Flux difference splitting for inviscid, real gases with non-equilibrium chemistry

A flux-difference splitting method is presented for the inviscid terms of the compressible flow equations for chemical non-equilibrium gases

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient finite difference scheme for three-dimensional, non-equilibrium flows using operator splitting

An efficient finite difference scheme is presented for the inviscid terms of the three-dimensional, compressible flow equations for chemical non-equilibrium gases. This scheme represents an extension and an improvement of one proposed by the author, and includes operator splitting.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized 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 linearized problem. 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 non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Holocene environmental changes in the lower Thames Valley, London, UK: implications for our understanding of the history of Taxus woodland

A radiocarbon-dated multiproxy palaeoenvironmental record from the Lower Thames Valley at Hornchurch Marshes has provided a reconstruction of the timing and nature of vegetation succession against a background of Holocene climate change, relative sea level movement and human activities. The investigation recorded widespread peat formation between c. 6300 and 3900 cal. yr BP (marine ‘regression’), succeeded by evidence for marine incursion. The multiproxy analyses of these sediments, comprising pollen, Coleoptera, diatoms, and plant and wood macrofossils, have indicated significant changes in both the wetland and dryland environment, including the establishment of Alnus (Alder) carr woodland, and the decline of both Ulmus (Elm; c. 5740 cal. yr BP) and Tilia (Lime; c. 5600 cal. yr BP, and 4160–3710 cal. yr BP). The beetle faunas from the peat also suggest a thermal climate similar to that of the present day. At c. 4900 cal. yr BP, Taxus (L.; Yew) woodland colonised the peatland forming a plant community that has no known modern analogue in the UK. The precise reason, or reasons, for this event remain unclear, although changes in peatland hydrology seem most likely. The growth of Taxus on peatland not only has considerable importance for our knowledge of the vegetation history of southeast England, and NW Europe generally, but also has wider implications for the interpretation of Holocene palaeobotanical records. At c. 3900 cal. yr BP, Taxus declined on the peatland surface during a period of major hydrological change (marine incursion), an event also strongly associated with the decline of dryland woodland taxa, including Tilia and Quercus, and the appearance of anthropogenic indicators.

Holocene palaeoenvironmental history and the impact of prehistoric salt production in the Seille Valley, Eastern France

The Seille Valley in eastern France was home to one of Europe’s largest Iron Age salt industries. Sedimentology, palynology and geochronology have been integrated within ongoing archaeological investigations to reconstruct the Holocene palaeoenvironmental history of the Seille Valley and to elucidate the human–environment relationship of salt production. A sedimentary model of the valley has been constructed from a borehole survey of the floodplain and pollen analyses have been undertaken to reconstruct the vegetation history. Alluvial records have been successfully dated using optically stimulated luminescence and radiocarbon techniques, thereby providing a robust chronological framework. The results have provided an insight into the development of favourable conditions for salt production and there is evidence in the sedimentary record to suggest that salt production may have taken place during the mid-to-late Bronze Age. The latter has yet to be identified in the archaeological record and targeted excavation is therefore underway to test this finding. The development of the Iron Age industry had a major impact on the hydrological regime of the valley and its sedimentological history, with evidence for accelerated alluviation arising from floodplain erosion at salt production sites and modification of the local fluvial regime due to briquetage accumulation on the floodplain. This research provides an important insight into the environmental implications of early industrial activities, in addition to advancing knowledge about the Holocene palaeoenvironmental and social history of this previously poorly studied region of France.