Four bugs on a rectangle

The problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of 10^427907250, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth’s double-arrow notation and level-index arithmetic are discussed

On the scaling behaviour of cross-tie domain wall structures in patterned NiFe elements

The cross-tie domain wall structure in micrometre and sub-micrometre wide patterned elements of NiFe, and a thickness range of 30 to 70nm, has been studied by Lorentz microscopy. Whilst the basic geometry of the cross-tie repeat units remains unchanged, their density increases when the cross-tie length is constrained to be smaller than the value associated with a continuous film. This occurs when element widths are sufficiently narrow or when the wall is forced to move close to an edge under the action of an applied field. To a very good approximation the cross-tie density scales with the inverse of the distance between the main wall and the element edge. The experiments show that in confined structures, the wall constantly modifies its form and that the need to generate, and subsequently annihilate, extra vortex/anti-vortex pairs constitutes an additional source of hysteresis.Comment: 4 pages, 5 figures, accepted for publication in Europhysics Letters (EPL

Automatically-focusing microscope system for live tissue observation

System includes focus-sensing arrangement which controls servo to keep microscope constantly focused on target. Microscope objective is moved along optical axis. System includes two video cameras that are used as transducers for sensing focus. Incoming visual image is split by beam splitter so that one-half of information is fed to each camera

The prevalence, influential factors and mechanisms of relative age effects in UK Rugby League.

Relative age effects (RAEs), reflecting observed inequalities in participation and attainment as a result of annual age-grouping policies in youth sport, are common in most team sports. The aims of this study were to determine if and when RAEs become apparent in Rugby League, determine how influential variables (e.g., gender) lead and clarify whether player retention at junior representative levels can explain persistent RAEs. Player data were collected for the male and female community games ranging from Under 7s to Senior (N=15,060) levels, junior representative selections (i.e., Regional) and professional players (N=298). Chi-square analyses found significant (P<0.05) uneven birth date distributions beginning at the earliest stages of the game and throughout into senior professionals. In junior representative selections, 47.0% of Regional and 55.7% of National representative players were born in Quartile 1, with RAE risk increasing with performance level. Gender and nationality were also found to moderate RAE risk. When tracking representative juniors, over 50% were retained for similar competition the following season. Findings clearly demonstrate that RAEs exist throughout Rugby League with early selection, performance level and retention processes, appearing to be key contributing factors responsible for RAE persistence

Parks, people and pixels: evaluating landscape effects of an East African national park on its surroundings

Landscapes surrounding protected areas, while still containing considerable biodiversity, have rapidly growing human populations and associated agricultural development in most of the developing world that tend to isolate them, potentially reducing their conservation value. Using field studies and multi-temporal Landsat imagery, we examine a forest park, Kibale National Park in western Uganda, its changes over time, and related land cover change in the surrounding landscape. We find Kibale has successfully defended its borders and prevents within-park deforestation and other land incursions, and has maintained tree cover throughout the time period of the study. Outside the park there was a significant increase in tea plantations and continued forest fragmentation and wetland loss. The question of whether the park is a conservation success because of the network of forest fragments and wetlands or in spite of them remains unanswered

Trends and Variability in Localized Precipitation Around Kibale National Park, Uganda, Africa

Our objective was to understand and describe local spatial and temporal variability in precipitation around Kibale National Park, a tropical forest area of high conservation value. Continental or regional-scale trends are often relied upon to make policy and management decisions, but these analyses are often at too coarse a resolution to capture important variability at a finer scale where management actions operate. Monthly rainfall data derived from ten long-term station records (1941-1975) were used to evaluate local spatiotemporal variability in seasonal and annual rainfall for the area surrounding Kibale National Park. The magnitude, direction and significance of trends in seasonal and annual rainfall within the area surrounding the park were identified using the Mann-Kendall trend test and Sen’s slope estimator. The standardized precipitation index was calculated at 3- and 12-month periods to identify areas of relative wetness or dryness. Analysis of annual trends and precipitation indices indicated that patterns in annual time series do not reflect the direction and magnitude of seasonal trends nor the spatial variability in intra-annual rainfall at the local scale. Significant negative trends in the seasonal long rains, following dry season and short rains were identified at stations west of Kibale, while significant positive trends in the seasonal short rains occurred at stations north of the park. Stations along the western park boundary tended to have more years in which the two dry seasons were abnormally dry than those stations located further from the park

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.Comment: 18 pages, 10 figures, preprin

A perturbation density functional theory for the competition between inter and intramolecular association

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient

Modelling an isolated dust grain in a plasma using matched asymptotic expansions

The study of dusty plasmas is of significant practical use and scientific interest. A characteristic feature of dust grains in a plasma is that they are typically smaller than the electron Debye distance, a property which we exploit using the technique of matched asymptotic expansions. We first consider the case of a spherical dust particle in a stationary plasma, employing the Allen–Boyd–Reynolds theory, which assumes cold, collisionless ions. We derive analytical expressions for the electric potential, the ion number density and ion velocity. This requires only one computation that is not specific to a single set of dust–plasma parameters, and sheds new light on the shielding distance of a dust grain. The extension of this calculation to the case of uniform ion streaming past the dust grain, a scenario of interest in many dusty plasmas, is less straightforward. For streaming below a certain threshold we again establish asymptotic solutions but above the streaming threshold there appears to be a fundamental change in the behaviour of the system