Stability issues in vector electric field propagation

Demonstrates that although standard paraxial and wide-angle vector field propagation techniques lead to divergences for sufficiently small grid-point spacings and large refractive index differences, stability may be restored through either certain Pade approximates to the propagation operator or suitable boundary conditions. The authors also introduce a novel alternating directional implicit method applicable to less divergent discretizations of the vector wave equation     

A Preemptive Algorithm for Maximizing Disjoint Paths on Trees

We consider the on-line version of the maximum vertex disjoint path problem when the underlying network is a tree. In this problem, a sequence of requests arrives in an on-line fashion, where every request is a path in the tree. The on-line algorithm may accept a request only if it does not share a vertex with a previously accepted request. The goal is to maximize the number of accepted requests. It is known that no on-line algorithm can have a competitive ratio better than Ω(log n) for this problem, even if the algorithm is randomized and the tree is simply a line. Obviously, it is desirable to beat the logarithmic lower bound. Adler and Azar (Proc. of the 10th ACM-SIAM Symposium on Discrete Algorithm, pp. 1–10, 1999) showed that if preemption is allowed (namely, previously accepted requests may be discarded, but once a request is discarded it can no longer be accepted), then there is a randomized on-line algorithm that achieves constant competitive ratio on the line. In the current work we present a randomized on-line algorithm with preemption that has constant competitive ratio on any tree. Our results carry over to the related problem of maximizing the number of accepted paths subject to a capacity constraint on vertices (in the disjoint path problem this capacity is 1). Moreover, if the available capacity is at least 4, randomization is not needed and our on-line algorithm becomes deterministic.     

Trisomy 18 anomalies on sonography and calculated risk of chromosomal abnormalities during first trimester

Trisomy 18 is a chromosomal disorder giving multiple anomalies. Its frequency depends on maternal age. We report a 28-year-old woman in her first pregnancy, who underwent first trimester scanning for screening. Due to increased nuchal translucency and exomphalos, chorionic villous sampling was performed. Cytogenetic diagnosis was trisomy 18 and termination of pregnancy was carried out immediately.     

Aspects of the development of a copper electrowinning cell based on reactive electrodialysis

This paper reports work aimed at developing a new copper electrowinning cell based on reactive electrodialysis (RED) which uses Fe²⁺→Fe³⁺+e as anodic reaction. In this lab-scale cell, the anolyte (aqueous FeSO₄+H₂SO₄) and the catholyte (aqueous CuSO₄+H₂SO₄) are kept separate by an anion membrane which prevents cation and water transport between the electrolytes. Both solutions are agitated by recirculation. The kinetics of the anodic reaction have been studied via potentiodynamic experiments on various anode materials (lead, platinum, ruthenium oxide, iridium oxide and graphite). The highest oxidation rate was obtained on platinum and the lowest one on lead, whereas the remaining materials showed satisfactory performance. Results in the lab-scale RED cell show that, depending on experimental conditions, for a cell current density of , the cell voltage ranges from 1.81 to , the cathodic current efficiency from 97.2% to 98.3% and the specific energy consumption, from 1.53 to of deposited copper.     

Split-operator electric field reflection techniques

The authors have analyzed several approximations for the reflection coefficient of an electric field incident on the interface between two inhomogeneous dielectric media. While existing expressions agree with exact results in certain limits, realistic waveguides with discontinuous refractive index changes are often more accurately modeled by dividing the incoming electric field into segments coinciding with the intervals over which the interface is continuous, and subsequently superimposing the reflection from each segment.<>     

The Solubility of Fine Particles and the Supersaturated Solution

Supersaturated solutions equilibrated with fine particles remain stable, when thermostated for long periods, i.e., “Ostwald ripening” is rather slow. It is argued that this is because the “excess” solute is contained in the supersaturated solution in the form of bloc nuclei the size of which are nearly as large as that of the fine particles in suspension. In the case of real supersaturated solutions, which invariably contain impurities serving as heterogeneous nucleating agents, also, a quasi equilibrium of bloc nuclei of a narrow size-distribution is established. This is a logical consequence of the kinetic theory of embryal growth owing to local fluctuations. The heat released by the growing embryos (or bloc nuclei) at any moment is proportional to their increase in surface area.     

Speculations on a New Mechanism of Crystal Growth from Aqueous Solutions

The activity of lead ions to form heterogeneous nuclei in supersaturated KCl solutions was shown (in previous publications) to account quantitatively for the effect of these ions on the limit of stability of the supersaturated solutions, the rate of crystallization, and the co-precipitation of the lead ions with the crystallizing salt. Hence the process of crystal growth is described as the deposition of subcolloidal sized nuclei on the crystal seed. Many otherwise perplexing phenomena recorded in the literature, and observed in studies of various aspects related to the crystallization of KCl and NaCl, prove to be a direct consequence of this mechanism of crystallization. Other examples indicate that heteronucleation and a similar growth mechanism may be prevalent in the crystallization of several salts from their aqueous solutions. Some implications and possible applications of the proposed growth mechanism are also discussed.