An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Shallow water flow with cylindrical symmetry

A numerical scheme is presented tor the solution of the shallow water equations in a single radial coordinate. This can prove useful when testing codes for the two-dimensional shallow water equations. The scheme is applied with success to problems involving converging and diverging bores.

Bacterial pathogen evolution: breaking news

The immense social and economic impact of bacterial pathogens, from drug-resistant infections in hospitals to the devastation of agricultural resources, has resulted in major investment to understand the causes and conse- quences of pathogen evolution. Recent genome se- quencing projects have provided insight into the evolution of bacterial genome structures; revealing the impact of mobile DNA on genome restructuring and pathogenicity. Sequencing of multiple genomes of relat- ed strains has enabled the delineation of pathogen evo- lution and facilitated the tracking of bacterial pathogens globally. Other recent theoretical and empirical studies have shown that pathogen evolution is significantly influenced by ecological factors, such as the distribution of hosts within the environment and the effects of co- infection. We suggest that the time is ripe for experi- mentalists to use genomics in conjunction with evolu- tionary ecology experiments to further understanding of how bacterial pathogens evolve.

Construction of supramolecular helices and breaking the helicity by forming supramolecular β-sheet structures using suitable self-assembling pseudopeptide building blocks

Bis-valine derivatives or malonamide (Guha,S.; Drew, M.G.B. Small 2008, 4, 1993-2005) and a bis-valine derivative of 1,1-cyclopropone dicarboxamide were used as building blocks for the construction of supramolecular helical structures. The six-membered intramolecular hydrogen-bonded scaffold is formed, and this acts as a unique supramolecular synthon for the construction of a pseudopeptide-based supramolecular helical structure. However, in absence of this intramolecular hydrogen bond. intermolecular hydrogen bonds are formed among the peptide strands. This leads to a supramolecular beta-sheet structure. Proper selection of the supramolecular synthon (six-membered intramolecular hydrogenbonded scaffold) promotes supramolecular helix formation, and a deviation from this molecular structure dictates the disruption of supramolecular helicity. In this study, six crystal structures have been used to demonstrate that a change in the central angle and/or the central core structure of dicarboxamides can be used to design either a supramolecular helix or a beta-sheet.

Rotational symmetry of a methane molecule and the bond angle

The rotational symmetry of a methane molecule can be used to great advantage to calculate the bond angle. The problem is worked out in this article.

Breaking free from the industrial age paradigm of branding

The paper aims to inform readers of the themes that emerged at the 2007 Thought Leaders International Conference on Brand Management and challenges academics and practitioners to rethink the basics of branding. The paper encourages academics and practitioners to escape from the continued confines of industrial age branding and the ‘influencing’ mindset and embrace the age of openness and co-creation. It is argued that we need to evolve from the industrial age paradigm of branding that informed brand management for decades and adjust practice and research accordingly.

Real options and game theoretical approaches to real estate development projects: multiple equilibria and the implications of different tie-breaking rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.

An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm

Recent research has shown that Lighthill–Ford spontaneous gravity wave generation theory, when applied to numerical model data, can help predict areas of clear-air turbulence. It is hypothesized that this is the case because spontaneously generated atmospheric gravity waves may initiate turbulence by locally modifying the stability and wind shear. As an improvement on the original research, this paper describes the creation of an ‘operational’ algorithm (ULTURB) with three modifications to the original method: (1) extending the altitude range for which the method is effective downward to the top of the boundary layer, (2) adding turbulent kinetic energy production from the environment to the locally produced turbulent kinetic energy production, and, (3) transforming turbulent kinetic energy dissipation to eddy dissipation rate, the turbulence metric becoming the worldwide ‘standard’. In a comparison of ULTURB with the original method and with the Graphical Turbulence Guidance second version (GTG2) automated procedure for forecasting mid- and upper-level aircraft turbulence ULTURB performed better for all turbulence intensities. Since ULTURB, unlike GTG2, is founded on a self-consistent dynamical theory, it may offer forecasters better insight into the causes of the clear-air turbulence and may ultimately enhance its predictability.

On a stochastic Trotter formula with application to spontaneous localization models

We consider the relation between so called continuous localization models—i.e. non-linear stochastic Schrödinger evolutions—and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Wave-breaking characteristics of midlatitude blocking

In this article, Northern Hemisphere winter midlatitude blocking is analysed through its wave-breaking characteristics. Rossby wave breaking is identified as a key process in blocking occurrence, as it provides the mechanism for the meridional reversal pattern typical of blocking. Two indices are designed to detect the major properties of wave breaking, i.e. the orientation (cyclonic/anticyclonic–direction of breaking or DB index) and the relative contribution of air masses (warm/cold–relative intensity or RI index). The use of the DB index differentiates between the anticyclonic cases over Europe and Asia and the cyclonic events over the oceanic basins. One of the three regions displaying cyclonic type was found over the Atlantic Ocean, the other two being over the Pacific Ocean. The first of these is located over the western side of the Pacific and is dominated by warm air extrusions, whereas the second is placed northward of the exit region of the jet stream, where the meridional θ gradient is much weaker. Two European blocking types have been detected using the RI index, which separates out the cases dominated by warm and cold air masses. The latter cases in particular exhibited a well-structured dipole, with associated strong anomalies in both temperature and precipitation. Copyright © 2011 Royal Meteorological Society