Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Evidence of a universal scaling relationship for leaf CO2 drawdown along an aridity gradient

The leaf carbon isotope ratio (δ13C) of C3 plants is inversely related to the drawdown of CO2 concentration during photosynthesis, which increases towards drier environments. We aimed to discriminate between the hypothesis of universal scaling, which predicts between-species responses of δ13C to aridity similar to within-species responses, and biotic homoeostasis, which predicts offsets in the δ13C of species occupying adjacent ranges. The Northeast China Transect spans 130–900 mm annual precipitation within a narrow latitude and temperature range. Leaves of 171 species were sampled at 33 sites along the transect (18 at ≥ 5 sites) for dry matter, carbon (C) and nitrogen (N) content, specific leaf area (SLA) and δ13C. The δ13C of species generally followed a common relationship with the climatic moisture index (MI). Offsets between adjacent species were not observed. Trees and forbs diverged slightly at high MI. In C3 plants, δ13C predicted N per unit leaf area (Narea) better than MI. The δ13C of C4 plants was invariant with MI. SLA declined and Narea increased towards low MI in both C3 and C4 plants. The data are consistent with optimal stomatal regulation with respect to atmospheric dryness. They provide evidence for universal scaling of CO2 drawdown with aridity in C3 plants.

Infra-red laser ablative micromachining of parylene-C on SiO2substrates for rapid prototyping, high yield, human neuronal cell patterning

Cell patterning commonly employs photolithographic methods for the micro fabrication of structures on silicon chips. These require expensive photo-mask development and complex photolithographic processing. Laser based patterning of cells has been studied in vitro and laser ablation of polymers is an active area of research promising high aspect ratios. This paper disseminates how 800 nm femtosecond infrared (IR) laser radiation can be successfully used to perform laser ablative micromachining of parylene-C on SiO2 substrates for the patterning of human hNT astrocytes (derived from the human teratocarcinoma cell line (hNT)) whilst 248 nm nanosecond ultra-violet laser radiation produces photo-oxidization of the parylene-C and destroys cell patterning. In this work, we report the laser ablation methods used and the ablation characteristics of parylene-C for IR pulse fluences. Results follow that support the validity of using IR laser ablative micromachining for patterning human hNT astrocytes cells. We disseminate the variation in yield of patterned hNT astrocytes on parylene-C with laser pulse spacing, pulse number, pulse fluence and parylene-C strip width. The findings demonstrate how laser ablative micromachining of parylene-C on SiO2 substrates can offer an accessible alternative for rapid prototyping, high yield cell patterning with broad application to multi-electrode arrays, cellular micro-arrays and microfluidics.

Patterning and detailed study of human hNT astrocytes on parylene-C/silicon dioxide substrates to the single cell level

It is estimated that the adult human brain contains 100 billion neurons with 5–10 times as many astrocytes. Although it has been generally considered that the astrocyte is a simple supportive cell to the neuron, recent research has revealed new functionality of the astrocyte in the form of information transfer to neurons of the brain. In our previous work we developed a protocol to pattern the hNT neuron (derived from the human teratocarcinoma cell line (hNT)) on parylene-C/SiO2 substrates. In this work, we report how we have managed to pattern hNT astrocytes, on parylene-C/SiO2 substrates to single cell resolution. This article disseminates the nanofabrication and cell culturing steps necessary for the patterning of such cells. In addition, it reports the necessary strip lengths and strip width dimensions of parylene-C that encourage high degrees of cellular coverage and single cell isolation for this cell type. The significance in patterning the hNT astrocyte on silicon chip is that it will help enable single cell and network studies into the undiscovered functionality of this interesting cell, thus, contributing to closer pathological studies of the human brain.

