Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure

Distributed intelligence in pedestrian simulations

In order to accurately simulate pedestrian behaviour in complex situations, one is required to model both the physical environment and the strategic decision-making of individuals We present a method for integrating both of these model requirements, by distributing the computational complexity across discrete modules. These modules communicate with each other via XML messages. The approach also provides considerable flexibility for changing and evolving the model. The model is explained using an example of simulating hikers in the Swiss Alps.SNF, NFP 48, Habitats and Landscapes of the Alp

The blending region hybrid framework for the simulation of stochastic reaction-diffusion processes

The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to ignore stochastic fluctuations and use a more efficient coarse-grained simulation approach. Nevertheless, for multiscale systems which exhibit significant spatial variation in concentration, a coarse-grained approach may not be appropriate throughout the simulation domain. Such scenarios suggest a hybrid paradigm in which a computationally cheap, coarse-grained model is coupled to a more expensive, but more detailed fine-grained model enabling the accurate simulation of the fine-scale dynamics at a reasonable computational cost. In this paper, in order to couple two representations of reaction-diffusion at distinct spatial scales, we allow them to overlap in a "blending region". Both modelling paradigms provide a valid representation of the particle density in this region. From one end of the blending region to the other, control of the implementation of diffusion is passed from one modelling paradigm to another through the use of complementary "blending functions" which scale up or down the contribution of each model to the overall diffusion. We establish the reliability of our novel hybrid paradigm by demonstrating its simulation on four exemplar reaction-diffusion scenarios.Comment: 36 pages, 30 figure

Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures

Measures of Fluid Loss during Surfing: A Preliminary Analysis in Recreational Surfers

Surfing is a popular sport, but little is known about the extent to which recreational surfers experience fluid loss from this activity. The principal objective of this research was to estimate fluid loss during a surfing session through changes in pre- to post-session urine color (Ucol), urine osmolality (Uosm), and body mass (BM). Data were collected from 11 recreational surfers across 14 surf sessions conducted under various environmental (mean water temperature = 22.1 SD ± 2.3; range = 20-26oC; air temperature range = 13.1-31.5oC; relative humidity range = 37.5-88.1%) and surfing conditions (e.g. winter/summer, wave type, location, environmental and water conditions). Linear mixed effects models indicated that participants experienced significant pre- to post-session changes in BM (p \u3c 0.001), but not in Ucol or Uosm. These findings suggested that recreational surfers may experience fluid loss (measured by pre- to post-surfing BM) that may impact on their performance and health, and therefore they should adopt a hydration strategy to minimize this impact