Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains

Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is subdiffusion. Many models of subdiffusion include a history dependence. This greatly confounds efforts to incorporate domain growth. Here we derive the fractional partial differential equations that govern subdiffusion on a growing domain, based on a Continuous Time Random Walk. This requires the introduction of a new, comoving, fractional derivative.Comment: 12 pages, 1 figur

BIOMECHANICAL GOLF SWING ANALYSIS

The Biomechanics Laboratory of the Australian Institute of Sport has spent eight years developing a comprehensive golf swing analysis system. The system is designed to assist the golfer and professional golf coach in identifying problems within the goWs swing and enable corrections to be made so that the golfer may reach full potential. Correct weight transference is a major component of the perfect swing. The Golf Analysis System measures changes in the centre of pressure of the golfer during the swing which provides a measure of the golfer's weight transference pattern. The path the club follows during the swing is directly related to the quality of the swing. An automatic digitising system is used in the Golf Analysis System to capture the location of the club shaft every one two-hundredths of the second during the swing. This path is then reconstructed by computer, plotted on paper and animated on video for review purposes. Views from the front, side and above the club path plane are reconstructed in relation to the movement of the leading shoulder for examination. The absolute velocity of the club's head is obtained and plotted out for 0.1 sec. before impact to 0.1 seconds after impact. The velocity components of the club head in the forward, crosswise and vertical direction are also plotted out which provides information as to the direction the club head is moving at the time of ball contact. A graph of the angle that the club is making to the desired ball path is also graphed out from 0.02 seconds before impact to 0.02 seconds after impact. A split vision video image of the golf swing is f h e d during the swing. This is captured by way of two shuttered S-VHS video cameras located directly above and to the open side of the golfer. The video provides a complete visual image of each entire golf swing analyzed. The position of the golf club head during ball contact phase has a direct relationship to the path the ball will follow after ball contact. In the Golf Analysis System the path of the golf club head is captured by a high speed video camera (400 frames per second) several frames before ball contact to several frames after contact. Sensors in the tee-off platform provide immediate feedback on the velocity of the club head immediately before impact and velocity of the ball immediately after impact. The direction and elevation of ball flight is also measured by sensors. A printout of this information together with where the ball would have landed as a d tof the swing is also provided in printouts. The Golf Analysis System provides valuable information about the golfefs swing which if used properly can produce drastic improvement in the goWs game. To be most effective a professional golf coach should be utilised to eliminate faults which are disclosed by Golf Analysis System. The swing analysis of 65 third year apprentices in the Australian P.G.A. professional coaching course has come up with some interesting information. This information will be presented at the ISBS 1995 Symposium

Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains

Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a one-dimensional domain that is evolving. The model equations, which have been derived from generalized continuous time random walks, can incorporate complexities such as subdiffusive transport and inhomogeneous domain stretching and shrinking. A method for constructing analytic expressions for short time moments of the position of the particles is developed and moments calculated from this approach are shown to compare favourably with results from random walk simulations and numerical integration of the reaction transport equation. The results show the important role played by the initial condition. In particular, it strongly affects the time dependence of the moments in the short time regime by introducing additional drift and diffusion terms. We also discuss how our reaction transport equation could be applied to study the spreading of a population on an evolving interface.Comment: 38 pages, 10 figure

Effects of Preventative Ankle Taping on Planned Change-of-Direction and Reactive Agility Performance and Ankle Muscle Activity in Basketballers

This study investigated the effects of preventative ankle taping on planned change-of-direction and reactive agility performance and peak ankle muscle activity in basketballers. Twenty male basketballers (age = 22.30 ± 3.97 years; height = 1.84 ± 0.09 meters; body mass = 85.96 ± 11.88 kilograms) with no ankle pathologies attended two testing sessions. Within each session, subjects completed six planned and six reactive randomized trials (three to the left and three to the right for each condition) of the Y-shaped agility test, which was recorded by timing lights. In one session, subjects had both ankles un-taped. In the other, both ankles were taped using a modified subtalar sling. Peak tibialis anterior, peroneus longus (PL), peroneus brevis (PB), and soleus muscle activity was recorded for both the inside and outside legs across stance phase during the directional change, which was normalized against 10-meter sprint muscle activity (nEMG). Both the inside and outside cut legs during the change-of-direction step were investigated. Repeated measures ANOVA determined performance time and nEMG differences between un-taped and taped conditions. There were no differences in planned change-of-direction or reactive agility times between the conditions. Inside cut leg PL nEMG decreased when taped for the planned left, reactive left, and reactive right cuts (p = 0.01). Outside leg PB and soleus nEMG increased during the taped planned left cut (p = 0.02). There were no other nEMG changes during the cuts with taping. Taping did not affect change-of-direction or agility performance. Inside leg PL activity was decreased, possibly due to the tape following the line of muscle action. This may reduce the kinetic demand for the PL during cuts. In conclusion, ankle taping did not significantly affect planned change-of-direction or reactive agility performance, and did not demonstrate large changes in activity of the muscle complex in healthy basketballers

Genipin crosslinking decreases the mechanical wear and biochemical degradation of impacted cartilage in vitro

High energy trauma to cartilage causes surface fissures and microstructural damage, but the degree to which this damage renders the tissue more susceptible to wear and contributes to the progression of post-traumatic osteoarthritis (PTOA) is unknown. Additionally, no treatments are currently available to strengthen cartilage after joint trauma and to protect the tissue from subsequent degradation and wear. The purposes of this study were to investigate the role of mechanical damage in the degradation and wear of cartilage, to evaluate the effects of impact and subsequent genipin crosslinking on the changes in the viscoelastic parameters of articular cartilage, and to test the hypothesis that genipin crosslinking is an effective treatment to enhance the resistance to biochemical degradation and mechanical wear. Results demonstrate that cartilage stiffness decreases after impact loading, likely due to the formation of fissures and microarchitectural damage, and is partially or fully restored by crosslinking. The wear resistance of impacted articular cartilage was diminished compared to undamaged cartilage, suggesting that mechanical damage that is directly induced by the impact may contribute to the progression of PTOA. However, the decrease in wear resistance was completely reversed by the crosslinking treatments. Additionally, the crosslinking treatments improved the resistance to collagenase digestion at the impact-damaged articular surface. These results highlight the potential therapeutic value of collagen crosslinking via genipin in the prevention of cartilage degeneration after traumatic injury

Recycling bins, garbage cans or think tanks? Three myths regarding policy analysis institutes

The phrase 'think tank' has become ubiquitous – overworked and underspecified – in the political lexicon. It is entrenched in scholarly discussions of public policy as well as in the 'policy wonk' of journalists, lobbyists and spin-doctors. This does not mean that there is an agreed definition of think tank or consensual understanding of their roles and functions. Nevertheless, the majority of organizations with this label undertake policy research of some kind. The idea of think tanks as a research communication 'bridge' presupposes that there are discernible boundaries between (social) science and policy. This paper will investigate some of these boundaries. The frontiers are not only organizational and legal; they also exist in how the 'public interest' is conceived by these bodies and their financiers. Moreover, the social interactions and exchanges involved in 'bridging', themselves muddy the conception of 'boundary', allowing for analysis to go beyond the dualism imposed in seeing science on one side of the bridge, and the state on the other, to address the complex relations between experts and public policy