On the topological classification of rarefaction curves in systems of three conservation laws

In this paper we study the topological properties of integral curves of a system of implicit differential equations associated to rarefaction curves of a system of three conservation laws. This system of equations becomes singular at the points of eigenvalue of multiplicity greater or equal to two. We focus our attention to the generic case of multiplicity two and three. We give local weak topological models for these equations.     

Intersections of Hugoniot curves with the sonic surface in the wave manifold

Local 1-shock curve arcs and local reverse 2-shock curve arcs were constructed, in the geometric context of the wave manifold, in a previous paper. In that geometric context, sonic and sonic’ surfaces are the boundaries of admissible shock curve arcs; in order to introduce the concept of non-local 1-shock curve arcs and non-local reverse 2-shock curve arcs it is necessary to understand how a hugoniot curve intersects the sonic and sonic’ surfaces; intersections of such curves with sonic’ surface are well known. In this paper we present a complete study on how Hugoniot curves intersect the sonic surface for a quadratic system of two conservation laws.     

Spin-glass, antiferromagnetism and kondo behavior in Ce2Au1−x Co x Si3 alloys

Recently, the solid solution Ce₂Au_{1− x Co} xSi₃ has been shown to exhibit many magnetic anomalies associated with the competition between magnetic ordering and the Kondo effect. Here we report high pressure electrical resistivity of Ce₂AuSi₃, ac susceptibility (X) and magnetoresistance of various alloys of this solid solution in order to gain better knowledge of the magnetism of these alloys. High pressure resistivity behavior is consistent with the proposal that Ce₂AuSi₃ lies at the left-hand side of the maximum in Doniach’s magnetic phase diagram. The ac X data reveal that there are in fact two magnetic transitions, one at 2 K and the other at 3 K for this compound, both of which are spin-glass-like. However, as the Co concentration is increased, antiferromagnetism is stabilized for intermediate compositions before attaining non-magnetism for the Co end member.     

The growth of a single crystal of Sr3CuIrO6 and its magnetic behavior compared to polycrystals

We have grown single crystals of the psuedo-one-dimensional compound Sr₃CuIrO₆, a K₄CdCl₆-derived monoclinic structure with Cu-Ir chains along the [101] direction. We present the ac and dc magnetization behavior of the single crystals in comparison with that of the polycrystalline form reported earlier. There is a distinct evidence for at least two magnetic transitions, at 5 K (T ₁) and 19 K (T ₂), with different relative magnitudes in the single and polycrystals. The low temperature magnetic relaxation behavior of both the forms is found to be widely different, exhibiting unexpected time dependence.     

Combined effects of Ca2+ and humic acid on colloid transport through porous media

We report the separate and combined effects of humic acid and Ca²⁺ ions on the transport of colloidal particles through a sand-packed column. Polystyrene latex particles with a sulfate functional group were used as model colloids. The concentrations of both the inlet solution and the effluent solutions were measured during each experimental run. Breakthrough curves were obtained by taking the ratios of each effluent sample concentration to the inlet solution concentration. In the absence of humic acid, the results indicate that increasing the concentration of Ca²⁺ increases particle attachment to the sand, thus causing decreased transport rates of latex particles through the porous bed matrix. Once 4 mg/l humic acid was added to the system, changes were observed in the effect that Ca²⁺ has on latex particle breakthrough. In a system containing calcium, increasing the humic acid concentration was shown to reduce particle attachment and increase transport rates. In the absence of calcium, the ratios for the outlet-to-inlet concentrations were similar for each concentration of humic acid. The electrophoretic mobility was also measured in order to determine the role of electrostatic repulsion in the latex particle transport. The electrophoretic mobility of the latex particles was found to be dependent on humic acid concentration in the absence of Ca²⁺ but not in its presence. Received: 2 February 2001 Accepted: 6 2001     

Conditional random surveying for particle deposition on a mica surface.

In using microscopic imaging techniques, unbiased selection of sampling areas is often critical when judgment has to be used to find regions of interest. A conditional random sampling was designed to survey hematite particles on a mica surface using tapping-mode atomic force microscopy, based on three adapted-systematic-sampling methods designed to exclude subjective bias by limiting the freedom of arbitrarily selecting sampling areas. The results of these surveying methods were compared with the average particle surface density modeled by Poisson distribution. It was found that the conditional random sampling could survey particles effectively and improve the data reliability significantly. Ten population-known images from the same mica sheet were used to evaluate these methods, and an average relative error of 12% (maximum 21%) was obtained using the conditional random method with six sampling areas. It was used to investigate the effects of common organic pollutants, benzene, toluene, ethylbenzene, and xylenes on the transport of soil colloids.