A mode split,Godunov‐type model for nonhydrostatic,free surface flow

A previously developed model for nonhydrostatic, free surface flow is redesigned to improve computational efficiency without sacrificing accuracy. Both models solve the Reynolds averaged Navier–Stokes equations in a fractional step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. The hydrostatic solution is then corrected by including the nonhydrostatic pressure and requiring the velocity field to obey the incompressibility constraint. The original model requires the solution of a Riemann problem at every cell face for each vertical layer of cells, which is computationally expensive. The redesigned model instead solves the shallow water (long wave) equations for the hydrostatic solution. Vertical shear is computed by subtracting the shallow water equations from the full three dimensional equations, which removes the hydrostatic thrust terms. Therefore, the required fluxes may be more efficiently computed with velocity based upwind differencing rather than solving a Riemann problem in each vertical layer of cells. This approach is termed mode splitting and has been used in hydrostatic coastal and ocean circulation models, but not surf zone models. Numerical predictions are compared with analytical solutions and experimental data to show that the mode split model is as accurate as the original model, but requires significantly less computational effort especially for large numbers of cell layers. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

The Jordan canonical form for a class of zero-one matrices

Let f:N→N be a function. Let A_n=(a_ij) be the n×n matrix defined by a_ij=1 if i=f(j) for some i and j and a_ij=0 otherwise. We describe the Jordan canonical form of the matrix A_n in terms of the directed graph for which A_n is the adjacency matrix. We discuss several examples including a connection with the Collatz 3n+1 conjecture.     

Evaluation,Pitfalls and Recommendations for the “Water Layer Test” for Solid Contact Ion‐selective Electrodes

The “water layer test” is a crucial validation step of solid‐contact ion‐selective electrodes. It can confirm or contest the claim that the tested electrode is indeed a genuine solid contact electrode without an aqueous film between the ion‐selective membrane and its solid contact. Information about the presence of a water layer is essential for the interpretation of drifts in the electrode potentials commonly experienced with solid contact electrodes. Since its publication, the water layer test has been ubiquitously used, but without a standardized protocol the interpretation (or misinterpretation) of the test results led to uncertainties in the conclusions. Through both experiments and simulations based on theoretical models we have investigated the experimental parameters that can influence the results of the water layer test. We propose guidelines to minimize the possibility of misinterpretation of the results of the water layer test by considering the key factors that affect the shape of transients recorded during the water layer test. Most importantly, we emphasize the importance of allowing sufficient time for conditioning the tested electrode before the water layer test and providing adequate time for equilibration during the experiment. Using a thin ion‐selective membrane and thin solid‐contact layer for the tests is also recommended.     

A Synthesis of 7,7-Dimethyl-6,8-Dioxabicyclo[3.2.1]Octane a Constituent of the Hop,Humulus Lupulus

A synthesis of 7,7-dimethyl-6,8-dioxabicyclo-[3.2.1]octane, a component of hop oil, is described. The appproach focuses on 2-acetyl-3,4-dihydro-2H-pyran and 2-(carboxymethy)-3,4-dihydro-2H-pyran as intermediates.     

Studies Directed Towards a Practical Synthesis of Brevicomins (II)1 : A Novel Synthesis of 1, 5-Dimethyl-8-Oxobicyclo [3.2.1]octane-6-one

The recent interest in pheromones,² as means of controlling insect pests, has prompted us to examine syntheses which could be both simple and practical. We recently reported a three-step synthesis of brevicomin (3), the aggregating pheromone of the pine bark beetle, Dendroctonus brevicomis.³     

Die Adsorptionstheorie der geschichteten Niederschläge

Ohne Zusammenfassung     

Analytical performance characteristics of thin and thick film amperometric microcells

The analytical performance of amperometric microcells with different electrode geometries is compared for enzyme activity measurements. The microcells were fabricated with thin film photolithography or thick film screen-printing in four different designs. The cells made with the thin film process used flexible substrate with microelectrode array or a circular, disk-shaped working electrode. The screen-printed working electrodes had semicircle or disk shape on ceramic chips. Putrescine oxidase (PUO) activity measurement was used as a model. The determination of PUO activity is important in the clinical diagnosis of premature rupture of the amniotic membrane. An electropolymerized m-phenylenediamine size-exclusion layer was used to eliminate common interferences. The size exclusion layer revealed also to be advantageous in protecting the electrodes from fouling by putrescine (enzyme substrate). The electrode fouling of bare electrodes was insignificant for screen-printed electrodes, but very severe for electroplated platinum working electrodes. The microelectrode array electrodes demonstrated smaller RSD and higher normalized sensitivities for hydrogen peroxide and PUO activity. All the other electrodes were demonstrating comparable analytical performances.     

An investigation into the maximum entropy production principle in chaotic Rayleigh–Bénard convection

The hypothesis is made that the temperature and velocity fields in Rayleigh–Bénard convection can be expressed as a superposition of the active modes with time-dependent amplitudes, even in the chaotic regime. The maximum entropy production principle is interpreted as a variational principle in which the amplitudes of the modes are the variational degrees of freedom. For a given Rayleigh number, the maximum heat flow for any set of amplitudes is sought, subject only to the constraints that the energy equation be obeyed and the fluid be incompressible. The additional hypothesis is made that all temporal correlations between modes are zero, so that only the mean-squared amplitudes are optimising variables. The resulting maximal Nusselt number is close to experimental determinations. The Nusselt number would appear to be simply related to the number of active modes, in particular the number of distinct vertical modes. It is significant that reasonable results are obtained for the optimised Nusselt number in that the dynamics (the Navier–Stokes equation) is not used as a constraint. This suggests grounds for optimism that the maximum entropy production principle, interpreted in this variational manner, can provide a reasonable guide to the dynamic steady states of non-equilibrium systems whose detailed dynamics are unknown.