On the accuracy of conservation of adiabatic invariants in slow-fast systems

Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in analytic systems. An iso-energetic reduction and canonical transformations are applied to transform the slow-fast systems to form of systems depending on slowly varying parameters in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given for such systems.Comment: 27 pages, 14 figure

Gravitational Constraint Combinations Generate a Lie Algebra

We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of finding alternative constraints for canonical gravity. The new scalars may be used in place of the hamiltonian constraint of general relativity and, together with the usual momentum constraints, replace the Dirac algebra for pure gravity with a true Lie algebra: the semidirect product of the Abelian algebra of the new constraint combinations with the algebra of spatial diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section 3 is expanded and an additional solution provided, minor errors correcte

The use of MCQs within team based learning: choosing the right approach to foster student learning

Team Based Learning (TBL) is a learning and assessment strategy that aims to foster learning through the facilitation and development of group cohesiveness which transforms small groups into effective learning teams. It is based on four principles: large teams; student accountability; use of assignments which promote learning and team development and frequent and immediate feedback. The latter two are the focus of this presentation. An outline of the how TBL operates in the classroom will be presented following which there will be a focus on assessment strategies. The key assessment strategy used in TBL is the multiple choice test (MCQ) which is used to assess the extent to which students have engaged with the pre-sessional learning activities. This is known as the readiness assurance test (RAT) and focusses on the understanding of key concepts. Students take the test individually (iRAT), and then take the same test as a group (tRAT). Each group is encouraged to discuss, to debate, to refer back to pre-sessional material, to propose, justify and eventually come to a group decision on what they believe to be the correct answer. Immediate feedback is a key feature of the RATs. MCQs as a commonly used assessment technique is re-visited in the context of its use in TBL. The challenges and benefits of different approaches to the MCQ tests are considered and the factors which influenced the final decision about which approach to use are discussed. The importance of immediacy of feedback in TBL is also outlined. Within the TBL process, following the iRAT and the tRAT, students work in groups on an application activity such as a case study following which each group will make a specific decision based on the information provided, drawing on their collective knowledge, understanding and ability to apply concepts covered in the pre-sessional learning materials. Groups report simultaneously on the choice made and the decision making process. It will be argued that TBL is a teaching and learning strategy which, through the use of specific learning and assessment activities, gives students immediate and on-going feedback and insight into their performance, promotes higher order learning and facilitates the development of interpersonal skills which are particularly appropriate for students on professional programmes

Higher Descent Data as a Homotopy Limit

We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of $n$-groupoids thus providing an analogous presentation of "descent data" in higher dimensions.Comment: Appeared in JHR

Two-proton events in the 17F(p,2p)16O reaction

In a recent experimental study (Gomez del Campo et al, PRL 86, 43 (2001)) of the reaction 17F(p,2p)16O, two-proton events were measured from excitations near a 1-, E*=6.15 MeV state in 18Ne. We calculate by means of R-matrix theory the resonant two-proton production cross section and branching ratios. We conclude that it is unlikely that two-proton production via population of the 1- state is sufficient to explain the observed two-proton events. Alternative sources of such events are discussed.Comment: 4 pages, 4 figures. Resubmission to Physical Review C (first received 6 March 2001

A New Star-Formation Rate Calibration from Polycyclic Aromatic Hydrocarbon Emission Features and Application to High Redshift Galaxies

We calibrate the integrated luminosity from the polycyclic aromatic hydrocarbon (PAH) features at 6.2\micron, 7.7\micron\ and 11.3\micron\ in galaxies as a measure of the star-formation rate (SFR). These features are strong (containing as much as 5-10\% of the total infrared luminosity) and suffer minimal extinction. Our calibration uses \spitzer\ Infrared Spectrograph (IRS) measurements of 105 galaxies at $0 < z < 0.4$, infrared (IR) luminosities of 10^9 - 10^{12} \lsol, combined with other well-calibrated SFR indicators. The PAH luminosity correlates linearly with the SFR as measured by the extinction-corrected \ha\ luminosity over the range of luminosities in our calibration sample. The scatter is 0.14 dex comparable to that between SFRs derived from the \paa\ and extinction-corrected \ha\ emission lines, implying the PAH features may be as accurate a SFR indicator as hydrogen recombination lines. The PAH SFR relation depends on gas-phase metallicity, for which we supply an empirical correction for galaxies with 0.2 < \mathrm{Z} \lsim 0.7~\zsol. We present a case study in advance of the \textit{James Webb Space Telescope} (\jwst), which will be capable of measuring SFRs from PAHs in distant galaxies at the peak of the SFR density in the universe ($z\sim2$) with SFRs as low as $\sim$~10~\sfrunits. We use \spitzer/IRS observations of the PAH features and \paa\ emission plus \ha\ measurements in lensed star-forming galaxies at $1 < z < 3$ to demonstrate the ability of the PAHs to derive accurate SFRs. We also demonstrate that because the PAH features dominate the mid-IR fluxes, broad-band mid-IR photometric measurements from \jwst\ will trace both the SFR and provide a way to exclude galaxies dominated by an AGN.Comment: Accepted for publication in Ap