An anti-symmetric exclusion process for two particles on an infinite 1D lattice

A system of two biased, mutually exclusive random walkers on an infinite 1D lattice is studied whereby the intrinsic bias of one particle is equal and opposite to that of the other. The propogator for this system is solved exactly and expressions for the mean displacement and mean square displacement (MSD) are found. Depending on the nature of the intrinsic bias, the system's behaviour displays two regimes, characterised by (i) the particles moving towards each other and (ii) away from each other, both qualitatively different from the case of no bias. The continuous-space limit of the propogator is found and is shown to solve a Fokker-Planck equation for two biased, mutually exclusive Brownian particles with equal and opposite drift velocity.Comment: 19 pages, 5 figure

Validation of the aerodynamic loading on basic flying disc geometries derived from CFD simulations

The present study in spin stabilised disc aerodynamics builds on previous experimental wind tunnel work to broaden the knowledge base through CFD simulation without the necessity for high facility or time cost. The current experimental database from previous studies is extensive enough for sufficient validation to be conducted on known geometries. From there, the limitations of CFD studies for this application on such complex highly separated bluff body flows can be understood. All of the results are for non-spinning discs to reduce computational time, this step is justifiable as the spinning case has previously been shown to have minimal effect on the aerodynamic loads at typical throw release spin rates. The work builds CFD simulation cases carefully and systematically starting with cylindrical discs with thickness to chord (diameter) ratio of 0.01 and 0.1, then to introduce a cavity to one flat side analogous to the Frisbee disc, before moving to look at a generic discus geometry from field athletics. The aerodynamic loading results compare very well to experimental data for the low angle of attack range, however, at higher angles of attack the CFD curves are divergent. It is possible that the generated mesh, for each geometry, does not capture the wake with enough resolution at high angles of attack, note that for sports disc applications the high angle of attack range is very important towards the end of the flight from a human throw. Therefore, further investigations are required to extend this initial study to a modified meshing regime with further refinement, prior to moving forward with any parametric design studies. Keyword - Spin-stabilised; sports disc; discwing; gyroscopic; aerodynamics; cf

Experimental validation of dynamic stability analysis applied to dart flight

The game of darts attracts a large international following and can be fiercely competitive. Despite its popularity, and the large equipment market, no previous peer-reviewed studies have examined the trajectory of a dart in flight. This study used high-speed video techniques to measure the trajectories of 225 dart throws from 19 amateur players. The dart’s pitch and angle of attack were found to oscillate during flight in a manner that is analogous to damped harmonic motion. It was also found that the dart’s oscillation frequency was strongly correlated to launch speed, whilst its characteristic wavelength and damping ratio were independent of launch speed. The measured wavelength of oscillation (2.16 m) was found to be similar to the regulation throwing distance (2.37 m). It is proposed that the dart is ‘tuned’ to the throwing distance such that it undergoes one full oscillation before striking the board. The dart flight was modelled using a classical dynamic stability analysis and good agreement was found between the experimental observations and the theoretical predictions. The success of the model confirms that the approach can be used to explore the dynamics of different dart designs through parametric sensitivity analyses

Reversing insect pollinator decline

Pollination by insects enables the reproduction of flowering plants and is critical to UK agriculture.1 Insect pollinators have declined globally, with implications for food security and wild habitats. This POSTnote summarises the causes for the recent trends, gaps in knowledge and possible strategies for reversing pollinator decline

Numerical Investigation of the Flow around a Feather Shuttlecock with Rotation

This paper presents the first scale resolving computational fluid dynamic (CFD) investigation of a geometrically realistic feather shuttlecock with rotation at a high Reynolds number. Rotation was found to reduce the drag coefficient of the shuttlecock. However, the drag coefficient is shown to be independent of the Reynolds number for both rotating and statically fixed shuttlecocks. Particular attention is given to the influence of rotation on the development of flow structures. Rotation is shown to have a clear influence on the formation of flow structures particularly from the feather vanes, and aft of the shuttlecock base. This further raises concerns regarding wind tunnel studies that use traditional experimental sting mounts; typically inserted into this aft region, they have potential to compromise both flow structure and resultant drag forces. As CFD does not necessitate use of a sting with proper application, it has great potential for a detailed study and analysis of shuttlecocks

Comparison of turbulence modelling approaches in simulation of a feather shuttle; a porous conical bluff body

The aerodynamics of a feather shuttlecock, a porous conical bluff body, are unique in comparison to other sports projectiles. Experimental wind tunnel studies have been published that present values of drag coefficient (Cd) for traditional feather shuttles that vary widely (0.48 < Cd < 0.74). It is difficult to compare published experimental data, due to a lack of clarity concerning experimental apparatus. All studies have used traditional sting mounts inserted aft of the shuttle base, and it is believed this has a strong influence on Cd, as significant air movement is known to occur in this region. Flow passes through gaps formed by individual feather shafts, or rachis, inserted into the shuttle base. The use of computational fluid dynamic (CFD) simulation in the analysis of shuttles has great potential as analysis can be performed without the need of an experimental sting. This study presents the first CFD simulations of a geometrically realistic feather shuttle. Careful consideration must be given to applied grids, numeric, and turbulence models (unsteady RANS vs scale resolving) if results obtained are to be reliable. CFD results present detailed insights of shuttle aerodynamics, and the significance of flow passage between the feather rachis and internal to the shuttle. The study raises significant concerns regarding the appropriateness of rear sting mounts in shuttle wind tunnel experiments

Partial differential equation techniques for analysing animal movement: a comparison of different methods

Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement