Revised time-of-flight calculations for high-latitude geomagnetic pulsations using a realistic magnetospheric magnetic field model

We present a simple time-of-flight analysis of Alfvén pulsations standing on closed terrestrial magnetic field lines. The technique employed in this study in order to calculate the characteristic period of such oscillations builds upon earlier time-of-flight estimates via the implementation of a more recent magnetospheric magnetic field model. In this case the model employed is the Tsyganenko (1996) field model, which includes realistic magnetospheric currents and the consequences of the partial penetration of the interplanetary magnetic field into the dayside magnetopause. By employing a simple description of magnetospheric plasma density, we are therefore able to estimate the period of standing Alfvén waves on geomagnetic field lines over a significantly wider range of latitudes and magnetic local times than in previous studies. Furthermore, we investigate the influence of changing season and upstream interplanetary conditions upon the period of such pulsations. Finally, the eigenfrequencies of magnetic field lines computed by the time-of-flight technique are compared with corresponding numerical solutions to the wave equation and experimentally observed pulsations on geomagnetic field lines

Modelling crystal aggregation and deposition\ud in the catheterised lower urinary tract

Urethral catheters often become encrusted with crystals of magnesium struvite and calcium phosphate. The encrustation can block the catheter, which can cause urine retention in the bladder and reflux into the kidneys. We develop a mathematical model to investigate crystal deposition on the catheter surface, modelling the bladder as a reservoir of fluid and the urethral catheter as a rigid channel. At a constant rate, fluid containing crystal particles of unit size enters the reservoir, and flows from the reservoir through the channel and out of the system. The crystal particles aggregate, which we model using Becker–Döring coagulation theory, and are advected through the channel, where they continue to aggregate and are deposited on the channel’s walls. Inhibitor particles also enter the reservoir, and can bind to the crystals, preventing further aggregation and deposition. The crystal concentrations are spatially homogeneous in the reservoir, whereas the channel concentrations vary spatially as a result of advection, diffusion and deposition. We investigate the effect of inhibitor particles on the amount of deposition. For all parameter values, we find that crystals deposit along the full length of the channel, with maximum deposition close to the channel’s entrance

Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media

We study dynamics emergent from a two-dimensional reaction--diffusion process modelled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution of cells in a bioactive porous medium, with evolution of the local cell density depending on a coupled quasi--static fluid flow problem. We demonstrate differences emergent from the choice of a discrete lattice or a continuum for the spatial domain of such a process. We find long--time oscillations and steady states in cell density in both lattice and continuum models, but that the continuum model only exhibits solutions with vertical symmetry, independent of initial data, whereas the finite lattice admits asymmetric oscillations and steady states arising from symmetry-breaking bifurcations. We conjecture that it is the structure of the finite lattice which allows for more complicated asymmetric dynamics. Our analysis suggests that the origin of both types of oscillations is a nonlocal reaction-diffusion mechanism mediated by quasi-static fluid flow.Comment: 30 pages, 21 figure

Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport, and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold, and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models, and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.Comment: 38 pages, 16 figures. This version includes a much-expanded introduction, and a new section on nonlinear diffusion in addition to polish throughou

Trajectory and propulsion characteristics of comet rendezvous opportunities

Trajectory and propulsion characteristics of spacecraft rendezvous mission opportunities to comets during 1975 to 199

The Thermal Structure of the Circumstellar Disk Surrounding the Classical Be Star gamma Cassiopeia

We have computed radiative equilibrium models for the gas in the circumstellar envelope surrounding the hot, classical Be star $\gamma$Cassiopeia. This calculation is performed using a code that incorporates a number of improvements over previous treatments of the disk's thermal structure by \citet{mil98} and \citet{jon04}; most importantly, heating and cooling rates are computed with atomic models for H, He, CNO, Mg, Si, Ca, & Fe and their relevant ions. Thus, for the first time, the thermal structure of a Be disk is computed for a gas with a solar chemical composition as opposed to assuming a pure hydrogen envelope. We compare the predicted average disk temperature, the total energy loss in H$\alpha$, and the near-IR excess with observations and find that all can be accounted for by a disk that is in vertical hydrostatic equilibrium with a density in the equatorial plane of $\rho(R)\approx 3$ to $5\cdot 10^{-11} (R/R_*)^{-2.5} \rm g cm^{-3}$. We also discuss the changes in the disk's thermal structure that result from the additional heating and cooling processes available to a gas with a solar chemical composition over those available to a pure hydrogen plasma.Comment: 11 pages, 8 figures high resolution figures available at http://inverse.astro.uwo.ca/sig_jon07.htm

A Second Mortuary Hiatus on Lake Baikal in Siberia and the Arrival of Small-Scale Pastoralism

Peer reviewedPublisher PD

Crystallinity versus mass-loss rate in Asymptotic Giant Branch stars

Infrared Space Observatory (ISO) observations have shown that O-rich Asymptotic Giant Branch (AGB) stars exhibit crystalline silicate features in their spectra only if their mass-loss rate is higher than a certain threshold value. Usually, this is interpreted as evidence that crystalline silicates are not present in the dust shells of low mass-loss rate objects. In this study, radiative transfer calculations have been performed to search for an alternative explanation to the lack of crystalline silicate features in the spectrum of low mass-loss rate AGB stars. It is shown that due to a temperature difference between amorphous and crystalline silicates it is possible to include up to 40% of crystalline silicate material in the circumstellar dust shell, without the spectra showing the characteristic spectral features. Since this implies that low mass-loss rate AGB stars might also form crystalline silicates and deposit them into the Interstellar Medium (ISM), the described observational selection effect may put the process of dust formation around AGB stars and the composition of the predominantly amorphous dust in the Interstellar Medium in a different light. Our model calculations result in a diagnostic tool to determine the crystallinity of an AGB star with a known mass-loss rate.Comment: accepted by A&A, 10 pages, 11 figure