An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme

'Special K' and a loss of cell-to-cell adhesion in proximal tubule-derived epithelial cells: modulation of the adherens junction complex by ketamine

Ketamine, a mild hallucinogenic class C drug, is the fastest growing ‘party drug’ used by 16–24 year olds in the UK. As the recreational use of Ketamine increases we are beginning to see the signs of major renal and bladder complications. To date however, we know nothing of a role for Ketamine in modulating both structure and function of the human renal proximal tubule. In the current study we have used an established model cell line for human epithelial cells of the proximal tubule (HK2) to demonstrate that Ketamine evokes early changes in expression of proteins central to the adherens junction complex. Furthermore we use AFM single-cell force spectroscopy to assess if these changes functionally uncouple cells of the proximal tubule ahead of any overt loss in epithelial cell function. Our data suggests that Ketamine (24–48 hrs) produces gross changes in cell morphology and cytoskeletal architecture towards a fibrotic phenotype. These physical changes matched the concentration-dependent (0.1–1 mg/mL) cytotoxic effect of Ketamine and reflect a loss in expression of the key adherens junction proteins epithelial (E)- and neural (N)-cadherin and β-catenin. Down-regulation of protein expression does not involve the pro-fibrotic cytokine TGFβ, nor is it regulated by the usual increase in expression of Slug or Snail, the transcriptional regulators for E-cadherin. However, the loss in E-cadherin can be partially rescued pharmacologically by blocking p38 MAPK using SB203580. These data provide compelling evidence that Ketamine alters epithelial cell-to-cell adhesion and cell-coupling in the proximal kidney via a non-classical pro-fibrotic mechanism and the data provides the first indication that this illicit substance can have major implications on renal function. Understanding Ketamine-induced renal pathology may identify targets for future therapeutic intervention

An explanation for metallicity effects on X-ray Binary properties

We show that irradiation induced stellar winds can explain two important metallicity effects in X-ray binaries - the higher numbers and the softer spectra of the X-ray binaries in metal rich globular clusters compared to the metal poor ones. As has been previously noted by Iben, Tutukov and Fedorova, the winds should be stronger at lower metallicity due to less efficient line cooling. This will speed up the evolution of the LMXBs in metal poor clusters, hence reducing their numbers. These winds can also provide extra material near the accreting object which may create an intrinsic absorber to harden the X-ray spectra of the metal poor cluster systems relative to the metal rich ones, as suggested by observations. We outline some additional observational predictions of the model.Comment: 6 pages, no figures, accepted to Ap

Blue Straggler Stars: The Spectacular Population in M80

Using HST-WFPC2 observations in two ultraviolet (UV) filters (F225W and F336W) of the central region of the high density Galactic Globular cluster (GGC) M80 we have identified 305 Blue Straggler Stars (BSS) which represents the largest and most concentrated population of BSS ever observed in a GGC. We also identify the largest, clean sample of evolved BSS yet found. The high stellar density alone cannot explain the BSS, and we suggest that in M80 we are witnessing a transient dynamical state, during which stellar interactions are delaying the core-collapse process leading to an exceptionally large population of collisional-BSS.Comment: 15 pages, 5 figures, Astrophysical Journal Letters, in pres

Globular Clusters and X-ray Point Sources in Centaurus A (NGC 5128)

We detect 353 X-ray point sources, mostly low-mass X-ray binaries (LMXBs), in four Chandra observations of Centaurus A (NGC 5128), the nearest giant early-type galaxy, and correlate this point source population with the largest available ensemble of confirmed and likely globular clusters associated with this galaxy. Of the X-ray sources, 31 are coincident with 30 globular clusters that are confirmed members of the galaxy by radial velocity measurement (2 X-ray sources match one globular cluster within our search radius), while 1 X-ray source coincides with a globular cluster resolved by HST images. Another 36 X-ray point sources match probable, but spectroscopically unconfirmed, globular cluster candidates. The color distribution of globular clusters and cluster candidates in Cen A is bimodal, and the probability that a red, metal rich GC candidate contains an LMXB is at least 1.7 times that of a blue, metal poor one. If we consider only spectroscopically confirmed GCs, this ratio increases to ~3. We find that LMXBs appear preferentially in more luminous (massive) GCs. These two effects are independent, and the latter is likely a consequence of enhanced dynamical encounter rates in more massive clusters which have on average denser cores. The X-ray luminosity functions of the LMXBs found in GCs and of those that are unmatched with GCs reveal similar underlying populations, though there is some indication that fewer X-ray faint LMXBs are found in globular clusters than X-ray bright ones. Our results agree with previous observations of the connection of GCs and LMXBs in early-type galaxies and extend previous work on Centaurus A.Comment: 34 pages, 10 figures, 2 tables, Accepted for Publication in The Astrophysical Journa

Another Non-segregated Blue Straggler Population in a Globular Cluster: the Case of NGC 2419

