Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is \C_+. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C^{m,\al}, $m\ge4$.Comment: 9 pages, v2:final version, to be publishe

Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.Comment: 12 pages, REVTEX, 7 figures, submitted to Physical Review

Metamagnetism in the XXZ model with next-to-nearest-neighbor coupling

We investigate groundstate energies and magnetization curves in the one dimensional XXZ-model with next to nearest neighbour coupling $\alpha>0$ and anisotropy $\Delta$ ($-1 \le \Delta \le 1$) at T=0. In between the familiar ferro- and antiferromagnetic phase we find a transition region -- called metamagnetic phase -- where the magnetization curve is discontinuous at a critical field $B_c(\alpha,\Delta)$.Comment: LaTeX file (text) + 5 PS files (5 figures

VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia

Vascular endothelial growth factor (VEGF-A) is a major regulator of blood vessel formation and function. it controls several processes in endothelial cells, such as proliferation, survival, and migration, but it is not known how these are coordinately regulated to result in more complex morphogenetic events, such as tubular sprouting, fusion, and network formation. We show here that VEGF-A controls angiogenic sprouting in the early postnatal retina by guiding filopodial extension from specialized endothelial cells situated at the tips of the vascular sprouts. The tip cells respond to VEGF-A only by guided migration; the proliferative response to VEGF-A occurs in the sprout stalks. These two cellular responses are both mediated by agonistic activity of VEGF-A on VEGF receptor 2. Whereas tip cell migration depends on a gradient of VEGF-A, proliferation is regulated by its concentration. Thus, vessel patterning during retinal angiogenesis depends on the balance between two different qualities of the extracellular VEGF-A distribution, which regulate distinct cellular responses in defined populations of endothelial cells

Mean Curvature Flow of Spacelike Graphs

We prove the mean curvature flow of a spacelike graph in $(\Sigma_1\times \Sigma_2, g_1-g_2)$ of a map $f:\Sigma_1\to \Sigma_2$ from a closed Riemannian manifold $(\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(\Sigma_2,g_2)$ with bounded curvature tensor and derivatives, and with sectional curvatures satisfying $K_2\leq K_1$, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption $K_2\leq K_1$, that if $K_1>0$, or if $Ricci_1>0$ and $K_2\leq -c$, $c>0$ constant, any map $f:\Sigma_1\to \Sigma_2$ is trivially homotopic provided $f^*g_2<\rho g_1$ where $\rho=\min_{\Sigma_1}K_1/\sup_{\Sigma_2}K_2^+\geq 0$, in case $K_1>0$, and $\rho=+\infty$ in case $K_2\leq 0$. This largely extends some known results for $K_i$ constant and $\Sigma_2$ compact, obtained using the Riemannian structure of $\Sigma_1\times \Sigma_2$, and also shows how regularity theory on the mean curvature flow is simpler and more natural in pseudo-Riemannian setting then in the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages: we replace the condition $K_1\geq 0$ by the the weaker one $Ricci_1\geq 0$. The proofs are essentially the same. We change the title to a shorter one. We add an applicatio

The Metal-Enriched Outer Disk of NGC 2915

We present optical emission-line spectra for outlying HII regions in the extended neutral gas disk surrounding the blue compact dwarf galaxy NGC 2915. Using a combination of strong-line R23 and direct oxygen abundance measurements, we report a flat, possibly increasing, metallicity gradient out to 1.2 times the Holmberg radius. We find the outer-disk of NGC 2915 to be enriched to a metallicity of 0.4 Z_solar. An analysis of the metal yields shows that the outer disk of NGC 2915 is overabundant for its gas fraction, while the central star-foming core is similarly under-abundant for its gas fraction. Star formation rates derived from very deep ~14 ks GALEX FUV exposures indicate that the low-level of star formation observed at large radii is not sufficient to have produced the measured oxygen abundances at these galactocentric distances. We consider 3 plausible mechanisms that may explain the metal-enriched outer gaseous disk of NGC 2915: radial redistribution of centrally generated metals, strong galactic winds with subsequent fallback, and galaxy accretion. Our results have implications for the physical origin of the mass-metallicity relation for gas-rich dwarf galaxies.Comment: 11 pages, 4 figures, accepted to ApJ April 8th, 201

Simulated dynamics of optically pumped dilute nitride 1300 nm spin vertical-cavity surface-emitting lasers

The authors report a theoretical analysis of optically pumped 1300 nm dilute nitride spin-polarised vertical-cavity surface-emitting lasers (VCSELs) using the spin-flip model to determine the regions of stability and instability. The dependence of the output polarisation ellipticity on that of the pump is investigated, and the results are presented in twodimensional contour maps of the pump polarisation against the magnitude of the optical pump. Rich dynamics and various forms of oscillatory behaviour causing self-sustained oscillations in the polarisation of the spin-VCSEL subject to continuouswave pumping have been found because of the competition of the spin-flip processes and birefringence. The authors also reveal the importance of considering both the birefringence rate and the linewidth enhancement factor when engineering a device for high-frequency applications. A very good agreement is found with the experimental results reported by the authors' group. © The Institution of Engineering and Technology 2014

Efficient coupling of photons to a single molecule and the observation of its resonance fluorescence

