Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order error estimate. The full discrete backward Euler method and the Crank-Nicolson-Galerkin scheme are also considered. Finally, a simple algorithm for solving the fully discrete problem is proposed

Nature and Nurture in Dark Matter Halos

Cosmological simulations consistently predict specific properties of dark matter halos, but these have not yet led to a physical understanding that is generally accepted. This is especially true for the central regions of these structures. Recently two major themes have emerged. In one, the dark matter halo is primarily a result of the sequential accretion of primordial structure (ie `Nature'); while in the other, dynamical relaxation (ie `Nurture') dominates at least in the central regions. Some relaxation is however required in either mechanism. In this paper we accept the recently established scale-free sub-structure of halos as an essential part of both mechanisms. Consequently; a simple model for the central relaxation based on a self-similar cascade of tidal interactions, is contrasted with a model based on the accretion of adiabatically self-similar, primordial structure. We conclude that a weak form of this relaxation is present in the simulations, but that is normally described as the radial orbit instability.Comment: 25 pages, 3 figures, fig with parts 1 to d, fig 3 with parts a to

3D lithium ion batteries—from fundamentals to fabrication

3D microbatteries are proposed as a step change in the energy and power per footprint of surface mountable rechargeable batteries for microelectromechanical systems (MEMS) and other small electronic devices. Within a battery electrode, a 3D nanoarchitecture gives mesoporosity, increasing power by reducing the length of the diffusion path; in the separator region it can form the basis of a robust but porous solid, isolating the electrodes and immobilising an otherwise fluid electrolyte. 3D microarchitecture of the whole cell allows fabrication of interdigitated or interpenetrating networks that minimise the ionic path length between the electrodes in a thick cell. This article outlines the design principles for 3D microbatteries and estimates the geometrical and physical requirements of the materials. It then gives selected examples of recent progress in the techniques available for fabrication of 3D battery structures by successive deposition of electrodes, electrolytes and current collectors onto microstructured substrates by self-assembly methods

Optimal Control of Nonlocal Thermistor Equations

We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of an optimal control is proved. The optimality system consisting of the state system coupled with adjoint equations is derived, together with a characterization of the optimal control. Uniqueness of solution to the optimality system, and therefore the uniqueness of the optimal control, is established. The last part is devoted to numerical simulations.Comment: Submitted 21-March-2012; revised 11-June-2012; accepted 13-June-2012; for publication in the International Journal of Contro

A hierarchy of voids: Much ado about nothing

We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution which is well-peaked about a characteristic void size which evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses which does not have a small-scale cut-off. In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids which happen to be embedded within a larger scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales. In the excursion set formulation of cluster abundance and evolution, solution of the cloud-in-cloud problem, i.e., counting as clusters only those objects which are not embedded in larger clusters, requires study of random walks crossing one barrier. We show that a similar formulation of void evolution requires study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects.Comment: 23 pages, 9 figures, submitted to MNRA

Field evaluation of 3-hydroxy-2-hexanone and ethanol as attractants for the cerambycid beetle pest of vineyards, Xylotrechus arvicola

BACKGROUND: The beetle Xylotrechus arvicola (Coleoptera: Cerambycidae) is a serious pest of vineyards in the Iberian Peninsula. In previous work, the male beetles, but not females, were shown to produce (R)-3-hydroxy-2-hexanone, and female beetles were attracted to this compound in a laboratory bioassay. In this study, release rates of 3-hydroxy-2-hexanone from different dispensers were measured in the laboratory and the attractiveness of these to X. arvicola adults determined in trapping tests in three traditional wine-growing regions in Spain. RESULTS: As a result of laboratory experiments, for field experiments 3-hydroxy-2-hexanone was formulated as 100 µl in a polyethylene sachet (50 mm x 50 mm x 250 µ) and ethanol was formulated as 1 ml in a polyethylene press-seal bag (76 mm x 57 mm x 50 µ). Field catches were similar at all three study sites. Catches in traps baited with 3-hydroxy-2-hexanone alone were not significantly different from those in unbaited control traps, but catches in traps baited with 3-hydroxy-2-hexanone and ethanol in separate sachets, with 3-hydroxy-2-hexanone and ethanol in the same sachet, or with ethanol alone, were significantly greater than those in control traps. These results confirm that the beetles are attracted to ethanol and addition of 3-hydroxy-2-hexanone does not seem to make any difference. CONCLUSIONS: Attraction of females for the male-produced compound, (R)-3-hydroxy-2-hexanone, has been observed in laboratory but not in field experiments. Traps baited with ethanol are highly attractive to both sexes of adults of X. arvicola, and these can be used for improved monitoring of the adult emergence and for population control by mass trapping

The Luminosity, Colour and Morphology dependence of galaxy filaments in the Sloan Digital Sky Survey Data Release Four