Isolating single primary rat hippocampal neurons & astrocytes on ultra-thin patterned parylene-C/silicon dioxide substrates

We report here the patterning of primary rat neurons and astrocytes from the postnatal hippocampus on ultra-thin parylene-C deposited on a silicon dioxide substrate, following observations of neuronal, astrocytic and nuclear coverage on strips of different lengths, widths and thicknesses. Neuronal and glial growth was characterized ‘on’, ‘adjacent to’ and ‘away from’ the parylene strips. In addition, the article reports how the same material combination can be used to isolate single cells along thin tracks of parylene-C. This is demonstrated with a series of high magnification images of the experimental observations for varying parylene strip widths and thicknesses. Thus, the findings demonstrate the possibility to culture cells on ultra-thin layers of parylene-C and localize single cells on thin strips. Such work is of interest and significance to the Neuroengineering and Multi-Electrode Array (MEA) communities, as it provides an alternative insulating material in the fabrication of embedded micro-electrodes, which can be used to facilitate single cell stimulation and recording in capacitive coupling mode.

First human hNT astrocytes patterned to single cell resolution on parylene-C/Silicon dioxide substrates

In our previous work we developed a successful protocol to pattern the human hNT neuron (derived from the human teratocarcinoma cell line (hNT)) on parylene-C/SiO2 substrates. This communication, reports how we have successfully managed to pattern the supportive cell to the neuron, the hNT astrocyte, on such substrates. Here we disseminate the nanofabrication, cell differentiation and cell culturing protocols necessary to successfully pattern the first human hNT astrocytes to single cell resolution on parylene-C/SiO2 substrates. This is performed for varying parylene strip widths providing excellent contrast to the SiO2 substrate and elegant single cell isolation at 10μm strip widths. The breakthrough in patterning human cells on a silicon chip has widespread implications and is valuable as a platform technology as it enables a detailed study of the human brain at the cellular and network level.

Nature of vegetation and building morphology characteristics across a city: influence on shadow patterns and mean radiant temperatures in London

Vegetation and building morphology characteristics are investigated at 19 sites on a north-south LiDAR transect across the megacity of London. Local maxima of mean building height and building plan area density at the city centre are evident. Surprisingly, the mean vegetation height (zv3) is also found to be highest in the city centre. From the LiDAR data various morphological parameters are derived as well as shadow patterns. Continuous images of the effects of buildings and of buildings plus vegetationon sky view factor (Ψ) are derived. A general reduction of Ψ is found, indicating the importance of including vegetation when deriving Ψ in urban areas. The contribution of vegetation to the shadowing at ground level is higher during summer than in autumn. Using these 3D data the influence on urban climate and mean radiant temperature (T mrt ) is calculated with SOLWEIG. The results from these simulations highlight that vegetation can be most effective at reducing heat stress within dense urban environments in summer. The daytime average T mrt is found to be lowest in the densest urban environments due to shadowing; foremost from buildings but also from trees. It is clearly shown that this method could be used to quantify the influence of vegetation on T mrt within the urban environment. The results presented in this paper highlight a number of possible climate sensitive planning practices for urban areas at the local scale (i.e. 102- 5 × 103 m).

Identification of forged Bank of England £20 banknotes using IR spectroscopy

Bank of England notes of £20 denomination have been studied using infrared spectroscopy in order to generate a method to identify forged notes. An aim of this work was to develop a non-destructive method so that a small, compact Fourier transform infrared spectrometer (FT-IR) instrument could be used by bank workers, police departments or others such as shop assistants to identify forged notes in a non-lab setting. The ease of use of the instrument is the key to this method, as well as the relatively low cost. The presence of a peak at 1400 cm−1 arising from νasym () from the blank paper section of a forged note proved to be a successful indicator of the note’s illegality for the notes that we studied. Moreover, differences between the spectra of forged and genuine £20 notes were observed in the ν(OH) (ca. 3500 cm−1), ν(CH) (ca. 2900 cm−1) and ν(CO) (ca. 1750 cm−1) regions of the IR spectrum recorded for the polymer film covering the holographic strip. In cases where these simple tests fail, we have shown how an infrared microscope can be used to further differentiate genuine and forged banknotes by producing infrared maps of selected areas of the note contrasting inks with background paper.

Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs

Wave solutions to a mechanochemical model for cytoskeletal activity are studied and the results applied to the waves of chemical and mechanical activity that sweep over an egg shortly after fertilization. The model takes into account the calcium-controlled presence of actively contractile units in the cytoplasm, and consists of a viscoelastic force equilibrium equation and a conservation equation for calcium. Using piecewise linear caricatures, we obtain analytic solutions for travelling waves on a strip and demonstrate uiat the full nonlinear system behaves as predicted by the analytic solutions. The equations are solved on a sphere and the numerical results are similar to the analytic solutions. We indicate how the speed of the waves can be used as a diagnostic tool with which the chemical reactivity of the egg surface can be measured.

Spatio-temporal variations of ozone and nitrogen dioxide concentrations under urban trees and in a nearby open area

The evergreen Quercus ilex L. is one of the most common trees in Italian urban environments and is considered effective in the uptake of particulate and gaseous atmospheric pollutants. However, the few available estimates on O3 and NO2 removal by urban Q. ilex originate from model-based studies (which indicate NO2/O3 removal capacity of Q. ilex) and not from direct measurements of air pollutant concentrations. Thus, in the urban area of Siena (central Italy) we began long-term monitoring of O3/NO2 concentrations using passive samplers at a distance of 1, 5, 10 m from a busy road, under the canopies of Q. ilex and in a nearby open-field. Measurements performed in the period June 2011-October 2013 showed always a greater decrease of NO2 concentrations under the Q. ilex canopy than in the open-field transect. Conversely, a decrease of average O3 concentrations under the tree canopy was found only in autumn after the typical Mediterranean post-summer rainfalls. Our results indicate that interactions between O3/NO2 concentrations and trees in Mediterranean urban ecosystems are affected by temporal variations in climatic conditions. We argue therefore that the direct measurement of atmospheric pollutant concentrations should be chosen to describe local changes of aerial pollution.

Palaeoenvironmental changes during the Valanginian: new insights from variations in phosphorus contents and bulk- and clay mineralogies in the western Tethys

Paleoenvironmental and paleoclimatic changes during the Valanginian carbon isotopic excursion (CIE) have been investigated in the western Tethys. For this purpose, bulk-rock and clay mineralogies, as well as phosphorus (P) contents were evaluated in a selection of five sections located in the Vocontian Basin (Angles, SE France; Alvier, E Switzerland; Malleval, E France), and the Lombardian Basin (Capriolo, N Italy; Breggia, S Switzerland). Within the CIE interval, bulk-rock and clay mineralogies are inferred to reflect mostly climate change. The onset of the CIE (Busnardoites campylotoxus ammonite Zone) is characterized by higher detrital index (DI: sum of the detrital minerals divided by calcite contents) values and the presence of kaolinite in their clay-mineral assemblages. In the late Valanginian (from the Saynoceras verrucosum Zone up to the end of the Valanginian), the samples show relatively variable DI and lower values or the absence of kaolinite. The variation in the mineralogical composition is interpreted as reflecting a change from a climate characterized by optimal weathering conditions associated with an increase in terrigenous input on the southern European margin during the CIE towards an overall unstable climate associated with drier conditions in the late Valanginian. This is contrasted by a dissymmetry (proximal vs distal) along the studied transect, the northern Tethyan margin being more sensitive to changes in continental input compared to the distal environments. P accumulation rates (PAR) present similar features. In the Vocontian basin, P content variations are associated with changes in terrigenous influx, whereas in the Lombardian basin (i.e. Capriolo and Breggia), PAR values are less well correlated. This is mainly because the deeper part of the Tethys was less sensitive to changes in continental inputs. The onset of the CIE (top of the B. campylotoxus Zone) records a general increase in PAR suggesting an increase in marine nutrient levels. This is linked to higher continental weathering rates and the enhanced influx of nutrients into the ocean. In the period corresponding to the shift itself, P contents show a dissymmetry between the Vocontian and Lombardian basins (proximal vs distal). For the sections of Malleval, Alvier and Angles, a decrease in P concentrations associated to a decrease in detrital input is observed. In Capriolo and Breggia, PAR show maximum values during the plateau, indicating a more complex interaction between different P sources. The time interval including the top of S. verrucosum Zone up to the end of the Valanginian is characterized by variable PAR values, suggesting variable nutrient influxes. These changes are in agreement with an evolution towards seasonally contrasted conditions in the late Valanginian.

