Dr Stanisław Waldemar Biber

Video recordings of two experimental campaigns considering golf ball bounce. Data published as part of the paper "Measurements and linearized models for golf ball bounce".

In this report we propose a modelling framework to analyse and optimise worldwide vaccine allocation strategies, with reference to the current COVID-19 pandemic. We model epidemiological transmission and vaccination in a system of M interacting countries, quantifying the social and economic costs incurred by each country due to the pandemic and the country's vaccination rate. Under constraints over global vaccine availability, we analyse best strategies of vaccine allocation: either with the aim of minimising global costs, or by taking the perspective of a competitive game where each country aims to minimise its own cost. We distinguish between the financial capabilities of different countries, and extend our framework to allow for vaccine donation from wealthier to poorer countries. Numerical simulations allow us to compare the best strategies of the above two approaches, and to analyse circumstances under which vaccine donation simultaneously benefits both donating and receiving countries.

We study chaotic rotations of a rigid ellipsoidal body due to the effects of gravitational torques, in the case where this body exhibits spin-orbit misalignment. After first deriving a simple model of a rigid ellipsoid of uniform mass distribution with principal axis of rotation directed slightly out of the orbital plane, we prove using the Melnikov method that this perturbation is sufficient to excite the ellipsoid to chaotically rotate for a circular orbit. We further verify this analytical result with numerical time series and Poincare sections for circular orbits. We then use numerical simulations to demonstrate that elliptical orbits provide further pathways to chaos. Our primary finding is that increasing the degree of spin-orbit misalignment will increase the prevalence of initial conditions leading to chaotic dynamics, for elliptical bodies on both circular and elliptical orbits. Indeed, our results suggest that chaotic rotation of elongated bodies exhibiting spin-orbit misalignment is somewhat common for large enough deviation of the principal axis of rotation from the normal to the orbital plane, provided the rigid body lacks rotational symmetry around its spin-axis and, furthermore, exhibits sufficiently small angular momentum so that the effects of gravitational torques are nontrivial.

Inspired by the turf-ball interaction in golf, this paper seeks to understand the bounce of a ball that can be modelled as a rigid sphere and the surface as supplying a viscoelastic contact force in addition to Coulomb friction. A general formulation is proposed that models the finite time interval of bounce from touch-down to lift-off. Key to the analysis is understanding transitions between slip and roll during the bounce. Starting from the rigid-body limit with an energetic or Poisson coefficient of restitution, it is shown that slip reversal during the contact phase cannot be captured in this case, which generalizes to the case of pure normal compliance. Yet, the introduction of linear tangential stiffness and damping does enable slip reversal. This result is extended to general weakly nonlinear normal and tangential compliance. An analysis using the Filippov theory of piecewise-smooth systems leads to an argument in a natural limit that lift-off while rolling is non-generic and that almost all trajectories that lift off do so under slip conditions. Moreover, there is a codimension-one surface in the space of incoming velocity and spin which divides balls that lift off with backspin from those that lift off with topspin. The results are compared with recent experimental measurements on golf ball bounce and the theory is shown to capture the main features of the data.

1. Passive acoustic telemetry is widely used to study the movements of aquatic animals. However, a holistic, mechanistic modelling framework that permits the reconstruction of fine-scale movements and emergent patterns of space use from detections at receivers remains lacking. 2. Here, we introduce an integrative modelling framework that recapitulates the movement and detection processes that generate detections to reconstruct fine-scale movements and patterns of space use. This framework is supported by a new family of algorithms designed for detection and depth observations and can be flexibly extended to incorporate other data types. Using simulation, we illustrate applications of our framework and evaluate algorithm utility and sensitivity in different settings. As a case study, we analyse movement data collected from the Critically Endangered flapper skate (Dipturus intermedius) in Scotland. 3. We show that our methods can be used to reconstruct fine-scale movement paths, patterns of space use and support habitat preference analyses. For reconstructing patterns of space use, simulations show that the methods are consistently more instructive than the most widely used alternative approach (the mean-position algorithm), particularly in clustered receiver arrays. For flapper skate, the reconstruction of movements reveals responses to disturbance, fine-scale spatial partitioning and patterns of space use with significant implications for marine management. 4. We conclude that this framework represents a widely applicable methodological advance with applications to studies of pelagic, demersal and benthic species across multiple spatiotemporal scales.

A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball on a green. Video analysis was used to capture ball's velocity and spin just before and after each bounce for a wide variety of landing conditions. Data are presented from two different turfs; one artificial and one from a typical tee. Measurement errors and repeatability are analysed. The data are compared to predictions from models of rigid bounce with friction, including Penner's modification to account for elasto-plasticity. Coefficients of restitution and friction, and Penner's effective contact angle are fit from the data. A better fit to the data is found using a non-physical piecewise-affine landing to lift-off relationship, which distinguishes between cases that bounce in pure slip from those that undergo rolling. Nevertheless, even balls that undergo rolling are typically found to lift-off slipping, having undergone spin reversal. The findings suggest that further effort needs to be spent on finding simple physics-based models of golf ball bounce on a green.