General tooth boundary conditions for equation free modelling

We are developing a framework for multiscale computation which enables models at a ``microscopic'' level of description, for example Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators, to perform modelling tasks at ``macroscopic'' length scales of interest. The plan is to use the microscopic rules restricted to small "patches" of the domain, the "teeth'', using interpolation to bridge the "gaps". Here we explore general boundary conditions coupling the widely separated ``teeth'' of the microscopic simulation that achieve high order accuracy over the macroscale. We present the simplest case when the microscopic simulator is the quintessential example of a partial differential equation. We argue that classic high-order interpolation of the macroscopic field provides the correct forcing in whatever boundary condition is required by the microsimulator. Such interpolation leads to Tooth Boundary Conditions which achieve arbitrarily high-order consistency. The high-order consistency is demonstrated on a class of linear partial differential equations in two ways: firstly through the eigenvalues of the scheme for selected numerical problems; and secondly using the dynamical systems approach of holistic discretisation on a general class of linear \textsc{pde}s. Analytic modelling shows that, for a wide class of microscopic systems, the subgrid fields and the effective macroscopic model are largely independent of the tooth size and the particular tooth boundary conditions. When applied to patches of microscopic simulations these tooth boundary conditions promise efficient macroscale simulation. We expect the same approach will also accurately couple patch simulations in higher spatial dimensions.Comment: 22 page

Modelling and simulation framework for reactive transport of organic contaminants in bed-sediments using a pure java object - oriented paradigm

Numerical modelling and simulation of organic contaminant reactive transport in the environment is being increasingly relied upon for a wide range of tasks associated with risk-based decision-making, such as prediction of contaminant profiles, optimisation of remediation methods, and monitoring of changes resulting from an implemented remediation scheme. The lack of integration of multiple mechanistic models to a single modelling framework, however, has prevented the field of reactive transport modelling in bed-sediments from developing a cohesive understanding of contaminant fate and behaviour in the aquatic sediment environment. This paper will investigate the problems involved in the model integration process, discuss modelling and software development approaches, and present preliminary results from use of CORETRANS, a predictive modelling framework that simulates 1-dimensional organic contaminant reaction and transport in bed-sediments

Anisotropic magnetoresistance contribution to measured domain wall resistances of in-plane magnetised (Ga,Mn)As

We demonstrate the presence of an important anisotropic magnetoresistance contribution to the domain wall resistance recently measured in thin-film (Ga,Mn)As with in-plane magnetic anisotropy. Analytic results for simple domain wall orientations supplemented by numerical results for more general cases show this previously omitted contribution can largely explain the observed negative resistance.Comment: 4 pages; submitted to Phys Rev

Soil sustainability in organic agricultural production

Traditionally, the assessment of soil sustainability and the potential impact of cultivation are based upon the application of chemical procedures. In the absence of a biological context, these measurements offer little in understanding longterm changes in soil husbandry. Detailed microcosm investigations were applied as a predictive tool for management change. The microcosms were designed with homogenised soils treated with organic amendments. Key soil functional relationships were quantified using stable isotope techniques, biochemical measurements and traditional approaches

Enterprise profiles in deprived areas: Are they distinctive?

This paper examines the extent to which segmenting business activity on the basis of the relative deprivation of a given area provides additional understanding (in terms of analysis and policy) that is not obtained by alternative divisions, e.g., by sector, size, etc. The paper is primarily motivated by the explicit inclusion of a deprived area dimension to many UK small business/enterprise policies introduced since 1997. We use two datasets drawn from the customer records of Barclays Bank PLC to obtain an initial analysis of the business stocks and dynamics in deprived and non-deprived areas of England. The data indicate that the deprived areas of England vary systematically from the wider economy in terms of several business stock characteristics and associated dynamics. These differences include a lower proportion of business service firms, lower female involvement in the owner-manager base and a poorer risk profile. The analysis supports the view that there are likely to be benefits from the tailoring of small business/ enterprise policies to sub-national levels