The first reported syntheses and characterisation of alkali metal trifluoronickelate(II) monohydrates,MNiF3 · H2O (M = NH4, Na or K)

Summary Ni(acac)₂ · (H₂O)₂ (1 mol) and alkali metal fluorides (4 mols), MF (M=NH₄, Na or K), react with an excess of 40% HF on a steam-bath. The product upon treatment with water gives light green crystalline alkali metal trifluoronickelate(II) monohydrate, MNiF₃ · H₂O in a high yield. Chemical analyses, pyrolysis at 120 °C, i.r. spectroscopic, and cryomagnetic (300–80 K) data have been used to characterise, and establish the identity of the compounds. While NH₄NiF₃ · H₂O behaves as a normal octahedral nickel(II) compound, NaNiF₃ · H₂O is ferromagnetic with Curie point 145 K, KNiF₃ · H₂O behaves antiferromagnetically; its Neel point is 230 K.     

Synchronization of four coupled van der Pol oscillators

It is possible that self-excited vibrations in turbomachine blades synchronize due to elastic coupling through the shaft. The synchronization of four coupled van der Pol oscillators is presented here as a simplified model. For quasilinear oscillations, a stability condition is derived from an analysis based on linearizing the original equation around an unperturbed limit cycle and transforming it into Hill’s equation. For the nonlinear case, numerical simulations show the existence of two well-defined regions of phase relationships in parameter space in which a multiplicity of periodic attractors is embedded. The size of these regions strongly depends on the values of the oscillator and coupling constants. For the coupling constant below a critical value, there exists a region in which a diversity of phase-shift attractors is present, whereas for values above the critical value an in-phase attractor is predominant. It is observed that the presence of an anti-phase attractor in the subcritical region is associated with sudden changes in the period of the coupled oscillators. The convergence of the coupled system to a particular periodic attractor is explored using several initial conditions. The study is extended to non-identical oscillators, and it is found that there is synchronization even over a wide range of difference among the oscillator constants.     

An inflow-outflow characterization of inhomogeneous permeable beds

It is proposed that the inflow to and outflow from a permeable bed be related by an integral. For vanishing fluid velocities, it is linear and its kernel is a material property characterizing the bed. Some of the properties of the kernel are considered here. The approach is particularly useful for tilted, fractured and other inhomogeneous beds, since no continuum characteristics need be assumed. The effects of nonlinearity are also discussed.     

Two-carrier conduction in Rb-TCNQ-II

Single crystal electrical resistivity and thermoelectric power (TEP) measurements as a function of temperature are repotted in Rb-TCNQ-II. Results suggest intrinsic conductivity by holes above 360 K with an activation energy of 0.44 eV. Below room temperature conductivity is extrinsic and is due to donors located 0.18 eV below the conduction band.     

Fluorescence from relaxed and unrelaxed excited state of benzil

This note reports the detection of fluorescence from unrelaxed S₁ state of benzil using Boxcar gating technique. The new emission exhibits mirror image relationship with absorption and blue shift in hydroxylic solvent. In order to ascertain wheter geometrical relaxation occurs in S₁ state, intensities of fluorescence from relaxed and unrelaxed state have been compared at various temperatures.     

Analysis of pair interaction in a bipolar mesogen 4‐(4‐hydroxylbutyloxy)‐4′‐cyano‐biphenyl: A comparative study based on semiempirical and DFT methods

Structure of 4‐(4‐hydroxylbutyloxy)‐4′‐cyano‐biphenyl (H4CBP) molecule has been optimized using density functional B3LYP with 6‐31G (d) basis set taking crystallographic geometry as input. Using the optimized geometry, electronic structure of the H4CBP molecule has been evaluated on the basis of semiempirical methods and DFT calculations. Intermolecular interaction energy between a pair of H4CBP molecules has been evaluated by using Rayleigh–Schrodinger perturbation theory modified with multicentered multipole expansion method for the electrostatic part while dispersion and repulsion terms have been calculated using Kitaigorodskii formula. The results obtained through semiempirical and DFT calculations have been compared for various interacting conditions, viz.: (a) stacking, (b) in‐plane, and (c) terminal interactions. A comparative analysis of the results has been carried out with a view to examine suitability of different methods to study molecular aggregations in moderately large organic systems. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Equilibrium strategies for multiple interdictors on a common network

In this work, we introduce multi-interdictor games, which model interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on shortest path multi-interdictor (SPMI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries attempting to traverse a common network. We first establish results regarding the existence of equilibria for SPMI games under both discrete and continuous interdiction strategies. To compute such an equilibrium, we present a reformulation of the SPMI game, which leads to a generalized Nash equilibrium problem (GNEP) with non-shared constraints. While such a problem is computationally challenging in general, we show that under continuous interdiction actions, an SPMI game can be formulated as a linear complementarity problem and solved by Lemke’s algorithm. In addition, we present decentralized heuristic algorithms based on best response dynamics for games under both continuous and discrete interdiction strategies. Finally, we establish theoretical lower bounds on the worst-case efficiency loss of equilibria in SPMI games, with such loss caused by the lack of coordination among noncooperative interdictors, and use the decentralized algorithms to numerically study the average-case efficiency loss.     

On the microhardness of some organic molecular solids

Microhardness measurements have been carried out on the (001) cleavage surfaces of anthracene, Phenanthrene and benzoic acid single crystals. The variation of the Vicker's Hardness Number (VHN) with load (P) shows a decrease in hardness with increasing load. Plots of load (P) vs the square of the diagonal (d²) and logarithm of load (log P) vs logarithm of diagonal (log d) are found to be linear. These observations are being explained in terms of the geometrical packing of molecules in these crystals which play an important role in causing slip.