We have used a combination of ACS-HST high-resolution and wide-field SUBARU data in order to study the Blue Straggler Star (BSS) population over the entire extension of the remote Galactic globular cluster NGC 2419. The BSS population presented here is among the largest ever observed in any stellar system, with more than 230 BSS in the brightest portion of the sequence. The radial distribution of the selected BSS is essentially the same as that of the other cluster stars. In this sense the BSS radial distribution is similar to that of omega Centauri and unlike that of all Galactic globular clusters studied to date, which have highly centrally segregated distributions and, in most cases, a pronounced upturn in the external regions. As in the case of omega Centauri, this evidence indicates that NGC 2419 is not yet relaxed even in the central regions. This observational fact is in agreement with estimated half-mass relaxation time, which is of the order of the cluster age.Comment: in press in the Ap

Dissipative dynamics of superfluid vortices at non-zero temperatures

We consider the evolution and dissipation of vortex rings in a condensate at non-zero temperature, in the context of the classical field approximation, based on the defocusing nonlinear Schr\"odinger equation. The temperature in such a system is fully determined by the total number density and the number density of the condensate. A vortex ring is introduced into a condensate in a state of thermal equilibrium, and interacts with non-condensed particles. These interactions lead to a gradual decrease in the vortex line density, until the vortex ring completely disappears. We show that the square of the vortex line length changes linearly with time, and obtain the corresponding universal decay law. We relate this to mutual friction coefficients in the fundamental equation of vortex motion in superfluids.Comment: 4 pages, 3 figure

Families' social backgrounds matter : socio-economic factors, home learning and young children's language, literacy and social outcomes

Parental support with children's learning is considered to be one pathway through which socio-economic factors influence child competencies. Utilising a national longitudinal sample from the Millennium Cohort Study, this study examined the relationship between home learning and parents' socio-economic status and their impact on young children's language/literacy and socio-emotional competence. The findings consistently showed that, irrespective of socio-economic status, parents engaged with various learning activities (except reading) roughly equally. The socio-economic factors examined in this study, i.e., family income and maternal educational qualifications, were found to have a stronger effect on children's language/literacy than on social-emotional competence. Socio-economic disadvantage, lack of maternal educational qualifications in particular, remained powerful in influencing competencies in children aged three and at the start of primary school. For children in the first decade of this century in England, these findings have equity implications, especially as the socio-economic gap in our society widens

Bilateral Differences in Vascular Stiffness and Blood Pressure of Female College Tennis Players and Controls

Vascular stiffness is highly correlated to cardiovascular disease (CVD) and has been attenuated by regular aerobic exercise in older adults. Additionally, body composition strongly predicts vascular stiffness and CVD risk. Previous research has documented that bilateral differences in shear stress lead to differences in vascular endothelial function in tennis players. However, whether this translates into bilateral differences in vascular stiffness and blood pressure remains to be elucidated. The SphygmoCor is a gold standard for assessing arterial stiffness but is not readily accessible. In comparison, the TicWatch GTH Pro, which uses the SphygmoCor algorithm to provide a cardiovascular health (CVH) score (ARTY score), could be a feasible way to monitor CVH, but its accuracy is unknown. PURPOSE: This study aimed to evaluate bilateral differences in vascular stiffness and blood pressure in Division III female college tennis players and recreationally active female students. A secondary aim was to determine if the TicWatch GTH Pro ARTY score relates to SphygmoCor outcomes. METHODS: Subjects from the Skidmore women’s tennis team (n=10) and recreationally active female students (n=10) underwent a single testing session where anthropometrics, body composition, bilateral cardiovascular measurements, and a TicWatch analysis were performed. RESULTS: There were no significant differences in weight, body fat percentage, or BMI between the two groups (p=0.96; p=0.83; p=0.69). Augmentation pressure and augmentation index were different between the dominant and non-dominant arms (p=0.02; p=0.02), but no interactions of the group by arm were observed (all, p\u3e0.05). In addition, the TicWatch ARTY score related significantly with brachial diastolic pressure, mean arterial pressure, and central diastolic pressure (r²= -0.52; r²= -0.50; r²= -0.56). CONCLUSION: In groups well-matched for age and body composition, two indices of vascular stiffness significantly differed between the arms, but this did not appear specific to this cohort of tennis players. The results also indicate that the TicWatch is an accurate device for assessing CVH indicators and may predict brachial diastolic pressure, central diastolic pressure, and mean arterial pressure

The surprising external upturn of the Blue Straggler radial distribution in M55

By combining high-resolution HST and wide-field ground based observations, in ultraviolet and optical bands, we study the Blue Straggler Star (BSS) population of the low density galactic globular cluster M55 (NGC 6809) over its entire radial extent. The BSS projected radial distribution is found to be bimodal, with a central peak, a broad minimum at intermediate radii, and an upturn at large radii. Similar bimodal distributions have been found in other globular clusters (M3, 47 Tucanae, NGC 6752, M5), but the external upturn in M55 is the largest found to date. This might indicate a large fraction of primordial binaries in the outer regions of M55, which seems somehow in contrast with the relatively low (\sim 10%) binary fraction recently measured in the core of this cluster.Comment: in press on Ap