Single dye molecules at cryogenic temperatures display many spectroscopic phenomena known from free atoms and are thus promising candidates for fundamental quantum optical studies. However, the existing techniques for the detection of single molecules have either sacrificed the information on the coherence of the excited state or have been inefficient. Here we show that these problems can be addressed by focusing the excitation light near to the absorption cross section of a molecule. Our detection scheme allows us to explore resonance fluorescence over 9 orders of magnitude of excitation intensity and to separate its coherent and incoherent parts. In the strong excitation regime, we demonstrate the first observation of the Mollow triplet from a single solid-state emitter. Under weak excitation we report the detection of a single molecule with an incident power as faint as 150 attoWatt, paving the way for studying nonlinear effects with only a few photons.Comment: 6 figure

Importance of exposure route for behavioural responses in Lumbriculus variegatus Müller (Oligochaeta: Lumbriculida) in short-term exposures to Pb

Abstract Goal, Scope and Background Lumbriculus variegatus Müller (Oligochaeta), a common freshwater sediment-dweller, has frequently been used in toxicokinetic studies, although has been less used in ecotoxicity tests. Methods For the first time the Multispecies Freshwater Biomonitor® (MFB) was applied in a short-term whole-sediment toxicity test. The MFB automatically and quantitatively recorded the spontaneous locomotory behaviour of Lumbriculus variegatus in exposures with two compartments, water and sediment. The study questioned, whether the animals altered their locomotion depending on the compartment which was spiked with lead (Pb). Results and Discussion As in the exposures to Pb-contaminated water/clean sediment, the animals exposed to Pb-contaminated sediment/clean water showed higher activities in intermediate Pb-concentrations. This indicates, that spontaneous locomotory activity is affected by Pb-concentrations at sublethal levels regardless of whether the Pb-concentration is found in the water or in the sediment, because these animals use both environmental compartments simultaneously. However, within the same Pb-levels, the animals showed higher locomotory activity in contaminated water compared with contaminated sediment. This indicates a possible tendency to withdraw from (‘avoidance’) contaminated water into the clean sediment compartment, whereas there was no withdrawal from contaminated sediment into clean water. The latter might be explained by the fact that withdrawal from sediment to water might increase the risk of predation and drift in nature, whereas retracting to sediment might provide shelter. Conclusions The study showed that spontaneous locomotory responses of L. variegatus to Pb depend on whether the water or sediment is contaminated. The study also concluded that the Multispecies Freshwater Biomonitor® can be applied effectively in sediment toxicity testing. Recommendations and Perspectives More emphasis should be given to the interactions of water/sediment in sediment ecotoxicity tests to better simulate field conditions and increase ecological realism in risk assessment, especially as quantitative recording methods exisit

Remodeling of an in vitro microvessel exposed to cyclic mechanical stretch.

In the lung, vascular endothelial cells experience cyclic mechanical strain resulting from rhythmic breathing motions and intraluminal blood pressure. Mechanical stress creates evident physiological, morphological, biochemical, and gene expression changes in vascular endothelial cells. However, the exact mechanisms of the mechanical signal transduction into biological response remain to be clarified. Besides, the level of mechanical stress is difficult to determine due to the complexity of the local distension patterns in the lung and thus assumed to be the same as the one acting on the alveolar epithelium. Existing in vitro models used to investigate the effect of mechanical stretch on endothelial cells are usually limited to two-dimensional (2D) cell culture platforms, which poorly mimic the typical three-dimensional structure of the vessels. Therefore, the development of an advanced in vitro vasculature model that closely mimics the dynamic of the human lung vasculatures is highly needed. Here, we present the first study that investigates the interplay of the three-dimensional (3D) mechanical cyclic stretch and its magnitude with vascular endothelial growth factor (VEGF) stimulation on a 3D perfusable vasculature in vitro. We studied the effects of the cyclic strain on a perfusable 3D vasculature, either made of human lung microvascular endothelial cells or human umbilical vein endothelial cells embedded in a gel layer. The in vitro 3D vessels underwent both in-vivo-like longitudinal and circumferential deformations, simultaneously. Our results showed that the responses of the human lung microvascular endothelial cells and human umbilical vein endothelial cells to cyclic stretch were in good agreement. Although our 3D model was in agreement with 2D model in predicting a cytoskeletal remodeling in response to different magnitudes of cyclic stretch, however we observed several phenomena in 3D model that 2D model was unable to predict to. Angiogenic sprouting induced by VEGF decreased significantly in presence of cyclic stretch. Similarly, while treatment with VEGF increased vascular permeability, the cyclic stretch restored vascular barrier tightness and significantly decreased vascular permeability. One of the major findings of this study was that a 3D microvasculature can be exposed to a much higher mechanical cyclic stress level than reported in the literature without any dysfunction of its barrier. For higher magnitudes of the cyclic stretch, the applied longitudinal strain level was 14% and the associated circumferential strain reached the equivalent of 63%. In sharp contrast with our findings, such strain typically leads to the disruption of the endothelial barrier in a 2D stretching assay and is considered pathological. This highlights the importance of 3D modeling to investigate mechanobiology effects rather than using a simple endothelial monolayer which truly recapitulates the in vivo situation