Hz. These spectra were analysed by using the ‘Bloch approximation’ in the rotating frame for the ‘high’ irradiation strengths and the ‘simple line’ approximation for the ‘low’ irradiation strengths. The analysis showed that the proton relaxation in this molecule can be described by interaction with isotropic random fields of nearly equal strengths at the two nuclei with no appreciable correlation between them. Internal dipole-dipole interaction is not a significant mechanism (at room temperature). It is shown that for analysing ‘low’ irradiation spectra the choice of certain functions of intensity changes would lead to a marked distinction between the different relaxation mechanisms.     

Coupled tapering/uptapering of soliton pairs in nonlinear media

Phenomenon of coupled tapering/uptapring of two mutually incoherent beams coaxially co-propagating in a nonlinear medium with small gain or loss has been investigated in this paper using standard parabolic equation approach (PEA) and the results are compared with the results obtained by Beam Propagation Method (BPM), i.e., by direct simulations of the underlying Nonlinear Schrödinger Equation (NLSE). The PEA results are shown to be in excellent agreement with the BPM results. It is seen that both beams of the pair induce uptapering in each other in presence of losses and tapering in presence of gain. When the medium offers gain to the first beam and losses to the other, both beams taper. When the medium offers gain/absorption to only one of the two beams, the beam undergoes self-tapering/self-uptapering and induces a taperd/uptaperd waveguide. The other beam (for which the medium is lossless) uptapers/tapers due to the taperd/uptaperd waveguide created by the first beam.     

Solutions of Yang's EuclideanR-gauge equations and self-duality

Under some assumptions and transformations of variables, Yang's equations forR-gauge fields on Euclidean space lead to conformally invariant equations permitting one to obtain infinitely many other solutions from any solution of these conformally invariant equations. These conformally invariant equations closely resemble the mathematically interesting generalized Lund-Regge equations. Some exact solutions of these conformally in variant equations are obtained. Except for some singular situations, these solutions are self-dual.     

Structural reconfiguration and informal coordination in administrative organizations

This paper considers the problem of determining the optimal design of public organizations in terms of maximizing their reliability against institutional failures. To capture both the individual and the system-level aspects of organizational decisionmaking, first we present an analytical model that characterizes the optimal decision behavior of a single decision maker (unit, agent, in general: DM) in the context of a binary decision task. In this sense, reliability of a DM against the two possible error types: implementation of the wrong policy (error of comission, Type I error) and failure to act when it is necessary (error of omission, Type II error) are interpreted as the result of a particular decision strategy. Individual expertise is represented in the form of a Relative Operating Characteristic (ROC) curve that, in turn, depicts the necessary trade-off between the two errors when selecting an appropriate decision strategy. Component decisions are then combined along the lines of organizational structure which is described using a graph formalism. We show that the task of finding the best organizational design involves a joint optimization over structure and strategy, and implement the normative model in the context of a detailed example. Our numerical results suggest that when DMs coordinate their decision rules, there is little difference in the performance of various organizational structures.This work was supported by the Office of Naval Research under ONR contract #N0014-93-I-0793.     

Synthesis and structural characterisation of new Re(III) complexes using aldimines of α-amino acids as coligands

Complexes of the general formula [Re^III(L)Cl(PPh₃)₂] have been synthesised by reacting H₂L and [ReOCl₃(PPh₃)₂] in ethanol. Here H₂L represents imines of α-amino acids (glycine, l-alanine, l-valine, l-phenylalanine) derived from salicylaldehyde and naphthaldehyde. The crystal structure of one complex has been determined. The complexes are mononuclear, paramagnetic and display paramagnetic ¹H NMR in CDCl₃ solution. Their spectral and redox properties are scrutinised.     

The transition from bulk to nano as a phase transition

It is demonstrated that the chemical potential of bosons trapped in a harmonic potential shows a discontinuity as a function of the number of particles in the system. In the model used, it is shown that if the number of particles is of the order of 10⁶ or greater, bulk-like behaviour is exhibited by the system. This translates to a ratio of V/V_c>10⁶ for bulk behaviour, where V is the crystallite volume of the experimental sample and V_c is the volume of the unit cell. Several experimental results covering a wide range of physical phenomena that corroborate the fact that such a number-induced phase transition indeed exists are presented.     

InBr3-catalyzed sulfonation of indoles: a facile synthesis of 3-sulfonyl indoles

Indoles react smoothly with sulfonyl chlorides in the presence of a catalytic amount of indium tribromide at ambient temperature to afford the corresponding 3-arylsulfonyl indole derivatives in high yields with high regioselectivity.     

Synthesis and characterization of the novel l‐(substituted phenoxy/phenyl)‐2‐phospholene and phospholane 1‐oxide derivatives

The synthesis of the novel 1‐(substituted phenoxy/phenyl)‐2‐phospholene and phospholane 1‐oxide derivatives, which are analogs of sugars having a phosphorus atom in place of the ring oxygen of normal sugars, is described. All of the synthesized derivatives are structurally characterized by multi nuclear NMR, mass, and IR spectral data, elemental and X‐ray crystallographic analyses.