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.

Monthly average temperature modelling

This research is associated with the goal of the horticultural sector of the Colombian southwest, which is to obtain climatic information, specifically, to predict the monthly average temperature in sites where it has not been measured. The data correspond to monthly average temperature, and were recorded in meteorological stations at Valle del Cauca, Colombia, South America. Two components are identified in the data of this research: (1) a component due to the temporal aspects, determined by characteristics of the time series, distribution of the monthly average temperature through the months and the temporal phenomena, which increased (El Nino) and decreased (La Nina) the temperature values, and (2) a component due to the sites, which is determined for the clear differentiation of two populations, the valley and the mountains, which are associated with the pattern of monthly average temperature and with the altitude. Finally, due to the closeness between meteorological stations it is possible to find spatial correlation between data from nearby sites. In the first instance a random coefficient model without spatial covariance structure in the errors is obtained by month and geographical location (mountains and valley, respectively). Models for wet periods in mountains show a normal distribution in the errors; models for the valley and dry periods in mountains do not exhibit a normal pattern in the errors. In models of mountains and wet periods, omni-directional weighted variograms for residuals show spatial continuity. The random coefficient model without spatial covariance structure in the errors and the random coefficient model with spatial covariance structure in the errors are capturing the influence of the El Nino and La Nina phenomena, which indicates that the inclusion of the random part in the model is appropriate. The altitude variable contributes significantly in the models for mountains. In general, the cross-validation process indicates that the random coefficient model with spatial spherical and the random coefficient model with spatial Gaussian are the best models for the wet periods in mountains, and the worst model is the model used by the Colombian Institute for Meteorology, Hydrology and Environmental Studies (IDEAM) to predict temperature.

API-CALC 1.0: a computer program for calculating the average probability of identity allowing for substructure, inbreeding and the presence of close relatives

Individual identification via DNA profiling is important in molecular ecology, particularly in the case of noninvasive sampling. A key quantity in determining the number of loci required is the probability of identity (PIave), the probability of observing two copies of any profile in the population. Previously this has been calculated assuming no inbreeding or population structure. Here we introduce formulae that account for these factors, whilst also accounting for relatedness structure in the population. These formulae are implemented in API-CALC 1.0, which calculates PIave for either a specified value, or a range of values, for F-IS and F-ST.

Moving on: the challenges for foreign language learning on transition from primary to secondary school

Europe's commitment to language learning has resulted in higher percentages of pupils studying foreign languages during primary education. In England, recent policy decisions to expand foreign language learning at primary level by 2010 create major implications for transition to secondary. This paper presents findings on transition issues from case studies of a DfES-funded project evaluating 19 local authority Pathfinders piloting the introduction of foreign language learning at primary level. Research on transition in other countries sets these findings in context. Finally, it investigates the challenges England faces for transition in the light of this expansion and discusses future implications.

Simplified recursive identifier for ARMA processes

Symmetrical behaviour of the covariance matrix and the positive-definite criterion are used to simplify identification of single-input/single-output systems using recursive least squares. Simulation results are obtained and these are compared with ordinary recursive least squares. The adaptive nature of the identifier is verified by varying the system parameters on convergence.