We have tested for luminosity, colour and morphology dependence of the degree of filamentarity in seven nearly two dimensional strips from the Sloan Digital Sky Survey Data Release Four (SDSS DR4). The analysis is carried out at various levels of coarse graining allowing us to address different length-scales. We find that the brighter galaxies have a less filamentary distribution than the fainter ones at all levels of coarse graining. The distribution of red galaxies and ellipticals shows a higher degree of filamentarity compared to blue galaxies and spirals respectively at low levels of coarse graining. The behaviour is reversed at higher levels of coarse graining. We propose a picture where the ellipticals are densely distributed in the vicinity of the nodes where the filaments intersect while the spirals are sparsely distributed along the entire extent of the filaments. Our findings indicate that the regions with an excess of ellipticals are larger than galaxy clusters, protruding into the filaments. We have also compared the predictions of a semi-analytic model of galaxy formation (the Millennium Run galaxy catalogue) against our results for the SDSS. We find the two to be in agreement for the $M^{*}$ galaxies and for the red galaxies, while the model fails to correctly predict the filamentarity of the brighter galaxies and the blue galaxies.Comment: 14 Pages, 2 tables, 11 figures, Accepted for publication in MNRAS, new section added for a comparison with semi analytical models of galaxy formation, substantial revisio

The fully connected N-dimensional skeleton: probing the evolution of the cosmic web

A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the discreteness of the sampling. It can be applied within spaces of arbitrary dimensions and geometry. This recursive segmentation of space yields, for a $d$-dimensional space, a $d-1$ succession of $n$-dimensional subspaces that fully characterize the topology of the density field. The final 1D manifold of the hierarchy is the fully connected network of the primary critical lines of the field : the skeleton. It corresponds to the subset of lines linking maxima to saddle points, and provides a definition of the filaments that compose the cosmic web as a precise physical object, which makes it possible to compute any of its properties such as its length, curvature, connectivity etc... When the skeleton extraction is applied to initial conditions of cosmological N-body simulations and their present day non linear counterparts, it is shown that the time evolution of the cosmic web, as traced by the skeleton, is well accounted for by the Zel'dovich approximation. Comparing this skeleton to the initial skeleton undergoing the Zel'dovich mapping shows that two effects are competing during the formation of the cosmic web: a general dilation of the larger filaments that is captured by a simple deformation of the skeleton of the initial conditions on the one hand, and the shrinking, fusion and disappearance of the more numerous smaller filaments on the other hand. Other applications of the N dimensional skeleton and its peak patch hierarchy are discussed.Comment: Accepted for publication in MNRA

Neurocognitive function in HIV infected patients on antiretroviral therapy

OBJECTIVE To describe factors associated with neurocognitive (NC) function in HIV-positive patients on stable combination antiretroviral therapy. DESIGN We undertook a cross-sectional analysis assessing NC data obtained at baseline in patients entering the Protease-Inhibitor-Monotherapy-Versus-Ongoing-Triple therapy (PIVOT) trial. MAIN OUTCOME MEASURE NC testing comprised of 5 domains. Raw results were z-transformed using standard and demographically adjusted normative datasets (ND). Global z-scores (NPZ-5) were derived from averaging the 5 domains and percentage of subjects with test scores >1 standard deviation (SD) below population means in at least two domains (abnormal Frascati score) calculated. Patient characteristics associated with NC results were assessed using multivariable linear regression. RESULTS Of the 587 patients in PIVOT, 557 had full NC results and were included. 77% were male, 68% Caucasian and 28% of Black ethnicity. Mean (SD) baseline and nadir CD4+ lymphocyte counts were 553(217) and 177(117) cells/µL, respectively, and HIV RNA was <50 copies/mL in all. Median (IQR) NPZ-5 score was -0.5 (-1.2/-0) overall, and -0.3 (-0.7/0.1) and -1.4 (-2/-0.8) in subjects of Caucasian and Black ethnicity, respectively. Abnormal Frascati scores using the standard-ND were observed in 51%, 38%, and 81%, respectively, of subjects overall, Caucasian and Black ethnicity (p<0.001), but in 62% and 69% of Caucasian and Black subjects using demographically adjusted-ND (p = 0.20). In the multivariate analysis, only Black ethnicity was associated with poorer NPZ-5 scores (P<0.001). CONCLUSIONS In this large group of HIV-infected subjects with viral load suppression, ethnicity but not HIV-disease factors is closely associated with NC results. The prevalence of abnormal results is highly dependent on control datasets utilised. TRIAL REGISTRY ClinicalTrials.gov, NCT01230580

Gravitational Quenching by Clumpy Accretion in Cool Core Clusters: Convective Dynamical Response to Overheating

Many galaxy clusters pose a "cooling-flow problem", where the observed X-ray emission from their cores is not accompanied by enough cold gas or star formation. A continuous energy source is required to balance the cooling rate over the whole core volume. We address the feasibility of a gravitational heating mechanism, utilizing the gravitational energy released by the gas that streams into the potential well of the cluster dark-matter halo. We focus here on a specific form of gravitational heating in which the energy is transferred to the medium thorough the drag exerted on inflowing gas clumps. Using spheri-symmetric hydro simulations with a subgrid representation of these clumps, we confirm our earlier estimates that in haloes >=10^13 solar masses the gravitational heating is more efficient than the cooling everywhere. The worry was that this could overheat the core and generate an instability that might push it away from equilibrium. However, we find that the overheating does not change the global halo properties, and that convection can stabilize the cluster by carrying energy away from the overheated core. In a typical rich cluster of 10^{14-15}solar masses, with ~5% of the accreted baryons in gas clumps of ~10^8 solar masses, we derive upper and lower limits for the temperature and entropy profiles and show that they are consistent with those observed in cool-core clusters. We predict the density and mass of cold gas and the level of turbulence driven by the clump accretion. We conclude that gravitational heating is a feasible mechanism for preventing cooling flows in clusters.Comment: 16 pages, 7 figures, accepted by MNRA