arXiv subjects

Simon J. Cox

Publications and source records attributed to Simon J. Cox.

12 recordsLinked to original sources

arXiv2020

Characterisation and optimisation of foams for varicose vein sclerotherapy

In this study we characterise the properties of foams used for varicose vein sclerotherapy. Their effectiveness is evaluated by predicting their yield stress and their flow profiles within a model of a vein. This information is represented using a Bingham number, which also takes into account the foam liquid fraction and the Sauter mean of the bubble size distribution. Based on this modelling, the most effective foams have a Bingham number B = 600 for a vein of diameter 2mm, in addition to a narrow bubble size distribution.

cond-mat.soft↗

arXiv2020

An analytic velocity profile for pressure-driven flow of a Bingham fluid in a curved channel

We derive an expression for the velocity profile of a pressure-driven yield-stress fluid flow-ing around a two-dimensional concentric annulus. This result allows the prediction of the effects of channel curvature on the pressure gradient required to initiate flow for given yield stress, and for the width of the plug region and the flux through the channel at different curvatures. We use it to validate numerical simulations of the flow from a straight channel into a curved channel which show how the fluid first yields everywhere before reaching the predicted velocity profile.

physics.flu-dyn↗

arXiv2019

Semi-analytic velocity profile for a Bingham fluid in a curved channel

We derive an expression for the velocity profile of a pressure-driven yield-stress Bingham fluid flowing around a 2D concentric annulus. The formula requires the numerical solution of a nonlinear equation for the positions of the yield surfaces. The results allow the prediction of the effects of channel curvature on the pressure gradient required to initiate flow for given yield stress, and for the width of the plug region and the flux through the channel at different curvatures.

physics.flu-dyn↗

arXiv2017

When is a surface foam-phobic or foam-philic?

By integrating the Young-Laplace equation, including the effects of gravity, we have calculated the equilibrium shape of the two-dimensional Plateau borders along which a vertical soap film contacts two flat, horizontal solid substrates of given wettability. We show that the Plateau borders, where most of a foam's liquid resides, can only exist if the values of the Bond number ${\rm Bo}$ and of the liquid contact angle $θ_c$ lie within certain domains in $(θ_c,{\rm Bo})$ space: under these conditions the substrate is foam-philic. For values outside these domains, the substrate cannot support a soap film and is foam-phobic. In other words, on a substrate of a given wettability, only Plateau borders of a certain range of sizes can form. For given $(θ_c,{\rm Bo})$, the top Plateau border can never have greater width or cross-sectional area than the bottom one. Moreover, the top Plateau border cannot exist in a steady state for contact angles above 90$^\circ$. Our conclusions are validated by comparison with both experimental and numerical (Surface Evolver) data. We conjecture that these results will hold, with slight modifications, for non-planar soap films and bubbles. Our results are also relevant to the motion of bubbles and foams in channels, where the friction force of the substrate on the Plateau borders plays an important role.

cond-mat.soft↗

arXiv2016

Quasicrystalline three-dimensional foams

We present a numerical study of quasiperiodic foams, in which the bubbles are generated as duals of quasiperiodic Frank-Kasper phases. These foams are investigated as potential candidates to the celebrated Kelvin problem for the partition of three-dimensional space with equal volume bubbles and minimal surface area. Interestingly, one of the computed structures falls close (but still slightly above) the best known Weaire-Phelan periodic candidate. This gives additional clues to understanding the main geometrical ingredients driving the Kelvin problem.

cond-mat.soft↗

arXiv2015

Structured populations facilitate cooperation in policed Public Goods Games

Societies consisting of cooperative individuals seem to require for their continuing success that defectors be policed. The precise connection between punishers and benefits, population structure, and division of labour, however, remains ill-understood. Many models assume costly "peer punishment" to enforce cooperation, but results in the economics literature suggest that this assumption may not be generally valid. In many human and animal societies, there is a division of labour between a purely supportive majority and a dedicated minority of police-like enforcers. Here we present several extensions to the Public Goods Game with punishment which allow for this possibility, and evaluate their influence on the level of cooperative behaviour. We find that a structure of separate subpopulations, which only interact through migration of individuals, can have a strong effect on the evolutionary dynamics of a system and significantly facilitate cooperation. Forcing defectors to contribute and enabling fitness transfers to punishers both have a weak positive effect on cooperation levels. In the presence of group competition, however, evolutionary effects can paradoxically hinder cooperation.

