Sobolev Inequalities for Differential Forms and Lq,pL_{q,p}-cohomology

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is defined to be the quotient of the space of closed differential forms in $L^p(M)$ modulo the exact forms which are exterior differentials of forms in $L^q(M)$.Comment: This paper has appeared in the Journal of Geometric Analysis, (only minor changes have been made since verion 1

Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum–fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape—no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems

Five sepharose-bound ligands for the chromatographic purification of Clostridium collagenase and clostripain

Social media data have provoked a mixed response from researchers. While there is great enthusiasm for this new source of social data – Twitter data in particular – concerns are also expressed about their biases and unknown provenance and, consequently, their credibility for social research. This article seeks a middle path, arguing that we must develop better understanding of the construction and circulation of social media data to evaluate their appropriate uses and the claims that might be made from them. Building on sociotechnical approaches, we propose a high-level abstraction of the ‘pipeline’ through which social media data are constructed and circulated. In turn, we explore how this shapes the populations and samples that are present in social media data and the methods that generate data about them. We conclude with some broad principles for supporting methodologically informed social media research in the future

An engineered, non-diazotrophic cyanobacterium and its application in bioelectrochemical nitrogen fixation

The reduction of chemically inert nitrogen to ammonia is a critical step in the global nitrogen cycle. Microbial nitrogen fixation is a promising way to realize nitrogen reduction and ammonia production at mild conditions. Here, we report an engineered, non-diazotrophic Synechococcus elongatus PCC 7942 strain with nitrogen fixation activity that is constructed by integrating a modified nitrogenase gene cluster into the genome. The engineered S. elongatus PCC 7942 strain is employed in a bioelectrochemical nitrogen-fixation (e-BNF) system for ammonia production. Because the e-BNF system supplies adequate external electrons for the turnover of nitrogenase, the nitrogen fixation activity of the engineered S. elongatus PCC 7942 strain is significantly improved. After 48 h of reaction, the e-BNF system accumulates 173 μM of NH3, which is 21 times higher than that generated from solely photosynthesis-driven nitrogen fixation, with faradaic efficiency of 6.85%. This work may provide new insight into biological nitrogen-fixation systems and ammonium production

Analysis of travelling waves associated with the modelling of aerosolised skin grafts

A previous model developed by the authors investigates the growth patterns of keratinocyte cell colonies after they have been applied to a burn site using a spray technique. In this paper, we investigate a simplified one-dimensional version of the model. This model yields travelling wave solutions and we analyse the behaviour of the travelling waves. Approximations for the rate of healing and maximum values for both the active healing and the healed cell densities are obtained

Turkdean Roman Villa, Gloucestershire: archaeological investigations 1997-1998

Before the transmission of the first ‘live’ Time Team television programme on 23 August 1997, the existence of a Roman villa near Chalkhill Barn in the parish of Turkdean, 12 miles north-east of Cirencester and 2 miles from the Fosse Way, was hardly known to the archaeological community (FIG. 1). That a Roman building did exist in this location had, however, been suspected for a number of years by the landowner, the late Mr Wilf Mustoe. Distinctive linear parchmarks suggestive of buildings had been clearly visible at ground level in the grass pasture each dry summer, and in 1976 Mr Mustoe made a measured sketch plan of them on the back of an envelope. Subsequently the sketch was drawn up into a scale plan entitled ‘Roman villa’ by Simon Goddard, a relation. There was little knowledge of the site outside of Mr Mustoe's family until it was independently ‘discovered’ by local archaeologist Roger Box in August 1996 whilst fortuitously flying over the site in a helicopter. In the evening light Mr Box instantly recognised the parchmarks of an unmistakable Roman villa and took a series of photographs (FIG. 2). Mr Box showed his photographs to Mr Mustoe, and with his agreement wrote to Time Team suggesting that this would be an excellent site for a television programme. Arrangements were duly set in place and the evidence of the cropmarks was confirmed by a trial geophysical survey in March 199

The Structure of IR Luminous Galaxies at 100 Microns

We have observed twenty two galaxies at 100 microns with the Kuiper Airborne Observatory in order to determine the size of their FIR emitting regions. Most of these galaxies are luminous far-infrared sources, with L_FIR > 10^11 L_sun. This data constitutes the highest spatial resolution ever achieved on luminous galaxies in the far infrared. Our data includes direct measurements of the spatial structure of the sources, in which we look for departures from point source profiles. Additionally, comparison of our small beam 100 micron fluxes with the large beam IRAS fluxes shows how much flux falls beyond our detectors but within the IRAS beam. Several sources with point- like cores show evidence for such a net flux deficit. We clearly resolved six of these galaxies at 100 microns and have some evidence for extension in seven others. Those galaxies which we have resolved can have little of their 100 micron flux directly emitted by a point-like active galactic nucleus (AGN). Dust heated to ~40 K by recent bursts of non-nuclear star formation provides the best explanation for their extreme FIR luminosity. In a few cases, heating of an extended region by a compact central source is also a plausible option. Assuming the FIR emission we see is from dust, we also use the sizes we derive to find the dust temperatures and optical depths at 100 microns which we translate into an effective visual extinction through the galaxy. Our work shows that studies of the far infrared structure of luminous infrared galaxies is clearly within the capabilities of new generation far infrared instrumentation, such as SOFIA and SIRTF.Comment: 8 tables, 23 figure

X-ray emitting young stars in the Orion Nebula

The Orion Nebula Cluster and the molecular cloud in its vicinity have been observed with the ACIS-I detector on board the Chandra X-ray Observatory with 23 hours exposure. We detect 1075 X-ray sources: 91% are spatially associated with known stellar members of the cluster, and 7% are newly identified deeply embedded cloud members. This provides the largest X-ray study of a pre-main sequence stellar population. We examine here the X-ray properties of Orion young stars as a function of mass. Results include: (a) the discovery of rapid variability in the O9.5 31 M_o star \theta^2A Ori, and several early B stars, inconsistent with the standard model of X-ray production in small wind shocks; (b) support for the hypothesis that intermediate-mass mid-B through A type stars do not themselves produce significant X-ray emission; (c) confirmation that low-mass G- through M-type T Tauri stars exhibit powerful flaring but typically at luminosities considerably below the `saturation' level; (d) confirmation that the presence or absence of a circumstellar disk has no discernable effect on X-ray emission; (e) evidence that T Tauri plasma temperatures are often very high with T >= 100 MK, even when luminosities are modest and flaring is not evident; and (f) detection of the largest sample of pre-main sequence very low mass objects showing high flaring levels and a decline in magnetic activity as they evolve into L- and T-type brown dwarfs.Comment: 82 pages, 16 figures, 6 tables. To appear in the Astrophysical Journal. For a version with high quality images and electronic tables, see ftp://ftp.astro.psu.edu/pub/edf/orion1