Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows

We study the effects of imposed {three-dimensional flows} on the trajectories and mixing of gyrotactic swimming micro-organisms, and identify new phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor--Green and ABC flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical `plume-like' structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. \note{Furthermore, studies of Lyapunov exponents reveal that as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds

Early warning signals in plant disease outbreaks

Infectious disease outbreaks in plants threaten ecosystems, agricultural crops and food trade. Currently, several fungal diseases are affecting forests worldwide, posing a major risk to tree species, habitats and consequently ecosystem decay. Prediction and control of disease spread are difficult, mainly due to the complexity of the interaction between individual components involved. In this work, we introduce a lattice-based epidemic model coupled with a stochastic process that mimics, in a very simplified way, the interaction between the hosts and pathogen. We studied the disease spread by measuring the propagation velocity of the pathogen on the susceptible hosts. Our quantitative results indicate the occurrence of a critical transition between two stable phases: local confinement and an extended epiphytotic outbreak that depends on the density of the susceptible individuals. Quantitative predictions of epiphytotics are performed using the framework early-warning indicators for impending regime shifts, widely applied on dynamical systems. These signals forecast successfully the outcome of the critical shift between the two stable phases before the system enters the epiphytotic regime. Our study demonstrates that early-warning indicators could be useful for the prediction of forest disease epidemics through mathematical and computational models suited to more specific pathogen–host-environmental interactions. Our results may also be useful to identify a suitable planting density to slow down disease spread and in the future, design highly resilient forests

Identification of Kelvin waves: numerical challenges

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at http://www.springerlink.co

The sensitivity of the vortex filament method to different reconnection models

We present a detailed analysis on the effect of using different algorithms to model the reconnection of vortices in quantum turbulence, using the thin-filament approach. We examine differences between four main algorithms for the case of turbulence driven by a counterflow. In calculating the velocity field we use both the local induction approximation (LIA) and the full Biot-Savart integral. We show that results of Biot-Savart simulations are not sensitive to the particular reconnection method used, but LIA results are.Comment: 9 pages, 9 figure

Estimating the reproduction number, Rₒ, from individual-based models of tree disease spread

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

Tree method for quantum vortex dynamics

We present a numerical method to compute the evolution of vortex filaments in superfluid helium. The method is based on a tree algorithm which considerably speeds up the calculation of Biot-Savart integrals. We show that the computational cost scales as Nlog{(N) rather than N squared, where $N$ is the number of discretization points. We test the method and its properties for a variety of vortex configurations, ranging from simple vortex rings to a counterflow vortex tangle, and compare results against the Local Induction Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure

Visualization of quantum turbulence in superfluid 3He-B:combined numerical and experimental study of Andreev reflection

We present a combined numerical and experimental study of Andreev scattering from quantum turbulence in superfluid $^3$He-B at ultralow temperatures. We simulate the evolution of moderately dense, three-dimensional, quasiclassical vortex tangles and the Andreev reflection of thermal quasiparticle excitations by these tangles. This numerical simulation enables us to generate the two-dimensional map of local Andreev reflections for excitations incident on one of the faces of a cubic computational domain, and to calculate the total coefficient of Andreev reflection as a function of the vortex line density. Our numerical simulation is then compared with the experimental measurements probing quantum turbulence generated by a vibrating grid. We also address the question of whether the quasiclassical and ultraquantum regimes of quantum turbulence can be distinguished by their respective total Andreev reflectivities. We discuss the screening mechanisms which may strongly affect the total Andreev reflectivity of dense vortex tangles. Finally, we present combined numerical-experimental results for fluctuations of the Andreev reflection from a quasiclassical turbulent tangle and demonstrate that the spectral properties of the Andreev reflection reveal the nature and properties of quantum turbulence

The Kuiper Belt and Other Debris Disks

We discuss the current knowledge of the Solar system, focusing on bodies in the outer regions, on the information they provide concerning Solar system formation, and on the possible relationships that may exist between our system and the debris disks of other stars. Beyond the domains of the Terrestrial and giant planets, the comets in the Kuiper belt and the Oort cloud preserve some of our most pristine materials. The Kuiper belt, in particular, is a collisional dust source and a scientific bridge to the dusty "debris disks" observed around many nearby main-sequence stars. Study of the Solar system provides a level of detail that we cannot discern in the distant disks while observations of the disks may help to set the Solar system in proper context.Comment: 50 pages, 25 Figures. To appear in conference proceedings book "Astrophysics in the Next Decade

The importance of vortex bundles in quantum turbulence at absolute zero

This study is concerned with the existence of coherent bundles of quantized vortices, and their importance in creating a flow with the classical Kolmogorov scaling and energy cascade. We show that at finite (non-zero) temperatures, in the presence of turbulent normal fluid, quantized vortices are organized into coherent bundles. We also performed a number of simulations at zero temperature and demonstrate that for a Kolmogorov scaling, and hence a hydrodynamical energy cascade, vortices must be organized into coherent bundles. Finally we analyze the polarization of the vortex tangle and find good agreement with theoretical predictions

Proceedings of the 2013 UK national conference on geophysical, astrophysical and industrial magnetohydrodynamics at Glasgow

This document presents an accurate record of the scientific programme of the 2013 UK National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics held on 23rd and 24th of May 2013 at the School of Mathematics and Statistics of the University of Glasgow. The abstracts of presented contributions are listed in chronological order and a full list of participants and their affiliations is included