Second order splitting of a class of fourth order PDEs with point constraints

We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments

Formation of ultracold LiRb molecules by photoassociation near the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote

We report the production of ultracold 7Li85Rb molecules by photoassociation (PA) below the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We perform PA spectroscopy in a dual-species 7Li-85Rb magneto-optical trap (MOT) and detect the PA resonances using trap loss spectroscopy. We observe several strong PA resonances corresponding to the last few bound states, assign the lines and derive the long range C6 dispersion coefficients for the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We also report an excited-state molecule formation rate (P_LiRb) of ~10^7 s^-1 and a PA rate coefficient (K_PA) of ~4x10^-11 cm^3/s, which are both among the highest observed for heteronuclear bi-alkali molecules. These suggest that PA is a promising route for the creation of ultracold ground state LiRb molecules.Comment: 6 page

Diversity, Dilemmas and Transformation in Post-Compulsory Education: an Introduction to the Special Issue on Work Based Research

As governments recognize the central place of post-compulsory education in regenerating and modernizing the economic and social fabric of society (BIS 2008), it is appropriate for us as educational researchers to question whether this recognition beckons a different role for research in post-compulsory education. Much of this research is work based, using a broad interpretation of this term, and the majority of articles received by this journal (though the proportion published is a lower one) reflect this balance. Work based research in education poses particular challenges for the researcher and the practitioner, whether the focus is practitioner research, in which case the dilemmas can centre on potential role conflict between practitioner and researcher roles, or whether the work based research is observational – analyzing others’ professional practice, in which case the dilemmas can centre on power relations between researcher and researched, the politics of research, and ethical questions around care for participants and the degree of their involvement or non-involvement in the total research enterprise. This article reviews the prospects for work based research in post-compulsory education and introduces the articles in this special issue