Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

Electric generators of singlet delta oxygen for an oxygen-iodine laser

Experimental and theoretical research into electric generators of singlet delta oxygen (SDO) for an oxygen-iodine laser made at the Lebedev Physics Institute and TRINITI is discussed. Breakdown and current-voltage characteristics of self-sustained electric discharge in SDO were studied both experimentally and theoretically, indicating that SDO and pure oxygen have quite different electric features. The electric properties and spectroscopy of an e-beam sustained discharge (EBSD) in oxygen and oxygen gas mixtures were experimentally studied. A comprehensive numerical model describing SDO kinetics in different kinds of discharge was developed. The pulsed EBSD in pure oxygen and its mixtures with noble gases was shown to be very unstable and characterized by low input energy. When adding small amounts of carbon monoxide or hydrogen, the electric stability of the EBSD increases, the specific input energy (SIE) per molecular component being more than order of magnitude higher and coming to 6.5 kJ/(l atm(O₂ + CO)) for the gas mixture O₂: Ar: CO = 1: 1: 0.1. Theoretical calculations demonstrated that, for an SIE of 6.5 kJ/(l atm), the SDO yield may reach ∼20%, exceeding its threshold value needed for oxygen-iodine laser operation at room temperature. The calibration of the optical scheme for measuring the SDO absolute concentration and yield using the detection of luminescence of the SDO going from a chemical SDO generator was performed. The measurement of the SDO yield demonstrated that it was ∼10.5% for an SIE of ∼3.0 kJ/(l atm(O2 + CO)), which is about 1.5 times less than the results of theoretical calculations for such an SIE. SDO production in RF slab discharge ignited in oxygen gas mixtures was experimentally studied, experimental SDO yield being about 10%. The choice of electrode material was demonstrated to be very important. Original Text ? Astro, Ltd., 2006.     

Gauge-Related Deformations of Ordinary Linear Differential Operators with Constant Coefficients

Relations between the coefficients of gauge-related deformations and the solutions of a certain system of ordinary nonlinear differential equations are studied. These coefficients are found in an explicit form. Bibliography: 14 titles. Dedicated to P. V. Krauklis on the occasion of his seventieth birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 235–251.     

Dielectric and optical properties of polymer-liquid crystal composite

Dielectric properties of polymer-liquid crystal mixture, having constituent polymer, poly-butyl methacrylate (PBMA) and liquid crystal, cholesteryl nonanoate, are reported as a function of frequency and temperature. The measurement has been done in a temperature range of 300-375 K and frequency range of 100 Hz-10 MHz. The dielectric permittivity and dielectric loss shows significant changes with the addition of polymer molecules in liquid crystal. The significant feature of composite formation is that the pure liquid crystal and polymer do not show dielectric relaxation in the frequency range covered, while the composite shows relaxation peak at a particular frequency. The optical transmittance of pure liquid crystal and composite has also been measured and compared.     

Onset of crater formation during short pulse laser ablation

We report morphologic changes of metallic surfaces at the onset of ablation, starting from gentle ablation to the emergence of ablation craters. The evolution of both observed melting zones and of ablation craters therein are investigated in dependence of the ablation laser fluence for nanosecond ultraviolet laser pulses. Further, consequences of crater formation for cluster synthesis within the released atomic vapor are pointed out. PACS 52.38.Mf; 79.20.Ds; 65.40.De     

A warehouse-based design model for reverse logistics

In this paper, an MILP formulation is proposed for the design of a reverse logistics network based on a warehouse location–allocation model, which optimizes, simultaneously, the forward and reverse networks. A single product model with unlimited capacity is first defined. Subsequently, the model is extended to a multi-product capacitated recovery network model, where capacity limitations and a multi-product system can be considered. The proposed model is compared to published work in the field, where different model assumptions have been proposed. Two cases are described so as to gain a better insight into the model and allow a comparative analysis.