Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Constrains on the structure of Maio Island (Cape Verde) by a three-dimensional gravity model: Imaging partially exhumed magma chambers

We propose a 3-D gravity model for the volcanic structure of the island of Maio (Cape Verde archipelago) with the objective of solving some open questions concerning the geometry and depth of the intrusive Central Igneous Complex. A gravity survey was made covering almost the entire surface of the island. The gravity data was inverted through a non-linear 3-D approach which provided a model constructed in a random growth process. The residual Bouguer gravity field shows a single positive anomaly presenting an elliptic shape with a NWSE trending long axis. This Bouguer gravity anomaly is slightly off-centred with the island but its outline is concordant with the surface exposure of the Central Igneous Complex. The gravimetric modelling shows a high-density volume whose centre of mass is about 4500 m deep. With increasing depth, and despite the restricted gravimetric resolution, the horizontal sections of the model suggest the presence of two distinct bodies, whose relative position accounts for the elongated shape of the high positive Bouguer gravity anomaly. These bodies are interpreted as magma chambers whose coeval volcanic counterparts are no longer preserved. The orientation defined by the two bodies is similar to that of other structures known in the southern group of the Cape Verde islands, thus suggesting a possible structural control constraining the location of the plutonic intrusions.

Mechanical behavior and localized failure modes in a porous basalt from the Azores

Basaltic rocks are the main component of the oceanic upper crust, thus of potential interest for water and geothermal resources, storage of CO2 and volcanic edifice stability. In this work, we investigated experimentally the mechanical behavior and the failure modes of a porous basalt, with an initial connected porosity of 18%. Results were acquired under triaxial compression experiments at confining pressure in the range of 25-200 MPa on water saturated samples. In addition, a purely hydrostatic test was also performed to reach the pore collapse critical pressure P*. During hydrostatic loading, our results show that the permeability is highly pressure dependent, which suggests that the permeability is mainly controlled by pre-existing cracks. When the sample is deformed at pressure higher than the pore collapse pressure P*, some very small dilatancy develops due to microcracking, and an increase in permeability is observed. Under triaxial loading, two modes of deformation can be highlighted. At low confining pressure (Pc < 50 MPa), the samples are brittle and shear localization occurs. For confining pressure > 50 MPa, the stress-strain curves are characterized by strain hardening and volumetric compaction. Stress drops are also observed, suggesting that compaction may be localized. The presence of compaction bands is confirmed by our microstructure analysis. In addition, the mechanical data allows us to plot the full yield surface for this porous basalt, which follows an elliptic cap as previously observed in high porosity sandstones and limestones.