In classical inviscid fluids, antiparallel vortices perturbed by Kelvin waves exhibit the Crow instability, where the mutual interaction of the Kelvin modes renders them dynamically unstable. This results in the approach and reconnection of the vortices, leading to a cascaded decay into ever-smaller vortex loops. Through mean-field simulations we study the Crow instability of quantum vortex lines in a superfluid whose atoms are subject to the anisotropic, long-ranged dipole-dipole interaction. We observe that the direction of dipole polarization plays a crucial role in determining the dynamically favored Kelvin modes. The subsequent rate of the instability is linked to the mediation of the vortex curvature by the effective dipole-dipole interaction between the vortices themselves. The vortex curvature is strongly suppressed and modes of lower wavenumber are preferred when the dipole polarization is parallel to the vortices, whereas the curvature is maximized for polarizations along the vortices' separation axis. For polarizations along the binormal axis, modes of higher wavenumber are favorable but the instability rate is considerably inhibited. This paves the way to a deeper understanding of vortex reconnections, vortex loop cascades and turbulence in dipolar superfluids.

We simulate the dynamics of about 600 quantum vortices in a spinning-down cylindrical container using a Gross–Pitaevskii model. For the first time, we find convincing spatial-temporal evidence of avalanching behavior resulting from vortex depinning and collective motion. During a typical avalanche, about 10–20 vortices exit the container in a short period, producing a glitch in the superfluid angular momentum and a localized void in the vorticity. After the glitch, vortices continue to depin and circulate around the vorticity void in a similar manner to that seen in previous point-vortex simulations. We present evidence of collective vortex motion throughout this avalanche process. We also show that the effective Magnus force can be used to predict when and where avalanches will occur. Finally, we comment on the challenge of extrapolating these results to conditions in real neutron stars, which contain many orders of magnitude more vortices.

UK woodlands, forests, and urban treescapes are under threat from invasive species, exacerbated by climate change, trade, and transport. Invasive tree pests debilitate their host and disrupt forest ecosystems, thus it is imperative to quantitatively model and predict their spread. Addressing this, we model the spread of an invasive pest using a spatiotemporal reaction-diffusion equation, representing the spatial distribution as a population density field. We solve this intractable equation numerically and, from the solution, we determine first arrival times of the pest at locations in the field. The adopted model permits us to obtain the expansion rate of pest spread directly from the model parameters, which we infer in the Bayesian paradigm, using a Markov chain Monte Carlo scheme. We apply our framework to the ongoing spread of oak processionary moth in the UK, an outbreak which continues to grow despite management efforts. We demonstrate that our approach effectively captures the spread of the pest and that this has occurred at a non-constant expansion rate. The proposed framework is a powerful tool for quantitatively modelling the spread of an invasive tree pest and could underpin future prediction and management approaches.

We consider the mean-field vortex solutions and their stability within a two-component Bose Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantised vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation to the two-component vortex solution for a range of atom numbers of the in-filling component, by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the in-filling component away from the centre of the vortex core, thereby demonstrating their stability to small perturbations.

When a system undergoes a rapid quench from a disordered to an ordered phase, it does not order instantly but instead relaxes towards equilibrium over time. During this relaxation, the dynamical scaling hypothesis predicts that the length scale of ordered regions increases, with later patterns statistically similar to earlier ones except for a change in global scale. Quantum gases are one of many systems in which such out of equilibrium behaviour is predicted to occur. Here, we present a method for systematically testing when dynamical scaling is taking place, by quantifying the similarity of the rescaled two-point correlation function over time using the Mahalanobis distance. Data on the velocity field of a two-dimensional quantum fluid, generated from point vortex simulations, are used to illustrate the application of this method.

We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.

The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly–Glaberson instability.

The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole interaction-dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices.

We present a numerical study, using the vortex filament model, of vortex tangles in a flow of pure superfluid ^4 He in the T = 0 limit through a channel of width D = 1 mm for various applied velocities V. The flat channel walls are assumed to be microscopically rough such that vortices terminating at the walls are permanently pinned; vortices are liberated from their pinned ends exclusively through self-reconnection with their images. Sustained tangles were observed, for a period of 80 s, above the critical velocity V_c ∼ 0.20 cm s ^-1 = 20 κ/D . The coarse-grained velocity profile was akin to a classical parabolic profile of the laminar Poiseuille flow, albeit with a nonzero slip velocity ∼ 0.20 cm s ^-1 at the walls. The friction force was found to be proportional to the applied velocity. The effective kinematic viscosity was ν ' ∼ 0.1κ , and effective Reynolds numbers within Re' < 200 . The fraction of the polarised vortex length varied between zero in the middle of the channel and ∼ 60 ∼ D/4 from the walls. Therefore, we studied a state of statically polarised ultraquantum (Vinen) turbulence fuelled at short length scales by vortex reconnections, including those with vortex images due to the relative motion between the vortex tangle and the pinning rough surface.

Tree populations worldwide are facing an unprecedented threat from a variety of tree diseases and invasive pests. Their spread, exacerbated by increasing globalisation and climate change, has an enormous environmental, economic and social impact. Computational individual-based models are a popular tool for describing and forecasting the spread of tree diseases due to their flexibility and ability to reveal collective behaviours. In this paper we present a versatile individual-based model with a Gaussian infectivity kernel to describe the spread of a generic tree disease through a synthetic treescape. We then explore several methods of calculating the basic reproduction number R0, a characteristic measurement of disease infectivity, defining the expected number of new infections resulting from one newly infected individual throughout their infectious period. It is a useful comparative summary parameter of a disease and can be used to explore the threshold dynamics of epidemics through mathematical models. We demonstrate several methods of estimating R0 through the individual-based model, including contact tracing, inferring the Kermack–McKendrick SIR model parameters using the linear noise approximation, and an analytical approximation. As an illustrative example, we then use the model and each of the methods to calculate estimates of R0 for the ash dieback epidemic in the UK.

We present a numerical study of finite-temperature superfluid turbulence using the vortex filament model for superfluid helium. We examine the phenomenon of vorticity locking between the normal and superfluid components across a wide range of temperatures, using two different structures of external normal fluid drive. We show that vorticity locking increases with temperature leading to the superfluid flow being more influenced by the characteristics of the normal fluid. This also results in stronger superfluid polarization and turbulent intermittency. We also examine how these properties influence the pressure field and attempt to verify a long-standing $P_k\propto k^{-7/3}$ theoretical quantum signature within the spatial pressure spectrum.

We consider the case of performing Bayesian inference for stochastic epidemic compartment models, using incomplete time course data consisting of incidence counts that are either the number of new infections or removals in time intervals of fixed length. We eschew the most natural Markov jump process representation for reasons of computational efficiency, and focus on a stochastic differential equation representation. This is further approximated to give a tractable Gaussian process, that is, the linear noise approximation (LNA). Unless the observation model linking the LNA to data is both linear and Gaussian, the observed data likelihood remains intractable. It is in this setting that we consider two approaches for marginalising over the latent process: a correlated pseudo-marginal method and analytic marginalisation via a Gaussian approximation of the observation model. We compare and contrast these approaches using synthetic data before applying the best performing method to real data consisting of removal incidence of oak processionary moth nests in Richmond Park, London. Our approach further allows comparison between various competing compartment models.

When the intensity of turbulence is increased (by increasing the Reynolds number, e.g. by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a non-zero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the context of liquid helium, a quantum fluid which becomes effectively inviscid at low temperatures achievable in the laboratory. By performing numerical simulations and identifying the superfluid Reynolds number, here we show evidence for a superfluid analog to the classical dissipation anomaly. Our numerics indeed show that as the superfluid Reynolds number increases, smaller and smaller structures are generated on the quantized vortex lines on which the superfluid vorticity is confined, balancing the effect of weaker and weaker dissipation.

