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.

Formation of triple helical nanofibers using self-assembling chiral benzene-1,3,5-tricarboxamides and reversal of the nanostructure's handedness using mirror image building blocks

Intertwining triple helical nanofibers with an overall handedness have been formed from self-assembling chiral benzene-1,3,5-tricarboxamides 1, 2 and 3, whereas the achiralbenzene-1,3,5-tricarboxamide 4 upon self-association gives rise to straight nanofibers without any twist and transmission electron microscopy images of chiral compounds clearly demonstrate that the handedness of the triple helical nanofibers can be reversed by using the enantiomeric benzene-1,3,5-tricarboxamide building blocks.

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.

The perception of emotion from body movement in point-light displays of interpersonal dialogue

We examined whether it is possible to identify the emotional content of behaviour from point-light displays where pairs of actors are engaged in interpersonal communication. These actors displayed a series of emotions, which included sadness, anger, joy, disgust, fear, and romantic love. In experiment 1, subjects viewed brief clips of these point-light displays presented the right way up and upside down. In experiment 2, the importance of the interaction between the two figures in the recognition of emotion was examined. Subjects were shown upright versions of (i) the original pairs (dyads), (ii) a single actor (monad), and (iii) a dyad comprising a single actor and his/her mirror image (reflected dyad). In each experiment, the subjects rated the emotional content of the displays by moving a slider along a horizontal scale. All of the emotions received a rating for every clip. In experiment 1, when the displays were upright, the correct emotions were identified in each case except disgust; but, when the displays were inverted, performance was significantly diminished for some ernotions. In experiment 2, the recognition of love and joy was impaired by the absence of the acting partner, and the recognition of sadness, joy, and fear was impaired in the non-veridical (mirror image) displays. These findings both support and extend previous research by showing that biological motion is sufficient for the perception of emotion, although inversion affects performance. Moreover, emotion perception from biological motion can be affected by the veridical or non-veridical social context within the displays.