The bialternate matrix product revisited

The well known bialternate product of two square matrices is re-examined together with another matrix product defined by means of the permanent function and having similar properties. Old and new results concerning both products are presented in a unified manner. A simple and elegant relation with the Kronecker product of matrices is also given.     

Carbon and nitrogen isotope analysis of atrazine and desethylatrazine at sub-microgram per liter concentrations in groundwater

Environmental degradation of organic micropollutants is difficult to monitor due to their diffuse and ubiquitous input. Current approaches—concentration measurements over time, or daughter-to-parent compound ratios—may fall short, because they do not consider dilution, compound-specific sorption characteristics or alternative degradation pathways. Compound-specific isotope analysis (CSIA) offers an alternative approach based on evidence from isotope values. Until now, however, the relatively high limits for precise isotope analysis by gas chromatography—isotope ratio mass spectrometry (GC-IRMS) have impeded CSIA of sub-microgram-per-liter scale micropollutant concentrations in field samples. This study presents the first measurements of C and N isotope ratios of the herbicide atrazine and its metabolite desethylatrazine at concentrations of 100 to 1,000 ng/L in natural groundwater samples. Solid-phase extraction and preparative HPLC were tested and validated for preconcentration and cleanup of groundwater samples of up to 10 L without bias by isotope effects. Matrix interferences after solid-phase extraction could be greatly reduced by a preparative HPLC cleanup step prior to GC-IRMS analysis. Sensitivity was increased by a factor of 6 to 8 by changing the injection method from large-volume to cold-on-column injection on the GC-IRMS system. Carbon and nitrogen isotope values of field samples showed no obvious correlation with concentrations or desethylatrazine-to-atrazine ratios. Contrary to expectations, however, δ ¹³ C values of desethylatrazine were consistently less negative than those of atrazine from the same sites. Potentially, this line of evidence may contain information about further desethylatrazine degradation. In such a case, the common practice of using desethylatrazine-to-atrazine ratios would underestimate natural atrazine degradation.     

Comparison of Two Unsteady Intermittency Models for Bypass Transition Prediction on a Turbine Blade Profile

The present paper evaluates two unsteady transition modelling approaches: the prescribed unsteady intermittency method PUIM, developed at Cambridge University and the dynamic unsteady intermittency method developed at Ghent University. The methods are validated against experimental data for the N3-60 steam turbine stator profile for steady and for unsteady inlet flow conditions. The characteristic features of the test case are moderately high Reynolds number and high inlet turbulence intensity, which causes bypass transition. The tested models rely both on the intermittency parameter and are unsteady approaches. In the prescribed method, the time-dependent intermittency distribution is obtained from integral relations. In the dynamic method, the intermittency distribution follows from time-dependent differential equations. For unsteady computations, self-similar wake profiles are prescribed at the inlet of the computational domain. Joint validation of the prescribed and the dynamic unsteady intermittency models against experimental data shows that both methods are able to reproduce the global features of the periodical evolution of the boundary layer under the influence of a periodically impinging wake. The overall quality of the dynamic method is better than that of the prescribed method.     

Statistical verification of crystallization in hard sphere packings under densification

The performance of various structure characteristics in the task of indicating structural peculiarities in packings of hard spheres is investigated. Various characteristics based on Voronoi polyhedra, spherical harmonics, and Delaunay simplices are considered together with the pair correlation function and the mean number of r-close triples. They are applied to a set of hard sphere packings of density φ from 0.62 to 0.72. It turns out that all used structure characteristics are able to indicate changes of order from non-crystalline to crystalline packings. However, not all of them are sensitive enough to indicate different stages of structure transformation under densification. The characteristics based on Delaunay simplices turn out to be the most sensitive for this purpose. For the models considered three principal structure classes are found: packings of densities lower than the known critical value 0.64 showing a non-crystalline behavior; packings with considerable crystalline regions for φ up to 0.66–0.67; rather complete crystals although with numerous defects for φ above 0.67.