Invasive woodland pests have substantial ecological, economic, and social impacts, harming biodiversity and ecosystem services. Mathematical modelling informed by Bayesian inference can deepen our understanding of the fundamental behaviours of invasive pests and provide predictive tools for forecasting future spread. A key invasive pest of concern in the UK is the oak processionary moth (OPM). OPM was established in the UK in 2006; it is harmful to both oak trees and humans, and its infestation area is continually expanding. Here, we use a computational inference scheme to estimate the parameters for a two-node network epidemic model to describe the temporal dynamics of OPM in two geographically neighbouring parks (Bushy Park and Richmond Park, London). We show the applicability of such a network model to describing invasive pest dynamics and our results suggest that the infestation within Richmond Park has largely driven the infestation within Bushy Park.

When using mathematical models to predict the pathways of biofouled microplastic in the ocean, it is necessary to parametrise the impact of turbulence on their motions. In this paper, statistics on particle motion have been computed from simulations of small, spherical particles with time-dependent mass in cellular flow fields. The cellular flows are a prototype for Langmuir circulation and flows dominated by vortical motion. Upwelling regions lead to particle suspension and particles fall out at different times. The uncertainty of fallout time and a particle's vertical position is quantified across a range of parameters. A slight increase in settling velocities, for short times, is observed for particles with inertia due to clustering in fast downwelling regions for steady, background flow. For particles in time-dependent, chaotic flows, uncertainty is significantly reduced and we observe no significant increase in the average settling rates due to inertial effects.

The majority of buoyant, marine microplastics are missing from the ocean surface, however, their presence has been observed throughout the ocean water-column and in seafloor sediments. The accumulation of microorganisms on the microplastics' surface, termed biofouling, has been proposed as a mechanism contributing substantially to their removal from the ocean surface by changing the particles' buoyancy. Mathematical models outlining the biofouling processes on microplastics have been implemented in General Ocean Circulation models (OGCMs) in an effort to predict their long-time transport in the ocean. The resolution of OGCMs is extremely course and sub-grid turbulent motions so far have either been neglected or parameterised via stochastic perturbations through an eddy diffusivity term. Accurately capturing the sub-grid turbulent motions, and quantifying the uncertainty they introduce to particle trajectories, is critical to establishing predictive maps of biofouled microplastic transport in the ocean. As an intuitive first step using representative models of oceanic, turbulent motions to define a more accurate parameterisation, we use the Maxey-Riley-Gatignol equations for the motion of small particles and analyse the trajectories of both individual and many particles with increasing, negative buoyancy in steady and unsteady deterministic, Taylor-Green vortex flow. We quantify the uncertainty these vortical flows introduce across parameter ranges of interest to microplastic and oceanic turbulence, finding that coherent turbulent structures, such as Langmuir circulations, could lead to errors in vertical position prediction on the order of kilometres. Comparatively, a stochastic parameterisation is shown to significantly under-approximate the dispersion of particles from the vortical flow, suggesting that the current standard using an eddy diffusivity term to capture turbulent mixing may be too simplistic.

In the quasiclassical regime of quantum turbulence, it has long been hypothesized that there exist coherent vortical structures, made up of bundles of quantized vortices. More recently, there has been significant experimental evidence that points to their presence. Here, we perform a quantitative study of the reconnection of bundles of quantized vorticity and show that the approach and separation of bundles during a reconnection is consistent with the symmetric δ ∼ t^1/2 scaling which is consistent with studies of individual quantized vortex reconnection and classical vortex reconnections. We also examined the phenomena of “bridge” structures that form between the vortex bundles during the reconnection process and have also been observed during the reconnection of classical vortices. We study their persistence and suggest that their dissipation is driven by vortex-vortex interactions within the bridge itself.

Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South-East England, OPM continues to spread. Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state-of-the-art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time-varying infestation rate to describe the spread of OPM. We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R0 between one and two). This shows further controls must be taken to reduce R0 below one and stop the advance of OPM into other areas of England. Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time-varying infestation rate, applicable to other partially observed time series epidemic data.