Contact angle of a hemispherical bubble: An analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace's equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity. (C) 2009 Elsevier Inc. All rights reserved.

Surgical proven location of the facial nerve in the vicinity of cerebellopontine angle tumours depicted pre-operatively by tractography

Purpose/Introduction: To determine the clinical utility of pre-operative diffusion tensor (DT) tractography of the facial nerve in the vicinity of cerebellopontine angle (CPA) tumours. The location of the facial nerve was established pre-operatively by tractography and compared with in-vivo electrode stimulation during microsurgery of vestibular schwannomas and rare CPA masses (meningiomas and arachnoid cysts).

The effect of the angle of incidence on the aqueous corrosion of ion implanted M50 steel substrates

Following work on tantalum and chromium implanted flat M50 steel substrates, this work reports on the electrochemical behaviour of M50 steel implanted with tantalum and chromium and the effect of the angle of incidence. Proposed optimum doses for resistance to chloride attack were based on the interpretation of results obtained during long-term and accelerated electrochemical testing. After dose optimization from the corrosion viewpoint, substrates were implanted at different angles of incidence (15°, 30°, 45°, 60°, 75°, 90°) and their susceptibility to localized corrosion assessed using open-circuit measurements, step by step polarization and cyclic voltammetry at several scan rates (5–50 mV s-1). Results showed, for tantalum implanted samples, an ennoblement of the pitting potential of approximately 0.5 V for an angle of incidence of 90°. A retained dose of 5 × 1016 atoms cm-2 was found by depth profiling with Rutherford backscattering spectrometry. The retained dose decreases rapidly with angle of incidence. The breakdown potential varies roughly linearly with the angle of incidence up to 30° falling fast to reach -0.1 V (vs. a saturated calomel electrode (SCE)) for 15°. Chromium was found to behave differently. Maximum corrosion resistance was found for angles of 45°–60° according to current densities and breakdown potentials. Cr+ depth profiles ((p,γ) resonance broadening method), showed that retained doses up to an angle of 60° did not change much from the implanted dose at 90°, 2 × 1017 Cr atoms cm-2. The retained implantation dose for tantalum and chromium was found to follow a (cos θ)8/3 dependence where θ is the angle between the sample normal and the beam direction.

Deep crustal structure across a young passive margin from wide-angle and reflection seismic data (The Sardinia Experiment) - I. Gulf of Lion's margin

The conjugate margins system of the Gulf of Lion and West Sardinia (GLWS) represents a unique natural laboratory for addressing fundamental questions about rifting due to its landlocked situation, its youth, its thick sedimentary layers, including prominent palaeo-marker such as the MSC event, and the amount of available data and multidisciplinary studies. The main goals of the SARDINIA experiment, were to (i) investigate the deep structure of the entire system within the two conjugate margins: the Gulf of Lion and West Sardinia, (ii) characterize the nature of the crust, and (iii) define the geometry of the basin and provide important constrains on its genesis. This paper presents the results of P-wave velocity modelling on three coincident near-vertical reflection multi-channel seismic (MCS) and wide-angle seismic profiles acquired in the Gulf of Lion, to a depth of 35 km. A companion paper [part II Afilhado et al., 2015] addresses the results of two other SARDINIA profiles located on the oriental conjugate West Sardinian margin. Forward wide-angle modelling of both data sets confirms that the margin is characterised by three distinct domains following the onshore unthinned, 33 km-thick continental crust domain: Domain I is bounded by two necking zones, where the crust thins respectively from 30 to 20 and from 20 to 7 km over a width of about 170 km; the outermost necking is imprinted by the well-known T-reflector at its crustal base; Domain II is characterised by a 7 km-thick crust with anomalous velocities ranging from 6 to 7.5 km/s; it represents the transition between the thinned continental crust (Domain I) and a very thin (only 4-5 km) "atypical" oceanic crust (Domain III). In Domain II, the hypothesis of the presence of exhumed mantle is falsified by our results: this domain may likely consist of a thin exhumed lower continental crust overlying a heterogeneous, intruded lower layer. Moreover, despite the difference in their magnetic signatures, Domains II and III present the very similar seismic velocities profiles, and we discuss the possibility of a connection between these two different domains.

Deep crustal structure across a young passive margin from wide-angle and reflection seismic data (The Sardinia Experiment) - II. Sardinia's margin

Geophysical data acquired on the conjugate margins system of the Gulf of Lion and West Sardinia (GLWS) is unique in its ability to address fundamental questions about rifting (i.e. crustal thinning, the nature of the continent-ocean transition zone, the style of rifting and subsequent evolution, and the connection between deep and surface processes). While the Gulf of Lion (GoL) was the site of several deep seismic experiments, which occurred before the SARDINIA Experiment (ESP and ECORS Experiments in 1981 and 1988 respectively), the crustal structure of the West Sardinia margin remains unknown. This paper describes the first modeling of wide-angle and near-vertical reflection multi-channel seismic (MCS) profiles crossing the West Sardinia margin, in the Mediterranean Sea. The profiles were acquired, together with the exact conjugate of the profiles crossing the GoL, during the SARDINIA experiment in December 2006 with the French R/V L'Atalante. Forward wide-angle modeling of both data sets (wide-angle and multi-channel seismic) confirms that the margin is characterized by three distinct domains following the onshore unthinned, 26 km-thick continental crust : Domain V, where the crust thins from 26 to 6 km in a width of about 75 km; Domain IV where the basement is characterized by high velocity gradients and lower crustal seismic velocities from 6.8 to 7.25 km/s, which are atypical for either crustal or upper mantle material, and Domain III composed of "atypical" oceanic crust.The structure observed on the West Sardinian margin presents a distribution of seismic velocities that is symmetrical with those observed on the Gulf of Lion's side, except for the dimension of each domain and with respect to the initiation of seafloor spreading. This result does not support the hypothesis of simple shear mechanism operating along a lithospheric detachment during the formation of the Liguro-Provencal basin.