A scale-dependent equation for solute transport in porous media

The governing equation describing solute transport in porous media is reformulated using standard volume averaging techniques. The alternative formulation is based on a modified definition of the deviation, which allows for variation of macroscopic velocity across the REV. The new equation contains additional scale-dependent terms which are functions of the size of the averaging volume (REV). This result indicates that the scale-dependent nature of the dispersion phenomenon is inherent even at the scale of the REV.     

Automated antenna positioning algorithms for wireless fixed-access networks

This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.     

Subdirect decomposition of rings and the axiom of choice

The second author is supported in part by a research grant of the Council of Scientific and Industrial Research of South Africa.     

Reactions of Azolium cations. II [1]. Regioselective N2 alkylation of 5-aryltetrazoles with isopropyl alcohol in sulfuric acid media: Effect of electronic properties of aryl substituents on the reaction rate

Kinetics of regioselective N2 alkylation of a series of 5-(R-phenyl)tetrazoles with isopropyl alcohol has been studied in 88.2, 94.3, and 98.3% (w/w) sulfuric acid at 25°. The true rate constants were evaluated, logarithms of which were found to correlate with σ° constants of phenyl substituents as log k = ?0.488 σ° ? 0.417. Small value of Hammett constant ρ is evidence of a considerable isolation of the reaction center from the influence of the substituent at position C5 of the heteroring. This conclusion is confirmed by results of MNDO quantum chemical calculations of a series of 5-substituted tetrazolium cations. A correlation between logarithms of the true rate constants and the calculated net effective charges on atoms N2(N3) for 5-(R-phenyl)tetrazolium cations has been revealed. © 1995 John Wiley & Sons, Inc.     

Microdetermination of osmium by oxygen-flask combustion of the sample

A relatively simple and convenient procedure for the determination of osmium in its compounds has been worked out. It is based on the oxygen-flask combustion of the sample followed by the spectrophotometric determination of osmium with 4-(2-pyridylazo)-resorcinol. Possible modifications of the final method are suggested in order to overcome interferences caused by sulfur.     

Charge separation in ground-state 1,2,4,5-tetra-substituted benzene derivatives

The conditions required for a formal biradical to exist in a zwitterionic form in the ground state are discussed following the recent experimental observation of zwitterionic structure in the ground state of a quinoid molecule (di-tert-butyl derivative of 2,5-diamino-1,4-benzoquinonediimine, I). A unique characteristic of molecules of this class is the fact that they may be considered as being formed by the union of two radicals, each having an odd number of pi electrons. In the case of I, one fragment carries the two amino group having 7 pi electrons; it acts as the electron donor. The other fragment carries the two oxygen atoms (carrying 5 pi electrons) and acts as an electron acceptor. A model that predicts the properties of these systems is presented, based on previous work on non-Kekule hydrocarbons(2,3) and on the electron donating and attracting properties of the donor and acceptor groups, respectively. The zwitterion is formed by an electron transfer leading to two subunits carrying 6 pi electrons each and may become more stable than the triplet biradical even in the gas phase (i.e., in the absence of an external field) if the ionization potential of the donor is small (of the order of 3-4 eV). In some cases solvation in a polar solvent is required to make the zwitterionic form the lowest energy species on the ground-state surface. The 'spacer' between the donor and acceptor groups (which need not be necessarily derived from an aromatic structure) can be varied and influences the overall dipole moment that is calculated in some cases to be quite large (over 20 D in the gas phase).     

Ar ion laser assisted chemical etching of via holes in tungsten sheets in air

Ar ion laser assisted chemical etching of 150 m thick annealed tungsten sheets in air is reported. The material removal mechanism involves local heating by the laser to temperatures in the range of 1000–1500 °C that causes rapid oxidation of the W to WO₃ which volatilizes readily. Holes with straight walls and slightly enlarged entrances near the surface were drilled with etch rates as high as 11.5 m/s at 13.8 W, and a minimum hole diameter of 21 m at 8.1 W. The diameters of the holes and the etch rates were measured and found to increase as a function of the laser power. It was found that by increasing the laser power above 11–12 W, no change was observed in the hole diameters which remained constant at about 31 m, whereas the etch rates continued to increase even faster than at low powers. Distinct adjacent holes of 25 m diameter could be drilled with their centers separated by as little as 60 m. This is therefore also the etching resolution in the present study.     

Quantum theory of photodissociation of polyatomic molecules: Application to HCN

A theory of direct collinear photodissociation is presented wherein the correct and different normal modes appropriate to the initial molecular state and the photofragments are employed. This remedies a serious deficiency in previous theories which assume that the reaction coordinates for the photodissociation is also a normal mode in the initial electronic state and that the remaining normal modes are the same for both. The theory provides an analytical expression for the vibrational energy distribution of the photofragments, and provides simple criteria for the occurrence of population inversions. Calculated vibrational distributions for HCN photodissociation are in agreement with experiment.     

Beitrag zur Frage der Eichung von Flüssigkeitskondensatoren für DK-Messungen

Zusammenfassung Es wird darauf hingewiesen, daß die neuzeitlichen Richtungen der dielektrischen Polarisationsuntersuchungen durch den Mangel an zuverlässigen Eichwerten und Temperaturkoeffizienten behindert werden und daß es wünschenswert sei, Absolutmessungen mit entsprechender Präzision Zur Frage der Eichung von Flüssigkeitskondensatoren für DK-Messungen.I. Mittlg.,E. Treiber undG. Porod, Mh. Chem.80, 481 (1949).— II. Mittlg.,E. Treiber undH. Koren, ibid. Mh. Chem.81, 627 (1950).—III. Mittlg.,E. Treiber, H. Koren undJ. Schurz, Z. Naturforsch.5 a, 208 (1950).