GeneralizedM-diffusion model of molecular rotations

The widely usedM-model of rotational diffusion of molecules in fluid phases is generalized. The ordinaryM-model assumes that intermolecular collisions causeinstantaneous changes in the orientation of an otherwise free rotor. The present scheme takes cognizance of the ubiquitous intermolecular torques which should make the molecular orientation a continuously variable random function of time. It is assumed here that the component of the angular velocity, which is conjugate to the angle specifying the orientation of the molecule, is a stationary Gaussian-Markov process. The ordinaryM-model emerges then as a special case of the more general treatment presented here. The results derived for the dipole correlation function of a linear rotor on the basis of the generalized scheme are applied to a series of infrared data. The observed agreement is highly satisfactory. The present analysis affords a justification for the Gordon scheme which generalizes theM-model by assigning to the mean rate of collision anad-hoc dependence on the angular speed of the rotor. It is argued also that the model treated here incorporates certain memory effects which are ignored in the ordinaryM-model, and may yield, in some cases, results which are similar to those based on certain memory function formalisms.     

Study of precipitation in NaCl:Pb2+ by light scattering and ultramicroscopy

The formation and dissolution behaviour of precipitates in NaCl : Pb²⁺ single crystals is studied by light scattering and ultramicroscopy. Measurements of Rayleigh ratio together with ultramicroscopic observations during isochronal annealing indicate the presence of two types of precipitates in as-grown crystals. Isochronal annealing after suitable thermal and thermomechanical treatments shows that precipitates of first type (I) which form and dissolve at lower temperatures, are due to homogeneous nucleation. Precipitates of the second category (II) which form and dissolve at higher temperatures are aligned along crystallographic directions and have their origin in stress-assisted processes. Isothermal annealing has been used to study the dissolution kinetics of the precipitated fraction, and it is found that the kinetics is of first order. The enthalpy of solution is determined from a study of the temperature dependence of the kinetic rate constant, in conjunction with available information on the migration energy of Pb²⁺ in NaCl. The enthalpy so deduced is in good agreement with the value as usually obtained from the concentration dependence of the dissolution temperature.     

Growth of monodisperse nanocrystals of cerium oxide during synthesis and annealing

Monodisperse cerium oxide nanocrystals have been successfully synthesised using simple ammonia precipitation technique from cerium(III) nitrate solution at different temperatures in the range 35–80 °C. The activation energy for growth of CeO₂ nanocrystals during the precipitation is calculated as 11.54 kJ/mol using Arrhenius plot. Average crystal diameter was obtained from XRD analysis, HR-TEM and light scattering (PCS). The analysis of size data from HR-TEM images and PCS clearly indicated the formation of highly crystalline CeO₂ particles in narrow size range. CeO₂ nanocrystals precipitated at 35 °C were further annealed at temperatures in the range 300–700 °C. The activation energy for crystal growth during annealing is also calculated and is close to the reported values. An effort is made to predict the mechanism of crystal growth during the precipitation and annealing.     

Synthesis and characterization of Bi-doped zirconia for solid electrolyte

(100-x)ZrO₂(x)Bi₂O₃ (x = 5, 10, 15) system has been synthesized by solid-state reaction technique. Tetragonal Bi_7.38Zr_0.62O_12.31 phase has formed in all the samples after sintering at 850 °C for 24 h. Apart from this, ZrO₂ and Bi₂O₃ are also identified as minority phases. The volume fraction of Bi_7.38Zr_0.62O_12.31 phase increases with increasing concentration of Bi₂O₃. The AC conductivity plots exhibit phase transition at 570 °C and 460 °C for x = 10 and x = 15 samples, respectively. The maximum conductivity is observed (1.60 mS/cm) in x = 15 sample. These results are correlated and supported with microstructural and thermal analysis.     

Interacting branching process as a simple model of innovation

We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/τ at each generation. In contrast with mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For τ = ∞, surviving processes exhibit a bottleneck before exploding superexponentially-a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p→0.     

Generalized Univex Functions in Nonsmooth Multiobjective Optimization

In this paper, we have considered a nonsmooth multiobjective optimization problem where the objective and constraint functions involved are directionally differentiable. A new class of generalized functions (d???ρ???η???θ)-type I univex is introduced which generalizes many earlier classes cited in literature. Based upon these generalized functions, we have derived weak, strong, converse and strict converse duality theorems for mixed type multiobjective dual program in order to relate the efficient and weak efficient solutions of primal and dual problem.