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Terrestrial experiments on active particles, such as Volvox, involve gravitational forces, torques and accompanying monopolar fluid flows. Taking these into account, we analyse the dynamics of a pair of self-propelling, self-spinning active particles confined between parallel planes. Neglecting flow reflected by the planes, the dynamics of orientation and horizontal separation is symplectic, with a Hamiltonian exactly determining limit cycle oscillations. Near the bottom plane, gravitational torque damps and reflected flow excites this oscillator, sustaining a second limit cycle that can be perturbatively related to the first. Our work provides a theory for dancing Volvox and highlights the importance of monopolar flow in active matter.Since Lighthill's seminal work on the squirming motion of a sphere [1,2], it has been understood that freely moving active particles produce hydrodynamic flows that disallow monopoles and antisymmetric dipoles [3]. The representing of active flows by the symmetric dipole, the leading term consistent with force-free, torque freemotion, has been the basis of much theoretical work in both particle [4][5][6] and field representations of active matter [7,8]. The importance of multipoles beyond leading order in representing experimentally measured flows around active particles has now been recognized and and their effects have been included in recent theoretical work [9,10]. Less recognised, however, is the fact that active particles in typical experiments [4,[11][12][13][14][15][16] are neither force-nor torque-free: mismatches between particle and solvent densities lead to net gravitational forces while mismatches between the gravitational and geometric centers lead to net gravitational torques. Then, both monopolar and antisymmetric dipolar flows are allowed and become dominant, at long distances, over active contributions. It is of great interest, therefore, to understand how these components influence the dynamics of active particles and, more generally, of active matter.Previous studies of this aspect of active matter are limited. Sedimentation equilibrium of hydrodynamically interacting run-and-tumble particles and their dynamics in harmonic confinement has been investigated using lattice Boltzmann [17] and boundary integral methods [18] and the role of re-orientation by the vorticity of monopolar flow has been identified as the key mechanism in the emergence of the pumping state. Monopolar flows near boundaries have also been identified as the operative mechanism behind flow-induced phase separation [19]. However, none of these studies have focussed on the dynamics of pairs, which forms the foundation for understanding collective motion, or attempted an analytical description of motion.In this Letter, we provide a theory for the dynamics of density-mismatched, bottom-heavy, self-propelling and self-spinning active particles confined between parallel planes. Starting from the ten-dimensional equations for hydrodynamically interacting active motion in the pres-ence of forces and to...

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

No abstract

Micropolar active matter requires for its kinematic description both positional and orientational degrees of freedom. Activity generates dynamic coupling between these kinematic variables that are absent in micropolar passive matter, such as the oriented crystals first studied by the Cosserat brothers. Here we study the effect of uniaxial activity on the dynamics of an initially crystalline state of spheroidal colloids sedimenting slowly in a viscous fluid remote from confining boundaries. Despite frictional overdamping by the fluid, the crystalline lattice admits traveling waves of position and orientation. At long wavelengths these obey a vector wave equation with Lamé constants determined by the activity. We find that at least one polarization mode of these waves is always unstable, leading to the melting of the crystal. These results are elucidated by identifying an odddimensional Poisson structure consisting of a Hamiltonian and an associated Casimir invariant, where linear combinations of position and orientation are identified as conjugate variables. Our results suggest that Poisson structures may exist generally for active particles in slow viscous flow and thereby allow equilibrium arguments to be applied in the presence of these dissipative systems.