Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

Approaches to the synthesis of novel photoactive side chain liquid crystalline polymers containing analogues of the cinnamate ester group

A series of chain liquid crystalline copolymers of 4-cyanophenyl 4′-(6-methacryloyloxyhexyloxy)benzoate and 2-methacryloyloxyethyl β-(1-naphthyl)-propenoate were prepared by free radical polymerization. The corresponding polyacrylates could not be prepared in the same way and an alternative method was used for their preparation involving the synthesis of copolymers of the mesogenic monomer and 2-hydroxyethyl acrylate followed by treatment of the resulting polymers with β-(1-naphthyl)propenoyl chloride. The materials are of interest as photoactive liquid crystalline polymers. The effect of introducing a bulky nonmesogenic group into a liquid crystalline copolymer generally lowers the clearing temperature and raises Tg but also gives rise to contrasting phase behaviour in these two series of polymers. Polymethacrylates which show mesomorphism have sharp transitions and continue to exhibit a highly ordered smectic phase over the bulk of their liquid crystal range. Polyacrylates, on the other hand, exhibit a weakening and broadening-out of their thermal transitions consistent with a lowering of order. These results emphasize the effect of the polymer backbone on phase behaviour.

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.

Geoarchaeology and the value of multidisciplinary palaeoenvironmental approaches: a case study from the Tehran Plain, Iran

Tepe Pardis, a significant Neolithic–Chalcolithic site on the Tehran Plain in Iran, is, like many sites in the area, under threat from development. The site contains detailed evidence of (1) the Neolithic–Chalcolithic transition, (2) an Iron Age cemetery and (3) how the inhabitants adapted to an unstable fan environment through resource exploitation (of clay deposits for relatively large-scale ceramic production by c. 5000 BC, and importantly, possible cutting of artificial water channels). Given this significance, models have been produced to better understand settlement distribution and change in the region. However, these models must be tied into a greater understanding of the impact of the geosphere on human development over this period. Forming part of a larger project focusing on the transformation of simple, egalitarian Neolithic communities into more hierarchical Chalcolithic ones, the site has become the focus of a multidisciplinary project to address this issue. Through the combined use of sedimentary and limited pollen analysis, radiocarbon and optically stimulated luminescence dating (the application of the last still rare in Iran), a greater understanding of the impact of alluvial fan development on human settlement through alluviation and the development of river channel sequences is possible. Notably, the findings presented here suggest that artificial irrigation was occurring at the site as early as 6.7±0.4 ka (4300–5100 BC).