On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Unit cell of graphene on Ru(0001): a 25 x 25 supercell with 1250 carbon atoms

The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure has been determined, whereby 25 x 25 graphene unit cells lie on 23 x 23 unit cells of Ru. Each supercell contains 2 x 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers, and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C-C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.Comment: 9 pages, 3 figures, paper submitted to peer reviewed journa

The enlargement of the Suez Canal and introduction of non-indigenous species to the Mediterranean Sea

The Suez Canal is one of the most important waterways in the world – during the last year 17,148 ships passed through the Canal – reducing emissions, saving time, and operating costs to shippers. The rapid increase in ship size from the “Post-Suezmax” (> 12,000 TEU) to the latest container vessels (> 19,000 TEU) now requires enlargements of port facilities and canals. A project of this magnitude, and with potentially negative environmental outcomes, requires a transparent and scientifically sound “Environmental Impact Assessment” (EIA). An explicit obligation on Parties to the Convention on Biological Diversity (https://www.cbd.int/doc/ legal/cbd-en.pdf) was made to consider transboundary impacts on biodiversity, particularly those associated with invasive non-indigenous species

Characterization of nanometer-sized, mechanically exfoliated graphene on the H-passivated Si(100) surface using scanning tunnelling microscopy

We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2x1:H surface. Room temperature, ultra-high vacuum (UHV) tunnelling spectroscopy measurements of nanometer-sized single-layer graphene reveal a size dependent energy gap ranging from 0.1-1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunnelling microscopy (STM) topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nanometer-sized graphene which can assist the development of graphene-based nanoelectronics.Comment: Accepted for publication in Nanotechnolog

Classification of non-indigenous species based on their impacts: Considerations for application in marine management

Assessment of the ecological and economic/societal impacts of the introduction of non-indigenous species (NIS) is one of the primary focus areas of bioinvasion science in terrestrial and aquatic environments, and is considered essential to management. A classification system of NIS, based on the magnitude of their environmental impacts, was recently proposed to assist management. Here, we consider the potential application of this classification scheme to the marine environment, and offer a complementary framework focussing on value sets in order to explicitly address marine management concerns. Since existing data on marine NIS impacts are scarce and successful marine removals are rare, we propose that management of marine NIS adopt a precautionary approach, which not only would emphasise preventing new incursions through pre-border and at-border controls but also should influence the categorisation of impacts. The study of marine invasion impacts requires urgent attention and significant investment, since we lack the luxury of waiting for the knowledge base to be acquired before the window of opportunity closes for feasible management

Ultrastructural characterization of calcification onset and progression in subdermally implanted aortic valves. Histochemical and spectrometric data

Detailed characterization of the subdermal model is a significant tool for better understanding of calcification mechanisms occurring in heart valves. In previous ultrastructural investigation on six-week-implantated aortic valve leaflets, modified pre-embedding glutaraldehyde-cuprolinic-blue reactions (GA-CB) enabled sample decalcification with concurrent retention/staining of lipid-containing polyanionic material, which lined cells and cell-derived matrix-vesicle-like bodies (phthalocyanin-positive layers: PPLs) co-localizing with the earliest apatite nucleation sites. Additional post-embedding silver staining (GA-CB-S) revealed PPLs to contain calcium-binding sites. This investigation concerns valve leaflets subjected to shorter implantation times to shed light on the modifications associated with PPLs generation and calcification onset/progression. Spectrometric estimations revealed time-dependent calcium increase, for unreacted samples, and copper modifications indicating an increase in acidic, non-glycanic material, for GA-CB-reacted samples. Two-day-implant thin sections showed emission and subsequent reabsorption of lamellipodium-like protrusions by cells, originating ECM-containing vacuoles, and/or degeneration stages characterized by the appearance of GA-CB-S-reactive, organule-derived dense bodies and progressive dissolution of all cell membranes. In one-week-implants, the first PPL-lined cells were found to co-exist with cells where GA-CB-S-reactive material accumulated, or exudated towards their edges, or outcropped at the ECM milieu, so acquiring PPL features. PPL-derived material was observed increasingly to affect the ECM on thin sections of one-week- to six-week-implants. These results show an endogenous source for PPLs and reveal that a peculiar cascade of cell degenerative steps is associated with valve mineralization in the subdermal model, providing new useful parameters for more reliable comparison of this experimental calcification process versus the physiological and pathological processes

Ripple modulated electronic structure of a 3D topological insulator

3D topological insulators, similar to the Dirac material graphene, host linearly dispersing states with unique properties and a strong potential for applications. A key, missing element in realizing some of the more exotic states in topological insulators is the ability to manipulate local electronic properties. Analogy with graphene suggests a possible avenue via a topographic route by the formation of superlattice structures such as a moir\'e patterns or ripples, which can induce controlled potential variations. However, while the charge and lattice degrees of freedom are intimately coupled in graphene, it is not clear a priori how a physical buckling or ripples might influence the electronic structure of topological insulators. Here we use Fourier transform scanning tunneling spectroscopy to determine the effects of a one-dimensional periodic buckling on the electronic properties of Bi2Te3. By tracking the spatial variations of the scattering vector of the interference patterns as well as features associated with bulk density of states, we show that the buckling creates a periodic potential modulation, which in turn modulates the surface and the bulk states. The strong correlation between the topographic ripples and electronic structure indicates that while doping alone is insufficient to create predetermined potential landscapes, creating ripples provides a path to controlling the potential seen by the Dirac electrons on a local scale. Such rippled features may be engineered by strain in thin films and may find use in future applications of topological insulators.Comment: Nature Communications (accepted

Homogeneously derived transit timings for 17 exoplanets and reassessed TTV trends for WASP-12 and WASP-4

19 pages, 4 figures, 6 tables; revised manuscript submitted to MNRAS; online-only supplements are in the download archiveWe homogeneously analyse ∼3.2 × 10 5 photometric measurements for ∼1100 transit light curves belonging to 17 exoplanet hosts. The photometric data cover 16 years (2004–2019) and include amateur and professional observations. Old archival light curves were reprocessed using up-to-date exoplanetary parameters and empirically debiased limb-darkening models. We also derive self-consistent transit and radial-velocity fits for 13 targets. We confirm the nonlinear transit timing variation (TTV) trend in the WASP-12 data at a high significance, and with a consistent magnitude. However, Doppler data reveal hints of a radial acceleration of about −7.5 ± 2.2 m s −1 yr −1, indicating the presence of unseen distant companions, and suggesting that roughly 10 per cent of the observed TTV was induced via the light-travel (or Roemer) effect. For WASP-4, a similar TTV trend suspected after the recent TESS observations appears controversial and model dependent. It is not supported by our homogeneous TTV sample, including 10 ground-based EXPANSION light curves obtained in 2018 simultaneously with TESS. Even if the TTV trend itself does exist in WASP-4, its magnitude and tidal nature are uncertain. Doppler data cannot entirely rule out the Roemer effect induced by possible distant companions.Peer reviewe