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

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

Supercritical biharmonic equations with power-type nonlinearity

The biharmonic supercritical equation $\Delta^2u=|u|^{p-1}u$, where $n>4$ and $p>(n+4)/(n-4)$, is studied in the whole space $\mathbb{R}^n$ as well as in a modified form with $\lambda(1+u)^p$ as right-hand-side with an additional eigenvalue parameter $\lambda>0$ in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the explicitly known radial {\it singular} solution, provided $p\in((n+4)/(n-4),p_c)$, where $p_c\in ((n+4)/(n-4),\infty]$ is a further critical exponent, which was introduced in a recent work by Gazzola and the second author. The third author proved already that these oscillations do not occur in the complementing case, where $p\ge p_c$. Concerning the Dirichlet problem we prove existence of at least one singular solution with corresponding eigenvalue parameter. Moreover, for the extremal solution in the bifurcation diagram for this nonlinear biharmonic eigenvalue problem, we prove smoothness as long as $p\in((n+4)/(n-4),p_c)$

Santorini volcano as a potential Martian analogue: The Balos Cove Basalts

The interpretation of geologic processes on Mars from sparse meteorite, remote sensing and rover data is influenced by knowledge gained from well-characterized terrestrial analogues. This calls for detailed study of candidate terrestrial analogues and comparison of their observable features to those encountered on the surface of Mars. We evaluated the mineralogical, geochemical, and physical properties of the Balos cove basalts (BCB) from the island of Santorini and compared them to Martian meteorites, Mars rover surface measurements, and other verified Martian analogues obtained from the International Space Analogue Rockstore (ISAR). Twenty rock samples were collected from the Balos cove area based on their freshness, integrity, and basaltic appearance in the field. Optical microscopy of BCB revealed a pilotaxitic to trachytic texture, with olivine and clinopyroxenephenocrysts in a fine groundmass of olivine, clinopyroxene, plagioclase, magnetite, and devitrified glass. All major minerals show normal zoning, including calcic plagioclase (An_(78–85) at the core and An_(60–76) at the rim), augite (En_(36-48)Wo_(41-44)Fs_(11–21)), and olivine (Fo_(74–88)). The dominant bands in the infrared-attenuated total reflectance (IR-ATR) spectra from BCB can be assigned to olivine (~875 cm−1), calcic plagioclase (~1130 cm^(−1)), and augite (~970 cm^(−1)). The whole-rock chemical compositions and mineralogy of the BCB are similar to published analyses of typical olivine-phyric shergottites and basalts and basaltic materials analyzed in Gusev and Gale craters on Mars. BCB porosity is in the range of 7–15% and is similar to the porosities of the ISAR samples. Although no terrestrial rock is ever a perfect match to Martian compositions, the differences in mineralogy and geochemistry between BCB and some classes of Martian samples are relatively subtle and the basalts of Santorini are as close a match as other accepted Mars basalt analogues. The Santorini site offers excellent field logistics that, together with the petrology of the outcrop, makes it a valuable locality for testing and calibration deployments, field training, and other activities related to current and future Mars exploration

Probing the stability of gravastars by dropping dust shells onto them

As a preparation for the dynamical investigations, this paper begins with a short review of the three-layer gravastar model with distinguished attention to the structure of the pertinent parameter space of gravastars in equilibrium. Then the radial stability of these types of gravastars is studied by determining their response for the totally inelastic collision of their surface layer with a dust shell. It is assumed that the dominant energy condition holds and the speed of sound does not exceed that of the light in the matter of the surface layer. While in the analytic setup the equation of state is kept to be generic, in the numerical investigations three functionally distinct classes of equations of states are applied. In the corresponding particular cases the maximal mass of the dust shell that may fall onto a gravastar without converting it into a black hole is determined. For those configurations which remain stable the excursion of their radius is assigned. It is found that even the most compact gravastars cannot get beyond the lower limit of the size of conventional stars, provided that the dominant energy condition holds in both cases. It is also shown---independent of any assumption concerning the matter interbridging the internal de Sitter and the external Schwarzschild regions---that the better is a gravastar in mimicking a black hole the easier is to get the system formed by a dust shell and the gravastar beyond the event horizon of the composite system. In addition, a generic description of the totally inelastic collision of spherical shells in spherically symmetric spacetimes is also provided in the appendix.Comment: 29 pages, 10 figure