Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Short-range urban dispersion experiments using fixed and moving sources

Four perfluorocarbon tracer dispersion experiments were carried out in central London, United Kingdom in 2004. These experiments were supplementary to the dispersion of air pollution and penetration into the local environment (DAPPLE) campaign and consisted of ground level releases, roof level releases and mobile releases; the latter are believed to be the first such experiments to be undertaken. A detailed description of the experiments including release, sampling, analysis and wind observations is given. The characteristics of dispersion from the fixed and mobile sources are discussed and contrasted, in particular, the decay in concentration levels away from the source location and the additional variability that results from the non-uniformity of vehicle speed. Copyright © 2009 Royal Meteorological Society

Imagining migration: Placing children's understanding of 'moving house' in Malawi and Lesotho

Research pertaining to children's geographies has mainly focused on children's physical experiences of space, with their 'imagined geographies' receiving far less attention. The few studies of children's imagined geographies that exist tend to focus on children's national identities and their understanding of distant places. However, children's lives are not necessarily static and they often move between places. Research has not so far considered children's images of these transitional spaces or how such images are constructed. Through an examination of over 800 thematic drawings and stories, regarding 'moving house, produced by children aged 10-17 years in urban and rural communities of Lesotho and Malawi, this paper explores southern African children's representations of migration. The research considers how ideas of migration are culturally-constructed based on notions of family, home and kinship, particularly in relation to the fluid family structure characteristic of most southern African societies. The results suggest that most children imagine migration as a household rather than an individual process.. rarely including micro -migrations between extended family households in their drawings. Further, children's images of migration are place-rooted in everyday life experiences. Their representations concentrate on the reasons for migration, both negative and positive, which are specifically related to their local social and environmental situations and whether house moves take place locally or over longer distances. The paper concludes by exploring the implications of these conceptualisations of moving house for children's contemporary migration experiences, particularly in light of changing family structures due to the effects of the HIV/AIDS pandernic. (c) 2005 Elsevier Ltd. All rights reserved

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - I. A universal approach to calculate thermal inertia

In this paper we pledge that physically based equations should be combined with remote sensing techniques to enable a more theoretically rigorous estimation of area-average soil heat flux, G. A standard physical equation (i.e. the analytical or exact method) for the estimation of G, in combination with a simple, but theoretically derived, equation for soil thermal inertia (F), provides the basis for a more transparent and readily interpretable method for the estimation of G; without the requirement for in situ instrumentation. Moreover, such an approach ensures a more universally applicable method than those derived from purely empirical studies (employing vegetation indices and albedo, for example). Hence, a new equation for the estimation of Gamma(for homogeneous soils) is discussed in this paper which only requires knowledge of soil type, which is readily obtainable from extant soil databases and surveys, in combination with a coarse estimate of moisture status. This approach can be used to obtain area-averaged estimates of Gamma(and thus G, as explained in paper II) which is important for large-scale energy balance studies that employ aircraft or satellite data. Furthermore, this method also relaxes the instrumental demand for studies at the plot and field scale (no requirement for in situ soil temperature sensors, soil heat flux plates and/or thermal conductivity sensors). In addition, this equation can be incorporated in soil-vegetation-atmosphere-transfer models that use the force restore method to update surface temperatures (such as the well-known ISBA model), to replace the thermal inertia coefficient.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - II. Diurnal shape of soil heat flux

For vegetated surfaces, calculation of soil heat flux, G, with the Exact or Analytical method requires a harmonic analysis of below-canopy soil surface temperature, to obtain the shape of the diurnal course of G. When determining G with remote sensing methods, only composite (vegetation plus soil) radiometric brightness temperature is available. This paper presents a simple equation that relates the sum of the harmonic terms derived for the composite radiometric surface temperature to that of belowcanopy soil surface temperature. The thermal inertia, Gamma(,) for which a simple equation has been presented in a companion paper, paper I, is used to set the magnitude of G. To assess the success of the method proposed in this paper for the estimation of the diurnal shape of G, a comparison was made between 'remote' and in situ calculated values from described field sites. This indicated that the proposed method was suitable for the estimation of the shape of G for a variety of vegetation types and densities. The approach outlined in paper I, to obtain Gamma, was then combined with the estimated harmonic terms to predict estimates of G, which were compared to values predicted by empirical remote methods found in the literature. This indicated that the method proposed in the combination of papers I and II gave reliable estimates of G, which, in comparison to the other methods, resulted in more realistic predictions for vegetated surfaces. This set of equations can also be used for bare and sparsely vegetated soils, making it a universally applicable method. (C) 2007 Elsevier B.V. All rights reserved.

Moving on. Where should the university map collection be going?

This paper argues for the importance of retaining a map library presence on UK university campuses at a time when many are under threat of closure, and access to geospatial data is increasingly moving to web-based services. It is suggested that the need for local expertise is undiminished and map curators need to redefine themselves as geoinformation specialists, preserving their paper map collections, but also meeting some of the challenges of GIS, and contributing to national developments in the construction of distributed geolibraries and the provision of metadata, especially with regard to local data sets.

Imagining migration: Placing children's understanding of 'moving house' in Malawi and Lesotho

Research pertaining to children's geographies has mainly focused on children's physical experiences of space, with their 'imagined geographies' receiving far less attention. The few studies of children's imagined geographies that exist tend to focus on children's national identities and their understanding of distant places. However, children's lives are not necessarily static and they often move between places. Research has not so far considered children's images of these transitional spaces or how such images are constructed. Through an examination of over 800 thematic drawings and stories, regarding 'moving house, produced by children aged 10-17 years in urban and rural communities of Lesotho and Malawi, this paper explores southern African children's representations of migration. The research considers how ideas of migration are culturally-constructed based on notions of family, home and kinship, particularly in relation to the fluid family structure characteristic of most southern African societies. The results suggest that most children imagine migration as a household rather than an individual process.. rarely including micro -migrations between extended family households in their drawings. Further, children's images of migration are place-rooted in everyday life experiences. Their representations concentrate on the reasons for migration, both negative and positive, which are specifically related to their local social and environmental situations and whether house moves take place locally or over longer distances. The paper concludes by exploring the implications of these conceptualisations of moving house for children's contemporary migration experiences, particularly in light of changing family structures due to the effects of the HIV/AIDS pandernic. (c) 2005 Elsevier Ltd. All rights reserved

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.