Testing projected wild bee distributions in agricultural habitats: predictive power depends on species traits and habitat type

Species distribution models (SDM) are increasingly used to understand the factors that regulate variation in biodiversity patterns and to help plan conservation strategies. However, these models are rarely validated with independently collected data and it is unclear whether SDM performance is maintained across distinct habitats and for species with different functional traits. Highly mobile species, such as bees, can be particularly challenging to model. Here, we use independent sets of occurrence data collected systematically in several agricultural habitats to test how the predictive performance of SDMs for wild bee species depends on species traits, habitat type, and sampling technique. We used a species distribution modeling approach parametrized for the Netherlands, with presence records from 1990 to 2010 for 193 Dutch wild bees. For each species, we built a Maxent model based on 13 climate and landscape variables. We tested the predictive performance of the SDMs with independent datasets collected from orchards and arable fields across the Netherlands from 2010 to 2013, using transect surveys or pan traps. Model predictive performance depended on species traits and habitat type. Occurrence of bee species specialized in habitat and diet was better predicted than generalist bees. Predictions of habitat suitability were also more precise for habitats that are temporally more stable (orchards) than for habitats that suffer regular alterations (arable), particularly for small, solitary bees. As a conservation tool, SDMs are best suited to modeling rarer, specialist species than more generalist and will work best in long-term stable habitats. The variability of complex, short-term habitats is difficult to capture in such models and historical land use generally has low thematic resolution. To improve SDMs’ usefulness, models require explanatory variables and collection data that include detailed landscape characteristics, for example, variability of crops and flower availability. Additionally, testing SDMs with field surveys should involve multiple collection techniques.

Using Africa’s protected area network to estimate the global population of a threatened and declining species: a case study of the critically endangered White-headed Vulture Trigonoceps occipitalis

The White-headed Vulture Trigonoceps occipitalis (WhV) is uncommon and largely restricted to protected areas across its range in sub-Saharan Africa. We used the World Database on Protected Areas to identify protected areas (PAs) likely to contain White-headed Vultures. Vulture occurrence on road transects in Southern, East, and West Africa was adjusted to nests per km2 using data from areas with known numbers of nests and corresponding road transect data. Nest density was used to calculate the number of WhV nests within identified PAs and from there extrapolated to estimate the global population. Across a fragmented range, 400 PAs are estimated to contain 1893 WhV nests. Eastern Africa is estimated to contain 721 nests, Central Africa 548 nests, Southern Africa 468 nests, and West Africa 156 nests. Including immature and nonbreeding birds, and accounting for data deficient PAs, the estimated global population is 5475 - 5493 birds. The identified distribution highlights are alarming: over 78% (n = 313) of identified PAs contain fewer than five nests. A further 17% (n = 68) of PAs contain 5 - 20 nests and 4% (n = 14) of identified PAs are estimated to contain >20 nests. Just 1% (n = 5) of PAs are estimated to contain >40 nests; none is located in West Africa. Whilst ranging behavior of WhVs is currently unknown, 35% of PAs large enough to hold >20 nests are isolated by more than 100 km from other PAs. Spatially discrete and unpredictable mortality events such as poisoning pose major threats to small localized vulture populations and will accelerate ongoing local extinctions. Apart from reducing the threat of poisoning events, conservation actions promoting linkages between protected areas should be pursued. Identifying potential areas for assisted re-establishment via translocation offers the potential to expand the range of this species and alleviate risk.