Converging and diverging convection around axisymmetric magnetic flux tubes

A numerical model of idealized sunspots and pores is presented, where axisymmetric cylindrical domains are used with aspect ratios (radius versus depth) up to 4. The model contains a compressible plasma with density and temperature gradients simulating the upper layer of the Sun's convection zone. Non-linear magnetohydrodynamic equations are solved numerically and time-dependent solutions are obtained where the magnetic field is pushed to the centre of the domain by convection cells. This central magnetic flux bundle is maintained by an inner convection cell, situated next to it and with a flow such that there is an inflow at the top of the numerical domain towards the flux bundle. For aspect ratio 4, a large inner cell persists in time, but for lower aspect ratios it becomes highly time dependent. For aspect ratios 2 and 3 this inner convection cell is smaller, tends to be situated towards the top of the domain next to the flux bundle, and appears and disappears with time. When it is gone, the neighbouring cell (with an opposite sense of rotation, i.e. outflow at the top) pulls the magnetic field away from the central axis. As this happens a new inner cell forms with an inflow which pushes the magnetic field towards the centre. This suggests that to maintain their form, both pores and sunspots need a neighbouring convection cell with inflow at the top towards the magnetic flux bundle. This convection cell does not have to be at the top of the convection zone and could be underneath the penumbral structure around sunspots. For an aspect ratio of 1, there is not enough space in the numerical domain for magnetic flux and convection to separate. In this case the solution oscillates between two steady states: two dominant convection cells threaded by magnetic field and one dominant cell that pushes magnetic flux towards the central axis

Thermodynamically consistent Reference Interaction Site Model theory of the tangent diatomic fluid

Thermodynamic and structural properties of the tangent diatomic fluid are studied in the framework provided by the Reference Interaction Site Model (RISM) theory, coupled with a Modified Hypernetted Chain closure. The enforcement of the internal thermodynamic consistency of the theory is described in detail. The results we obtain almost quantitatively agree with available or newly generated simulation data. We envisage the possibility to extend the consistent RISM formalism to generic, more realistic molecular fluids.Comment: Typeset with LaTeX, 6 pages, 3 figures (5 subfigures), 28 references, submitted to Chem. Phys. Let

Striation and convection in penumbral filaments

Observations with the 1-m Swedish Solar Telescope of the flows seen in penumbral filaments are presented. Time sequences of bright filaments show overturning motions strikingly similar to those seen along the walls of small isolated structures in the active regions. The filaments show outward propagating striations with inclination angles suggesting that they are aligned with the local magnetic field. We interpret it as the equivalent of the striations seen in the walls of small isolated magnetic structures. Their origin is then a corrugation of the boundary between an overturning convective flow inside the filament and the magnetic field wrapping around it. The outward propagation is a combination of a pattern motion due to the downflow observed along the sides of bright filaments, and the Evershed flow. The observed short wavelength of the striation argues against the existence of a dynamically significant horizontal field inside the bright filaments. Its intensity contrast is explained by the same physical effect that causes the dark cores of filaments, light bridges and `canals'. In this way striation represents an important clue to the physics of penumbral structure and its relation with other magnetic structures on the solar surface. We put this in perspective with results from the recent 3-D radiative hydrodynamic simulations.Comment: Accepted for publication in A&

Algorithm for numerical integration of the rigid-body equations of motion

A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in terms of either principal axes or quaternions. Due to specific features of the algorithm, orthonormality and unit norms of the orientational variables are integrals of motion, despite an approximate character of the produced trajectories. It is shown that the method presented appears to be the most efficient among all known algorithms of such a kind.Comment: 4 pages, 1 figur

Modelling H5N1 in Bangladesh across spatial scales : model complexity and zoonotic transmission risk

Highly pathogenic avian influenza H5N1 remains a persistent public health threat, capable of causing infection in humans with a high mortality rate while simultaneously negatively impacting the livestock industry. A central question is to determine regions that are likely sources of newly emerging influenza strains with pandemic causing potential. A suitable candidate is Bangladesh, being one of the most densely populated countries in the world and having an intensifying farming system. It is therefore vital to establish the key factors, specific to Bangladesh, that enable both continued transmission within poultry and spillover across the human–animal interface. We apply a modelling framework to H5N1 epidemics in the Dhaka region of Bangladesh, occurring from 2007 onwards, that resulted in large outbreaks in the poultry sector and a limited number of confirmed human cases. This model consisted of separate poultry transmission and zoonotic transmission components. Utilising poultry farm spatial and population information a set of competing nested models of varying complexity were fitted to the observed case data, with parameter inference carried out using Bayesian methodology and goodness-of-fit verified by stochastic simulations. For the poultry transmission component, successfully identifying a model of minimal complexity, which enabled the accurate prediction of the size and spatial distribution of cases in H5N1 outbreaks, was found to be dependent on the administration level being analysed. A consistent outcome of non-optimal reporting of infected premises materialised in each poultry epidemic of interest, though across the outbreaks analysed there were substantial differences in the estimated transmission parameters. The zoonotic transmission component found the main contributor to spillover transmission of H5N1 in Bangladesh was found to differ from one poultry epidemic to another. We conclude by discussing possible explanations for these discrepancies in transmission behaviour between epidemics, such as changes in surveillance sensitivity and biosecurity practices

Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles

We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable pile.Comment: 14 pages, Plain Te

Fine structure, magnetic field and heating of sunspot penumbrae

We interpret penumbral filaments as due to convection in field-free, radially aligned gaps just below the visible surface of the penumbra, intruding into a nearly potential field above. This solves the classical discrepancy between the large heat flux and the low vertical velocities observed in the penumbra. The presence of the gaps causes strong small-scale fluctuations in inclination, azimuth angle and field strength, but without strong forces acting on the gas. The field is nearly horizontal in a region around the cusp-shaped top of the gap, thereby providing an environment for Evershed flows. We identify this region with the recently discovered dark penumbral cores. Its darkness has the same cause as the dark lanes in umbral light-bridges, reproduced in numerical simulations by Nordlund and Stein (2005). We predict that the large vertical and horizontal gradients of the magnetic field inclination and azimuth in the potential field model will produce the net circular polarization seen in observations. The model also explains the significant elevation of bright filaments above their surroundings. It predicts that dark areas in the penumbra are of two different kinds: dark filament cores containing the most inclined (horizontal) fields, and regions between bright filaments, containing the least inclined field lines.Comment: submitted to A&

Yukawa potentials in systems with partial periodic boundary conditions I : Ewald sums for quasi-two dimensional systems

Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or Coulomb limit, the potential is long ranged. As it is well known in computer simulation, a simple truncation of the long ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of the space, has already been derived for Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996) and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459, (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. A special attention is paid to the Coulomb limit and its relation with the electroneutrality of systems.Comment: 40 pages, 5 figures and 4 table

The impact of surveillance and control on highly pathogenic avian influenza outbreaks in poultry in Dhaka division, Bangladesh

In Bangladesh, the poultry industry is an economically and socially important sector, but it is persistently threatened by the effects of H5N1 highly pathogenic avian influenza. Thus, identifying the optimal control policy in response to an emerging disease outbreak is a key challenge for policy-makers. To inform this aim, a common approach is to carry out simulation studies comparing plausible strategies, while accounting for known capacity restrictions. In this study we perform simulations of a previously developed H5N1 influenza transmission model framework, fitted to two separate historical outbreaks, to assess specific control objectives related to the burden or duration of H5N1 outbreaks among poultry farms in the Dhaka division of Bangladesh. In particular, we explore the optimal implementation of ring culling, ring vaccination and active surveillance measures when presuming disease transmission predominately occurs from premises-to-premises, versus a setting requiring the inclusion of external factors. Additionally, we determine the sensitivity of the management actions under consideration to differing levels of capacity constraints and outbreaks with disparate transmission dynamics. While we find that reactive culling and vaccination policies should pay close attention to these factors to ensure intervention targeting is optimised, across multiple settings the top performing control action amongst those under consideration were targeted proactive surveillance schemes. Our findings may advise the type of control measure, plus its intensity, that could potentially be applied in the event of a developing outbreak of H5N1 amongst originally H5N1 virus-free commercially-reared poultry in the Dhaka division of Bangladesh

Fitting to the UK COVID-19 outbreak, short-term forecasts and estimating the reproductive number

The COVID-19 pandemic has brought to the fore the need for policy makers to receive timely and ongoing scientific guidance in response to this recently emerged human infectious disease. Fitting mathematical models of infectious disease transmission to the available epidemiological data provides a key statistical tool for understanding the many quantities of interest that are not explicit in the underlying epidemiological data streams. Of these, the effective reproduction number, R, has taken on special significance in terms of the general understanding of whether the epidemic is under control (R < 1). Unfortunately, none of the epidemiological data streams are designed for modelling, hence assimilating information from multiple (often changing) sources of data is a major challenge that is particularly stark in novel disease outbreaks. Here, focusing on the dynamics of the first-wave (March-June 2020), we present in some detail the inference scheme employed for calibrating the Warwick COVID-19 model to the available public health data streams, which span hospitalisations, critical care occupancy, mortality and serological testing. We then perform computational simulations, making use of the acquired parameter posterior distributions, to assess how the accuracy of short-term predictions varied over the timecourse of the outbreak. To conclude, we compare how refinements to data streams and model structure impact estimates of epidemiological measures, including the estimated growth rate and daily incidence