Second order accurate upwind difference schemes for scalar conservation laws with source terms

A second order accurate, characteristic-based, finite difference scheme is developed for scalar conservation laws with source terms. The scheme is an extension of well-known second order scalar schemes for homogeneous conservation laws. Such schemes have proved immensely powerful when applied to homogeneous systems of conservation laws using flux-difference splitting. Many application areas, however, involve inhomogeneous systems of conservation laws with source terms, and the scheme presented here is applied to such systems in a subsequent paper.

The impact of minimum services laws on real estate brokerage competitive intensity

As many as fourteen US states have now mandated minimum service requirements for real estate brokerage relationships in residential transactions. This study attempts to determine whether these minimum service laws have any impact on brokerage competition. Federal government agencies allege such laws discourage competition because they limit the offering of nontraditional brokerage services. However, alternatively, a legislative “bright line” definition of the lowest level of acceptable service may reduce any perceived risk in offering non-traditional brokerage services and therefore encourage competition. Using several empirical strategies and state-level data over nine years (2000-08), we do not find any consistent and significant impact (positive/negative) of minimum services laws on number of licensees per 100 households, our proxy for competition. Interestingly, we also find that association strength, as measured by Realtor association membership penetration, has a strong deterring effect on competition.

A child’s burial in unconsecrated ground in early modern Dorchester

Re-examination of a child burial found during excavations in advance of the construction of new offices for Dorset County Council in the north-west quarter of Dorchester in 1937 indicates that it is of early modern, rather than of Roman date, as originally believed at the time of excavation. A possible context is explored for the burial of a child in unconsecrated ground in the 17th century.

Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

In situ preservation of wetland heritage: hydrological and chemical change in the burial environment of the Somerset Levels, UK.

In Situ preservation is a core strategy for the conservation and management of waterlogged remains at wetland sites. Inorganic and organic remains can, however, quickly become degraded, or lost entirely, as a result of chemical or hydrological changes. Monitoring is therefore crucial in identifying baseline data for a site, the extent of spatial and or temporal variability, and in evaluating the potential impacts of these variables on current and future In Situ preservation potential. Since August 2009, monthly monitoring has taken place at the internationally important Iron Age site of Glastonbury Lake Village in the Somerset Levels, UK. A spatial, stratigraphic, and analytical approach to the analysis of sediment horizons and monitoring of groundwater chemistry, redox potential, water table depth and soil moisture (using TDR) was used to characterize the site. Significant spatial and temporal variability has been identified, with results from water-table monitoring and some initial chemical analysis from Glastonbury presented here. It appears that during dry periods parts of this site are at risk from desiccation. Analysis of the chemical data, in addition to integrating the results from the other parameters, is ongoing, with the aim of clarifying the risk to the entire site.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.