A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterisation of Phosphorus Compounds By 31P,NX-Shift Correlated NMR Techniques in One and Two Dimensions

Abstract

Examples for 2-D shift correlations between ³¹P and another heteronucleus via ⁿX-detected 2D-INJZPT or ³¹P-detected HMQC experiments are presented. The former technique is best suited for ³¹P, ¹⁵N correlations and permits the determination of intramolecular connectivities as well as of relative signs of couplings.¹ The “inverse” HMQC expenment allows easy recording of the ⁷⁷Se NMR spectrum of an equilibrium mixture of 2 and 3³, disregarding the severe exchange broadening of the ⁷⁷Se-resonances     

An efficient heuristic approach to detecting graph isomorphism based on combinations of highly discriminating invariants

The search for an easily computable, finite, complete set of graph invariants remains a challenging research topic. All measures characterizing the topology of a graph that have been developed thus far exhibit some degree of degeneracy, i.e., an inability to distinguish between non-isomorphic graphs. In this paper, we show that certain graph invariants can be useful in substantially reducing the computational complexity of isomorphism testing. Our findings are underpinned by numerical results based on a large scale statistical analysis.