Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures

In a previous paper (math-ph/0205016) an Euler angle parameterization for SU(N) was given. Here we present a generalized Euler angle parameterization for U(N). The formula for the calculation of the volume for U(N), CP(N) as well as other SU(N) and U(N) cosets will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrices under this parameterization will also be derived.Comment: 26 pages, no figures; minor edits, to be published in J. Geom. Phy

Sound clocks and sonic relativity

Sound propagation within certain non-relativistic condensed matter models obeys a relativistic wave equation despite such systems admitting entirely non-relativistic descriptions. A natural question that arises upon consideration of this is, "do devices exist that will experience the relativity in these systems?" We describe a thought experiment in which 'acoustic observers' possess devices called sound clocks that can be connected to form chains. Careful investigation shows that appropriately constructed chains of stationary and moving sound clocks are perceived by observers on the other chain as undergoing the relativistic phenomena of length contraction and time dilation by the Lorentz factor, with c the speed of sound. Sound clocks within moving chains actually tick less frequently than stationary ones and must be separated by a shorter distance than when stationary to satisfy simultaneity conditions. Stationary sound clocks appear to be length contracted and time dilated to moving observers due to their misunderstanding of their own state of motion with respect to the laboratory. Observers restricted to using sound clocks describe a universe kinematically consistent with the theory of special relativity, despite the preferred frame of their universe in the laboratory. Such devices show promise in further probing analogue relativity models, for example in investigating phenomena that require careful consideration of the proper time elapsed for observers.Comment: (v2) consistent with published version; (v1) 15 pages, 9 figure

Sensitivity of desert dust emissions to model horizontal grid spacing during the Bodélé Dust Experiment 2005

The impact of model horizontal grid spacing on meteorology and dust emissions in the Bodélé depression was investigated during the well-documented period of the Bodélé Dust Experiment 2005 (BoDEx 2005). Five horizontal grid spacing ranging from 100 km to 5 km were tested. The main conclusion of these sensitivity tests is that the meteorology of the Bodélé depression is quite insensitive to model horizontal grid spacing below 50 km in agreement with Todd et al.'s (2008b) results. Below 50 km, dust emissions also appear relatively insensitive to model mesh size, the influence of model horizontal grid spacing on dust emissions tending towards an asymptotic behavior as model mesh size is reduced

Exploring the role of museums for socially isolated older people

Research suggests that social prescribing schemes can offer health and psychological wellbeing benefits to older people across a range of interventions. The present study sought to understand how museum programmes, designed to support socially isolated older adults, created opportunities to enhance wellbeing and change experiences of social isolation. A grounded theory approach was used to analyse initial interviews, 3-month follow-up interviews, and participant diaries, from 12 participants who took part in 10-week programmes across six different museums in London and Kent. A theoretical model was developed showing elements of museum programmes, such as the role of the facilitator, activities and physical space, that enabled both individual journeys and relational processes. In addition, individual journeys and relational processes influenced each other, enhancing the experience. These components operated within an interacting social context that was enriched by the museum programme. The theoretical model links with psychological concepts of attachment theory and self-esteem to explain how cultural group programmes could provide opportunities for change in older people. Limitations of the research, implications for clinical practice and recommendations for future research are discussed

On sharing NATO defence burdens in the 1990s and beyond

This article investigates NATO burden sharing in the 1990s in light of strategic, technological, political and membership changes. Both an ability-to-pay and a benefits-received analysis of burden sharing are conducted. During 1990-99, there is no evidence of disproportionate burden sharing, where the large allies shoulder the burdens of the small. Nevertheless, the theoretical model predicts that this disproportionality will plague NATO in the near future. Thus far, there is still a significant concordance between benefits received and defence burdens carried. When alternative expansion scenarios are studied, the extent of disproportionality of burden sharing increases as NATO grows in size. A broader security burden-sharing measure is devised and tested; based on this broader measure, there is still no disproportionality evident in the recent past.