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     

Characterization of isolated homogeneous hypersurface singularities in ℂ4

Let V be a hypersurface with an isolated singularity at the origin in ? ⁿ⁺¹. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface signularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau’s theorem remains true for singularities with geometric genus equal to zero.     

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.     

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     

Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

On decomposition of continuity

Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.     

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.     

Addendum to "On the L1-Condition Number of the Univariate Bernstein Basis"

The paper mentioned above is a contribution of the authors to Volume 18 (2002) of this journal, see . Recently, J. Domsta pointed out to us that the proof of Theorem 4.2 in that paper contains an error. The purpose of this addendum is to present a correct argument for it.