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

A novel putter design to minimise range variability in golf putts

Putting accounts for more shots in a round of golf than any other type of play. The percentage of putts holed decreases as putt length increases, because golfers struggle to achieve a consistent range and direction. Range variation has been partly attributed to the ball striking the club face away from the central plane of the putter face. Tests have shown a 30mm off-centre impact can reduce the roll distance of a putt by 13%. In this paper, changes in mass distribution of the putter body and the addition of a flexible striking surface are considered. Physical testing and Finite Element Analysis are used to produce a club design with more consistent roll distance. Redistribution of mass reduced the roll distance variation across the clubface. Combining this with a flexible impact surface reduced the variation between a central impact and one 20mm from centre to just 1%. The proposed design could significantly reduce distance variation; aiding golfers in holing putts. Future work will optimise the design and validate through physical prototyping

Aerodynamic performance of flying discs

The purpose of this paper is to examine geometrical design influence of various types of flying discs on their flight performance from the aerodynamics perspective. The lift, drag and moment coefficients of the discs were measured experimentally using a wind tunnel. Three types of golf discs and four sets of simpler parametric discs were studied to analyze and isolate the effect of design factors on these aerodynamic characteristics. Full six degree-of-freedom simulations of the discs were performed to visualize their flight trajectories and attitudes. These simulations, combined with the experimental data, provide details on the well-known “S-shaped” ground-path traced by a flying disc. This study reveals two key parameters to evaluate the flight performance of a disc: its coefficient of lift-to-drag ratio (CL/CD) and, more importantly, its coefficient of pitching moment (CM). The latter influences the tendency of the disc to roll from its intended path, and the former influences its throwing distance. The work suggests that to optimize the flight performance of a disc, the magnitudes and gradient of its CM should be minimized and its trim-point shifted from origin, while its CL/CD should be maximized with a flatter peak. In this study, the design parameters and the aerodynamic characteristics of various types of flying discs are analysed, compared and discussed in depth. Recommendations of design improvements to enhance the performance of any flying disc are offered as well

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

Weakly nonlinear analysis of a two-species non-local advection-diffusion system

Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a Ginzburg-Landau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the Ginzburg-Landau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimisers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions

Integrated Step Selection Analysis: Bridgingthe Gap Between Resource Selection and Animal Movement

A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define availability? Step selection analysis deals with this problem at the scale of the observed positional data, by matching each ‘used step’ (connecting two consecutive observed positions of the animal) with a set of ‘available steps’ randomly sampled from a distribution of observed steps or their characteristics. Here we present a simple extension to this approach, termed integrated step selection analysis (iSSA), which relaxes the implicit assumption that observed movement attributes (i.e. velocities and their temporal autocorrelations) are independent of resource selection. Instead, iSSA relies on simultaneously estimating movement and resource selection parameters, thus allowing simple likelihood‐based inference of resource selection within a mechanistic movement model. We provide theoretical underpinning of iSSA, as well as practical guidelines to its implementation. Using computer simulations, we evaluate the inferential and predictive capacity of iSSA compared to currently used methods. Our work demonstrates the utility of iSSA as a general, flexible and user‐friendly approach for both evaluating a variety of ecological hypotheses, and predicting future ecological patterns

Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge \alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q) in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure