Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Transport properties of polyphenylquinoxalines

The correlation between chemical structure and gas transport properties is considered for a new class of membrane materials based on structurally similar polyphenylquinoxalines that are characterized by different numbers of flexible-O-ether bonds in the repeating unit and different chain rigidities. Permeability, diffusion, and solubility coefficients have been estimated for the gases H₂, He, O₂, N₂, CO, CO₂, and CH₄; separation factors for various gas pairs have been determined. For the materials with a similar level of cohesive energy density, which characterizes interchain interactions, permeability decreases with a decrease in chain rigidity, whereas selectivity of gas separation increases.     

Electronic structure and elastic moduli of the simple cubic fullerite C24—A new allotropic carbon modification

The energy band structure, equation of state, density of states, and elastic moduli of a new allotropic carbon modification, namely, fullerite C₂₄ with a simple cubic lattice (known previously as cubic graphite), are calculated by the full-potential linearized augmented-plane-wave (FLAPW) method with geometry optimization for the first time. The dependence of the total energy on the lattice constant exhibits a minimum for a ₀ = 0.60546 nm. In this case, the lengths of the C-C bonds between fullerene molecules, the lengths of the 6,6-bonds shared by hexagons, and the lengths of the 4,6-bonds shared by a square and a hexagon are equal to 0.1614, 0.1503, and 0.1637 nm, respectively. An analysis of the energy band structure and the density of states demonstrates that the simple cubic fullerite C₂₄ is a direct-band-gap insulator or a semiconductor with a band gap of 1.6 eV. The calculated bulk modulus B ₀ = 196 GPa and the elastic moduli C ₁₁ = 338 GPa, C ₁₂ = 139 GPa, and C ₄₄ = 30 GPa indicate that the fullerite under investigation is a mechanically stable material. The inference is made that the simple cubic fullerite C₂₄ is a new diamond-like molecular zeolite with a unique combination of properties, such as the porosity and nonpolarizability, on the one hand, and the mechanical strength, chemical inertness, and high thermal conductivity, on the other hand. The simple cubic fullerite C₂₄ can be considered a promising low-dielectric-constant (low-k) material (?₀ < 5.7) for use in fabricating interconnections and substrates intended for integrated circuits and nanoelectronics.     

Nonlinear-optical and micro-Raman diagnostics of thin films and nanostructures of ABO3 ferroelectrics

Ferroelectric composite two-dimensional ferroelectric/aluminum oxide nanostructures were studied. A porous aluminum oxide matrix was used as a template into which a ferroelectric precursor was introduced, followed by annealing. The prepared nanostructures were studied using optical second harmonic generation and micro-Raman scattering.     

Electric currents generated by space-charge waves in high-resistivity semiconductors

Currents in high-resistivity semiconductors arising due to the rectification of space-charge waves are theoretically studied. Attention is primarily focused on the situation where the effective trap concentration is low. It is shown that, in this case, the dispersion law of trap-recharging waves changes from the inverse proportionality to a linear law and the drift waves no longer exist. In crystals with bipolar conduction, there are two modes of trap-recharging waves with a linear dispersion law. The dc and ac currents are found for the first time as functions of the trap concentration, the mobility and lifetime of carriers, the wavenumber of space-charge waves, and the applied electric field.     

Metallic films forming on the surface of alkali-halide crystals during thermal diffusion of intracrystalline immpurities

It was detected for the first time that films consisting of a transition-metal-based structure form (via thermal diffusion of intracrystalline impurities) on the surface of alkali-halide (LiF, NaF) crystals activated by transition metals Co, Ni, or Mn. The thickness, density, and composition of the films are shown to be different, depending on the heat treatment conditions. The crystals were annealed at temperatures varying from 473 to 1073 K in vacuum and air. The surface structures forming upon annealing in vacuum exhibit magnetic properties. The films were studied by optical, x-ray fluorescence, and electron spectroscopy to reveal the mechanisms of transition-metal film formation during thermal annealing.     

On the quantization of solid body rotation

A general method for solving the problem of quantization of a top is proposed that allows for finding the Hamiltonian eigenfunctions in the form of polynomials of various degree n in the Cartesian coordinates with the use of the Lamé functions. All three coordinates x, y, and z are equivalently involved in computations, as well as their relations with ellipsoidal coordinates, which makes the computations symmetric.     

Polymeric derivatives of dipterocarpol, a dammarane triterpenoid

Polymeric derivatives of dammarane triterpenoids with both labile and strong (covalent) polymer-triterpenoid bonds were prepared from N-vinylpyrrolidone copolymers.     

Identifying sets of key players in a social network

A procedure is described for finding sets of key players in a social network. A key assumption is that the optimal selection of key players depends on what they are needed for. Accordingly, two generic goals are articulated, called KPP-POS and KPP-NEG. KPP-POS is defined as the identification of key players for the purpose of optimally diffusing something through the network by using the key players as seeds. KPP-NEG is defined as the identification of key players for the purpose of disrupting or fragmenting the network by removing the key nodes. It is found that off-the-shelf centrality measures are not optimal for solving either generic problem, and therefore new measures are presented. Stephen P. Borgatti is Professor of Organization Studies at the Carroll School of Management, Boston College. His research is focused on social networks, social cognition and knowledge management. He is also interested in the application of social network analysis to the solution of managerial problems.     

Structural, electrical and optical properties of ZnS films deposited by close-spaced evaporation

ZnS films have been deposited on glass substrates by close-spaced evaporation (CSE) technique. The films were grown at different temperatures in the range, 200-350 °C. The layers have been characterized with X-ray diffractometer (XRD), atomic force microscope (AFM), energy dispersive analysis of X-rays (EDAX) and optical spectrophotometer to evaluate the quality of the layers for photovoltaic applications. The studies showed that the optimum substrate temperature for the growth of ZnS layers was 300 °C. The films grown at these temperatures exhibited cubic structure with nearly stoichiometric composition. The AFM data revealed that the films had nano-sized grains with a grain size of ∼40 nm. The optical studies exhibited direct allowed transition with an energy band gap of 3.61 eV. The other structural and optical parameters such as lattice stress, dislocation density, refractive index and extinction coefficient were also evaluated. The temperature-dependent conductivity measured in the range, 303-523 K showed a change in the conduction mechanism at 120 °C. The activation energy values evaluated using the temperature dependence of electrical conductivity are 7 and 29 meV at low and high temperature regions, respectively.