Convergent Chaos

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the 'butterfly effect' needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts

Assessment of an electronic voting system within the tutorial setting: a randomised controlled trial (ISRCTN54535861)

Background: Electronic voting systems have been used in various educational settings with little measurement of the educational impact on students. The goal of this study was to measure the effects of the inclusion of an electronic voting system within a small group tutorial. Method: A prospective randomised controlled trial was run at the Royal Adelaide Hospital, a teaching hospital in Adelaide, Australia. 102 students in their first clinical year of medical school participated in the study where an electronic voting system was introduced as a teaching aid into a standard tutorial. Long-term retention of knowledge and understanding of the topics discussed in the tutorials was measured and student response to the introduction of the electronic voting system was assessed. Results: Students using the electronic voting system had improved long-term retention of understanding of material taught in the tutorial. Students had a positive response to the use of this teaching aid. Conclusion: Electronic voting systems can provide a stimulating learning environment for students and in a small group tutorial may improve educational outcomes.Edward J. Palmer, Peter G. Devitt, Neville J. De Young and David Morri

Properties of the solvation force of a two-dimensional Ising strip in scaling regimes

We consider d=2 Ising strip with surface fields acting on boundary spins. Using the properties of the transfer matrix spectrum we identify two pseudotransition temperatures and show that they satisfy similar scaling relations as expected for real transition temperatures in strips with d>2. The solvation force between the boundaries of the strip is analysed as a function of temperature, surface fields and the width of the strip. For large widths the solvation force can be described by scaling functions in three different regimes: in the vicinity of the critical wetting temperature of 2D semi-infinite system, in the vicinity of the bulk critical temperature, and in the regime of weak surface fields where the critical wetting temperature tends towards the bulk critical temperature. The properties of the relevant scaling functions are discussed

TGRS Observations of Positron Annihilation in Classical Novae

The TGRS experiment on board the Wind spacecraft has many advantages as a sky monitor --- broad field of view (~2 pi) centered on the south ecliptic pole), long life (1994-present), and stable low background and continuous coverage due to Wind's high altitude high eccentricity orbit. The Ge detector has sufficient energy resolution (3-4 keV at 511 keV) to resolve a cosmic positron annihilation line from the strong background annihilation line from beta-decays induced by cosmic ray impacts on the instrument, if the cosmic line is Doppler-shifted by this amount. Such lines (blueshifted) are predicted from nucleosynthesis in classical novae. We have searched the entire TGRS database for 1995-1997 for this line, with negative results. In principle such a search could yield an unbiased upper limit on the highly-uncertain Galactic nova rate. We carefully examined the times around the known nova events during this period, also with negative results. The upper limit on the nova line flux in a 6-hr interval is typically <3.8 E-3 photon/(cm2 s) at 4.6 sigma. We performed the same analysis for times around the outburst of Nova Vel 1999, obtaining a worse limit due to recent degradation of the detector response caused by cosmic ray induced damage.Comment: 5 pp. inc. 3 figs. Proc. 5th Compton Symposium (AIP Conf. Series), ed. M. McConnell, in pres