q-bio.PE↗

arXiv2013

Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels

The velocity of a two-dimensional aqueous foam has been measured as it flows through two parallel channels, at a constant overall volumetric flow rate. The flux distribution between the two channels is studied as a function of the ratio of their widths. A peculiar dependence of the velocity ratio on the width ratio is observed when the foam structure in the narrower channel is either single staircase or bamboo. In particular, discontinuities in the velocity ratios are observed at the transitions between double and single staircase and between single staircase and bamboo. A theoretical model accounting for the viscous dissipation at the solid wall and the capillary pressure across a film pinned at the channel outlet predicts the observed non-monotonic evolution of the velocity ratio as a function of the width ratio. It also predicts quantitatively the intermittent temporal evolution of the velocity in the narrower channel when it is so narrow that film pinning at its outlet repeatedly brings the flow to a near stop.

physics.flu-dyn↗

arXiv2002

Modelling Oscillations in the Jet Emission from Microquasar GRS 1915+105

The variability in the infrared to millimetre emission from microquasar GRS 1915+105 is believed to be dominated by the system's relativistic jet. In this paper we develop a time-dependent version of the Blandford & Koenigl (1979) jet emission model and apply it to the oscillations in the infrared and millimetre emission from GRS 1915+105 observed by Fender & Pooley (2000). The resulting model provides a reasonable description of the observed flux oscillations from GRS 1915+105. From a fit of the observed time lag between the flux peaks in the infrared and millimetre emission together with the flux normalisation we were able to determine the model parameters for the GRS 1915+105 jet. We find that to achieve the observed flux levels with the model requires an unphysically large electron density within the jet. We therefore conclude that the Blandford & Koenigl (1979) model cannot explain these observations, either because it does not provide the correct description of the emission from microquasar jets, or because the observed emission variations do not originate in the jet.

astro-ph↗

arXiv2002

Modelling Oscillations in GRS 1915+105 Jet Emission

We have studied time variability in the flux from the flat spectrum synchrotron radiation of the Blandford & Konigl (1979) model for relativistic, conical jets. The resulting model has been applied to the flux variation of the flat spectrum of GRS 1915+105 observed by Fender & Pooley (2000). This comparison has highlighted a fundamental problem of the Blandford & Konigl (1979) model in that it requires unphysically large electron densities to explain the flux levels observed from the flat spectrum of GRS 1915+105.

astro-ph↗

arXiv2001

Vortex dynamics in two-dimensional systems at high driving forces

We study numerically the dynamics of two-dimensional vortex systems at zero temperature. In addition to pinned states and turbulent plastic flow, we find motion of vortices in rough channels along the direction of the driving force. In this decoupled channel regime we demonstrate how topological defects mediate the phase slip of different channels moving with different velocities. We thus provide important confirmation of recent analytical work describing vortex dynamics at high driving forces such as the moving glass theory of Giamarchi and Le Doussal. For the largest driving forces we find that the channels couple and observe elastic motion.

cond-mat↗

arXiv2000

Critical Transverse Forces in Weakly Pinned Driven Vortex Systems

We present simulation results of the moving Bragg glass regime of a driven two-dimensional vortex system in the presence of a smoothly varying weak pinning potential. We study the critical transverse force and (i) demonstrate that it can be an order of magnitude larger than previous estimates (ii) show that it is still observable when the system is driven along low higher-order lattice vectors. We confirm theoretical predictions that the critical transverse force is the order parameter of the so-called moving glass phase, and provide data to support experimentalists verifying the existence of a critical transverse force.

cond-mat.supr-con↗

arXiv2000

Efficient Methods for Handling Long-Range Forces in Particle-Particle Simulations

A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle-particle simulations. If a simple cut-off for the interaction is used, the system may find an equilibrium configuration at zero temperature that is not a regular lattice yet has an energy lower than the theoretically predicted minimum for the physical system. We demonstrate two methods to overcome these problems in Monte Carlo and molecular dynamics simulations. The first uses a smoothed potential to truncate the interaction in a single unit cell: this is appropriate for phenomenological characterisations, but may be applied to any potential. The second is a new method for summing the unmodified potential in an infinitely tiled periodic system, which is in excess of 20,000 times faster than previous naive methods which add periodic images in shells of increasing radius: this is suitable for quantitative studies. Finally we show that numerical experiments which do not handle the long-range force carefully may give misleading results: both of our proposed methods overcome these problems.

physics.comp-ph↗