Instability of steady states for nonlinear wave and heat equations

We consider time-independent solutions of hyperbolic equations such as \d_{tt}u -\Delta u= f(x,u) where $f$ is convex in $u$. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the instability occurs as a blow up in finite time. We prove the same result for parabolic equations such as \d_t u -\Delta u= f(x,u). Then we treat several examples under very sharp conditions, including equations with potential terms and equations with supercritical nonlinearities

Sharp bounds on 2m/r for static spherical objects

Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.Comment: We changed a footnote in which an earlier result of H\aa{}kan Andr\'{e}asson was not described correctl

Distribution of surficial sediments in the Southern Evoikos and Petalioi Gulfs, Greece

A series of 123 surficial sediment samples from the Southern Evoikos and Petalioi Gulfs was studied for grain-size properties, carbonate content and mineralogical composition. Distribution of the sediments revealed two sedimentary provinces. The first concerns the Southern Evoikos Gulf, characterised by silty sediments with relatively low carbonate content. Quartz, feldspars, micas, clay and carbonate minerals are the major mineralogical components of the sediments. These sediments are the result of the Asopos River supply during Holocene and they contribute to the formation of smooth bottom morphology. The second province concerns the Petalioi Gulf (Northern and Southern), where the surficial sediments are mainly sandy and characterised by very high carbonate content. Their mineralogical composition reflects the lithology of the drainage basin. Since the modern terrigenous solid supply is limited, these sediments are not considered as products of recent sedimentation, but older deposits (relict sands). Their presence at such depths is justified by sea-level fluctuations and their preservation is due to the low sedimentation rate in the Petalioi Gulf, in combination with the strong hydrodynamic status of the area

How schlieren affects beam transmissometers and LISST-Deep: an example from the stratified Danube River delta, NW Black Sea

The term ‘schlieren’ describes angular deflection of a light ray when it passes through a fluid region characterized by refractive index inhomogeneities. These inhomogeneities in the marine environment are generally caused by density variations, i.e. salinity and temperature anomalies. The influence of schlieren on transmissometers and the in situ particle sizer LISST-Deep of Sequoia Scientific are examined in the Danube delta during October 2007. A seasonal pycnocline driven mainly by an intense temperature gradient was identified as a major hydrological feature. It was associated with high buoyancy frequency values and minor changes of the refractive index of seawater. Measurements of two 25-cm path-length transmissometers (660 nm and 470 nm) showed distinguishable peaks at the pycnocline. LISST also uses a 5-cm transmissometer (670 nm), which proved to be very sensitive in both cases. This is mainly due to its very small acceptance angle, which enables enhanced light scattering outside the lens, thus increasing beam attenuation. Subsequently, LISST falsely predicts abundance of large particles within the pycnoclines. A buoyancy frequency N of 0.01 s-1 is the new proposed threshold for schlieren occurrence

Chromium and Nickel distribution in sediments of a coastal area impacted from metallurgical activities: the case of the Larymna Bay

In the present study, the distribution of Cr and Ni was investigated in the surface sediments from the Larymna Bay (Northern Evoikos Gulf) and in metallurgical slag samples discharged in the marine environment. The results were compared to concentrations of Cr and Ni in parent rocks that outcrop extensively in the catchment area of N. Evoikos in order to distinguish natural and anthropogenic sources of these two elements. Elevated concentrations of Cr and Ni as well as high values of magnetic susceptibility were determined in all samples. Low leachability was determined for Cr since chromite is the major crystalline phase of Cr in the samples analyzed whereas higher leachability was observed for Ni

Bounds on the mass-to-radius ratio for non-compact field configurations

It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here we investigate non-compact static configurations whose matter fields have a slow global spatial decay, bounded by a power law behavior. These matter distributions have no sharp boundaries. We derive an upper bound on the fundamental ratio max_r{2m(r)/r} which is valid throughout the bulk. In its simplest form, the bound implies that in any region of spacetime in which the radial pressure increases, or alternatively decreases not faster than some power law $r^{-(c+4)}$, one has $2m(r)/r \leq (2+2c)/(3+2c)$. [For $c \leq 0$ the bound degenerates to $2m(r)/r \leq 2/3$.] In its general version, the bound is expressed in terms of two physical parameters: the spatial decaying rate of the matter fields, and the highest occurring ratio of the trace of the pressure tensor to the local energy density.Comment: 4 page

Activity‐directed synthesis: A flexible approach for lead generation

Activity‐directed synthesis (ADS) is a structure‐blind, functional‐driven molecular discovery approach. In this Concept, four case studies highlight the general applicability of ADS and showcase its flexibility to support different medicinal chemistry strategies. ADS deliberately harnesses reactions with multiple possible outcomes, and allows many chemotypes to be evaluated in parallel. Resources are focused on bioactive molecules which emerge in tandem with associated synthetic routes. Some of the future challenges for ADS are highlighted, including the realisation of an autonomous molecular discovery platform. The prospects for ADS to become a mainstream lead generation approach are discussed

Geochemical characteristics of late Quaternary sediments from the southern Aegean Sea (Eastern Mediterranean)

Ten cores from the southern Aegean Sea have been logged for their lithological composition and seventy-three sub-samples were analysed for the determination of major and trace elements concentrations. Four lithological units were identified, namely, mud, volcanic, turbidite and sapropel. On the basis of the “Z-2” Minoan ash layer radiocarbon age sedimentation rates for the southern Aegean Sea were estimated at 3.26 to 4.15 cm kyr -1. Simple correlation analysis revealed three groups of elements associated with: (1) biogenic carbonates; (2) terrigenous alumino-silicates and (3) sapropelic layers. R-mode factor analysis applied on the carbonate-free corrected data-set defined four significant factors: (1) the “detrital alumino-silicate factor” represented by Si, Al, Na, K, Rb, Zr, Pb and inversely related to Ca, Mg, and Sr; (2) a “hydrothermal factor” loaded with Cr, Ni, Co, Cu, Fe; (3) the “volcanic ash factor” with high loadings for Ti, Al, Fe, Na and (4) a “sapropel factor” represented by Ba, Mo, and Zn. High factor scores for the “hydrothermal factor” were observed in sediment samples proximal to Nisyros Isl., suggesting a potential hydrothermal influence. Red-brown oxides and crusts dredged from this area support further this possibility. The use of factor analysis enabled for a better understanding of the chemical elements associations that remained obscured by correlation analysis