2015 researcher's mini-symposium

Postgraduate researchers from the Faculties of Science, Engineering, Medicine & Surgery and Health Sciences gathered for a forum to present their research interests. The symposium was held in the afternoon of 30 January 2015 in the Engineering Lecture Theatre. The symposium promoted multi-disciplinary networking between various university faculties. Participants were invited based on research topic diversity and gender balance.peer-reviewe

RPA vs. exact shell-model correlation energies

The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We find that in general HF+RPA gives a very good approximation to the ``exact'' ground state energy. In those cases where RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wavefunction.Comment: 6 pages, 7 figures, submitted to Phys Rev

Tests of the random phase approximation for transition strengths

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hbar\omega$ shell-model spaces. The RPA and shell-model results are in reasonable agreement for most transitions; however some very low-lying collective transitions, such as isoscalar quadrupole, are in serious disagreement. We suggest the failure lies with incomplete restoration of broken symmetries in the RPA. Furthermore we prove, analytically and numerically, that standard statements regarding the energy-weighted sum rule in the RPA do not hold if an exact symmetry is broken.Comment: 11 pages, 7 figures; Appendix added with new proof regarding violation of energy-weighted sum rul

Letters from William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of the mathematical community at the turn of the 20th century.Comment: documentclass amsart, 17 page

A PRELIMINARY ASSESSMENT OF THE MACROINVERTEBRATE BIODIVERSITY OF CORN CREEK

In order to provide baseline data for future research of Corn Creek in Young Harris Georgia, a survey of the macroinvertebrate community was performed in fall 2016 from October 3rd to November 3rd, to determine if diversity decreases downstream in relation to human impact. Human activity and development generally increases as distance from the headwaters increase. Four sites on Corn Creek were sampled for macroinvertebrates using Georgia Adopt-A-Stream protocols, and organisms were identified to family level when possible. The four sampled sites were located at the creek headwaters at an underground spring, upstream of an ~15 m falls, downstream of the falls and where the creek feeds into Brasstown Creek. Shannon and Simpson’s diversity indices were calculated from the data collected. The sampled site upstream of the falls was in proximity to an area used by vehicular traffic to cross the creek, and this may have had a negative impact on the diversity at that site. The samples themselves yielded a large number of Ephemeroptera and Plecoptera especially the families Heptagenniidae (flathead mayflies) and Peltoperlidae (roach-like stoneflies). However, preliminary analysis of the data does not appear to support the hypothesis that diversity decreases downstream in relation to human impac

Immobilisation and functional treatment for acute lateral ankle ligament injuries in adults

Prevention, Population and Disease management (PrePoD