Interactive visualization of a thin disc around a Schwarzschild black hole

In the first course of general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a Schwarzschild black hole can be determined interactively by means of an analytic solution to the geodesic equation processed on current high performance graphical processing units. This approach can, in principle, be customized for any other thin disc in a spacetime with geodesics given in closed form. The interactive visualization discussed here can be used either in a first course of general relativity for demonstration purposes only or as a thesis for an enthusiastic student in an advanced course with some basic knowledge of OpenGL and a programming language.Comment: 9 pages, 4 figure

Mass and Width of the Rho Meson in a Nuclear Medium from Brown-Rho Scaling and QCD Sum Rules

We explore the range of values of the in-medium width of a $\rho$-meson at rest which is compatibale with the QCD sum rule approach in a nuclear medium assuming vector meson dominance and a Brown-Rho scaling law of the $\rho$-meson mass with the chiral condensate. The lower and upper bounds for the in-medium width are found to be strongly increasing with the decreasing mass of the $\rho$-meson (increasing nuclear density). We also study the bounds for the in-medium width in models not satisfying the Brown-Rho scaling law. It is shown that the in-medium width depends on how rapidly the mass decreases in comparison to the change of the quark condensate. The bounds for the in-medium width increase with density only if the relative change of the quark condensate is stronger than the relative decrease in mass. This is important for experimental tests of the Brown-Rho scaling paradigm and other dropping $\rho$-mass scenarios.Comment: Revised and extended version. In this version we also study the in-medium width for decreasing $\rho$-masses in models that do not satisfy the Brown-Rho scalin la

Spatial Smoothing Techniques for the Assessment of Habitat Suitability

Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of the observations is often violated in practice since the points at which the observations are collected are spatially aligned. While several approaches have been developed to analyse and account for spatial correlation in regression models with normally distributed responses, far less work has been done in the context of generalised linear models. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations

Control theoretic models of pointing

This article presents an empirical comparison of four models from manual control theory on their ability to model targeting behaviour by human users using a mouse: McRuer’s Crossover, Costello’s Surge, second-order lag (2OL), and the Bang-bang model. Such dynamic models are generative, estimating not only movement time, but also pointer position, velocity, and acceleration on a moment-to-moment basis. We describe an experimental framework for acquiring pointing actions and automatically fitting the parameters of mathematical models to the empirical data. We present the use of time-series, phase space, and Hooke plot visualisations of the experimental data, to gain insight into human pointing dynamics. We find that the identified control models can generate a range of dynamic behaviours that captures aspects of human pointing behaviour to varying degrees. Conditions with a low index of difficulty (ID) showed poorer fit because their unconstrained nature leads naturally to more behavioural variability. We report on characteristics of human surge behaviour (the initial, ballistic sub-movement) in pointing, as well as differences in a number of controller performance measures, including overshoot, settling time, peak time, and rise time. We describe trade-offs among the models. We conclude that control theory offers a promising complement to Fitts’ law based approaches in HCI, with models providing representations and predictions of human pointing dynamics, which can improve our understanding of pointing and inform design