Vacuum Spacetimes with Future Trapped Surfaces

In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat. Further, this initial data will contain an annular region which is foliated by two-surfaces of topology $S^2$. These two-surfaces are future trapped in the language of Penrose. The Penrose singularity theorem guarantees that the vacuum spacetime which evolves from this initial data is future null incomplete.Comment: 19 page

An MBO scheme for minimizing the graph Ohta-Kawasaki functional

We study a graph based version of the Ohta-Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph based problems inspired by partial differential equations (PDEs) and varational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph based problems to pattern forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman-Bence-Osher (MBO) scheme for minimizing the graph Ohta-Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme Γ-converge to the Ohta-Kawasaki functional (which includes the standard graph based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta-Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta-Kawasaki functional with a mass constraint

Influential parameters on 3-D synthetic ground motions in a sedimentary basin derived from global sensitivity analysis

International audienceSUMMARY Which physical parameters are the most influential when predicting earthquake ground motions in a 3-D sedimentary basin? We answer quantitatively by doing a global sensitivity analysis of two quantities of interest: the peak ground motions (PGMs) and a time–frequency representation (the S transform) of ground motions resulting from the synthetic anelastic responses of the EUROSEISTEST. This domain of interest is modeled by two layers with uncertain depth-dependent mechanical properties and is illuminated by a plane S-wave propagating vertically upward in an uncertain homogeneous elastic bedrock. The global sensitivity analysis is conducted on 800+ physics-based simulations of the EUROSEISTEST requiring 8+ million core-hours (i.e. ≈ 900 yr of mono-core computation). The analysis of the PGMs at the free surface displays the spatial influence of the uncertain input parameters over the entire basin scale, while the analysis of the time–frequency representation shows their influence at a specific location inside the basin. The global sensitivity analysis done on the PGMs points out that their most influential parameter in the middle of the basin is the quality factor QS (it controls up to 80 per cent of the PGMs in certain locations where the sediments thickness is larger than 200 m). On the other hand, the geological layering configuration (here represented by the depth of a geological interface controlling the geological layering) strongly influences the PGMs close to the basin edges, up to 90 per cent. We also found that the shear wave velocity at the free surface of the basin and the one of the bedrock underlying the basin are to be considered on an equal footing, both influencing the PGMs in the middle of the basin and close to its edges. We highlight that the bedrock to basin amplification of the PGMs shows a clear increase with respect to the thickness of the sediments, but this amplification saturates from 200 m of sediments around the value of three and is frequency dependent. This PGMs amplification starts from about one tenth of the mean S-wavelength propagating in the basin. The global sensitivity analysis done on the S transform of the ground motions shows that (i) the own effect of the parameters fully controls the first S-wave train and mostly controls the direct arrival of the basin-induced surfaces waves, (ii) the quality factor QS controls 40–60 per cent of the decay of amplitude of coda waves, the remaining part being mainly controlled by interaction effects due to the coupling effect of several parameters and (iii) the interaction effects between the parameters increases with time, suggesting under the hypotheses of our study that the own effects control the ballistic wave propagation while the interaction effects control the diffusive wave propagation

Displasia fibrosa do clivus: relato de caso Fibrous dysplasia of the clivus: case report

Relatamos o caso de uma paciente de 43 anos com história de cefaléia crônica e diplopia. O exame neurorradiológico demonstrou aumento de volume e alteração na densidade óssea do clivus. Foi submetida a cirurgia e o exame anatomopatológico evidenciou displasia fibrosa. Foram relatados na literatura outros 14 casos de displasia fibrosa envolvendo o clivus. Discutimos essa rara apresentação da doença segundo o quadro clínico, exames de imagem, histologia e tratamento.<br>We describe the case of a 43 year-old woman with chronic headache and diplopia. The neurorradiologic exam showed volume increase and alteration in the bone density of the clivus. She was submitted to surgery and the anatomopathologic evidenced fibrous dysplasia. Other 14 of about fibrous dysplasia involving the clivus are related in the literature. We discuss clinical aspects, image exams, histology and treatment of this rare presentation of the disease

Travel time inversion from ground level to gallery: protocol for the characterization of P-wave seismic signature in a fractured-porous Urgonian platform at hectometric scale

International audienceA tomographic P-wave velocity model is inferred from a ground level-to-gallery vertical 500 m × 800 m seismic experiment conducted at the inter-Disciplinary Underground Science and Technology Laboratory (LSBB, France). No initial knowledge of the velocity structure of the surrounding fractured-porous carbonates was previously available. Ninety-four shots at the surface were recorded by a line of 189 seismometers on the steep slope of the topographic surface and by a line of 150 geophones in an 800 m-long, 250-500 m-depth gallery. The P-wave velocities inferred from first-arrival travel time inversion display a relatively large set of values ranging from 4000 to 6000 m/s. Such VP variations correlate well with the 5 to 20% porosity variations between the main geological units that consist of two sedimentary facies affected by a complex cemented fault zone. Taking advantage of the known geology of the site, this study explores the influence of the acquisition geometry impacted by the topography and of the near-surface weathered zone onto the shallow VP tomography resolution ability. Considering the mesoscopic scale of the targeted medium, reliable imaging of hectometric geological bodies with 10% contrasts in porosities can be achieved only with the simultaneous association of (i) a high density of sources and receivers in the monitoring array geometry, and (ii) the equal consideration of surface-to-gallery and surface-to-surface first-arrival travel times, as an essential constraint to correctly image the underlying structures