On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.Comment: 22 pages, 6 figure

Slip, Slop, Slap, Slide, Seek and Sport: A Systematic Scoping Review of Sun Protection in Sport in Australasia

Australia and New Zealand have the highest incidence of skin cancer. Sport is a fundamental part of Australasian culture, beginning in childhood, often with life-long participation. Participating in outdoor sports can contribute significantly to the lifetime ultraviolet radiation (UVR) dose individuals receive and their risk of developing skin cancer. This systematic scoping review explores the use of sun-protection by outdoor sporting participants in Australasia and considers how sun-protection practices may be improved and better evaluated in the community. A search of electronic databases using the search strategy “sun protection” AND “sport” AND “Australia” yielded 17 studies published in English from January 1992 to August 2021. Study methods included using UV-dosimeters to measure individual UVR-exposure; remote estimates of clothing-adjusted UVR-exposure; direct observation of sun-protection practices; and self-reported sun-exposure and sun-protection. Despite 40 years of ‘Slip, Slop, Slap’ campaigns in Australia, the use of sun-protection in most outdoor sports is inadequate. The paucity of comparable data limited our analyses, demonstrating a need for standardized, objective evaluation tools. Such tools, if used across a range of sports, should inform the development of workable recommendations that sporting clubs could implement and adopt into policy, thus empowering them to better protect the health of their participants