Characteristic Angles in the Wetting of an Angular Region: Deposit Growth

As was shown in an earlier paper [1], solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper [2], we theoretically investigate the evaporation rate, the flow field and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power Gamma of distance close to the vertex and as a stronger power Beta of distance further from the vertex. The power Gamma depends only slightly on the opening angle Alpha and stays between roughly -1/3 and 0. The power Beta varies from -1 to 0 as the opening angle increases from 0 to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process.Comment: v1: 36 pages, 21 figures, LaTeX; submitted to Physical Review E; v2: minor additions to Abstract and Introductio

Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. <br><br> The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.Comment: 17 pages, 19 figure

Persistence in a Stationary Time-series

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be considered as a limiting case of persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte

Can a “state of the art” chemistry transport model simulate Amazonian tropospheric chemistry?

We present an evaluation of a nested high-resolution Goddard Earth Observing System (GEOS)-Chem chemistry transport model simulation of tropospheric chemistry over tropical South America. The model has been constrained with two isoprene emission inventories: (1) the canopy-scale Model of Emissions of Gases and Aerosols from Nature (MEGAN) and (2) a leaf-scale algorithm coupled to the Lund-Potsdam-Jena General Ecosystem Simulator (LPJ-GUESS) dynamic vegetation model, and the model has been run using two different chemical mechanisms that contain alternative treatments of isoprene photo-oxidation. Large differences of up to 100 Tg C yr^(−1) exist between the isoprene emissions predicted by each inventory, with MEGAN emissions generally higher. Based on our simulations we estimate that tropical South America (30–85°W, 14°N–25°S) contributes about 15–35% of total global isoprene emissions. We have quantified the model sensitivity to changes in isoprene emissions, chemistry, boundary layer mixing, and soil NO_x emissions using ground-based and airborne observations. We find GEOS-Chem has difficulty reproducing several observed chemical species; typically hydroxyl concentrations are underestimated, whilst mixing ratios of isoprene and its oxidation products are overestimated. The magnitude of model formaldehyde (HCHO) columns are most sensitive to the choice of chemical mechanism and isoprene emission inventory. We find GEOS-Chem exhibits a significant positive bias (10–100%) when compared with HCHO columns from the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) and Ozone Monitoring Instrument (OMI) for the study year 2006. Simulations that use the more detailed chemical mechanism and/or lowest isoprene emissions provide the best agreement to the satellite data, since they result in lower-HCHO columns

Vitamin D supplementation in cutaneous malignant melanoma outcome (ViDMe): a randomized controlled trial.

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Ergodicity criteria for non-expanding transformations of 2-adic spheres

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems $$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius $2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of 2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ is assumed to be non-expanding and measure-preserving; that is, $f$ satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and $f$ preserves a natural probability measure on $\mathbb Z_2$, the Haar measure $\mu_2$ on $\mathbb Z_2$ which is normalized so that $\mu_2(\mathbb Z_2)=1$

Common extensor origin release in recalcitrant lateral epicondylitis - role justified?

The aim of our study was to analyse the efficacy of operative management in recalcitrant lateral epicondylitis of elbow. Forty patients included in this study were referred by general practitioners with a diagnosis of tennis elbow to the orthopaedic department at a district general hospital over a five year period. All had two or more steroid injections at the tender spot, without permanent relief of pain. All subsequently underwent simple fasciotomy of the extensor origin. Of forty patients thirty five had improvement in pain and function, two had persistent symptoms and three did not perceive any improvement. Twenty five had excellent, ten had well, two had fair and three had poor outcomes (recurrent problem; pain at rest and night). Two patients underwent revision surgery. Majority of the patients had improvement in pain and function following operative treatment. In this study, an extensor fasciotomy was demonstrated to be an effective treatment for refractory chronic lateral epicondylitis; however, further studies are warranted

High ecosystem service delivery potential of small woodlands in agricultural landscapes

Global forest loss and fragmentation have strongly increased the frequency of forest patches smaller than a few hectares. Little is known about the biodiversity and ecosystem service supply potential of such small woodlands in comparison to larger forests. As it is widely recognized that high biodiversity levels increase ecosystem functionality and the delivery of multiple ecosystem services, small, isolated woodlands are expected to have a lower potential for ecosystem service delivery than large forests hosting more species. We collected data on the diversity of six taxonomic groups covering invertebrates, plants and fungi, and on the supply potential of five ecosystem services and one disservice within 224 woodlands distributed across temperate Europe. We related their ability to simultaneously provide multiple ecosystem services (multiservice delivery potential) at different performance levels to biodiversity of all studied taxonomic groups (multidiversity), forest patch size and age, as well as habitat availability and connectivity within the landscape, while accounting for macroclimate, soil properties and forest structure. Unexpectedly, despite their lower multidiversity, smaller woodlands had the potential to deliver multiple services at higher performance levels per area than larger woodlands of similar age, probably due to positive edge effects on the supply potential of several ecosystem services. Biodiversity only affected multiservice delivery potential at a low performance level as well as some individual ecosystem services. The importance of other drivers of ecosystem service supply potential by small woodlands in agricultural landscapes also depended on the level of performance and varied with the individual ecosystem service considered. Synthesis and applications. Large, ancient woodlands host high levels of biodiversity and can therefore deliver a number of ecosystem services. In contrast, smaller woodlands in agricultural landscapes, especially ancient woodlands, have a higher potential to deliver multiple ecosystem services on a per area basis. Despite their important contribution to agricultural landscape multifunctionality, small woodlands are not currently considered by public policies. There is thus an urgent need for targeted policy instruments to ensure their adequate management and future conservation in order to either achieve multiservice delivery at high levels or to maximize the delivery of specific ecosystem services