Boundary value problems for second order linear difference equations: application to the computation of the inverse of generalized Jacobi matrices

We have named generalized Jacobi matrices to those that are practically tridiagonal, except for the two final entries and the two first entries of its first andits last row respectively. This class of matrices encompasses both standard Jacobiand periodic Jacobi matrices that appear in many contexts in pure and appliedmathematics. Therefore, the study of the inverse of these matrices becomes ofspecific interest. However, explicit formulas for inverses are known only in a fewcases, in particular when the coefficients of the diagonal entries are subjected tosome restrictions.We will show that the inverse of generalized Jacobi matrices can be raisedin terms of the resolution of a boundary value problem associated with a secondorder linear difference equation. In fact, recent advances in the study of lineardifference equations, allow us to compute the solution of this kind of boundaryvalue problems. So, the conditions that ensure the uniqueness of the solution ofthe boundary value problem leads to the invertibility conditions for the matrix,whereas that solutions for suitable problems provide explicitly the entries of theinverse matrix.Peer ReviewedPostprint (author's final draft

Lavoisier: A Low Altitude Balloon Network for Probing the Deep Atmosphere and Surface of Venus

The in-situ exploration of the low atmosphere and surface of Venus is clearly the next step of Venus exploration. Understanding the geochemistry of the low atmosphere, interacting with rocks, and the way the integrated Venus system evolved, under the combined effects of inner planet cooling and intense atmospheric greenhouse, is a major challenge of modern planetology. Due to the dense atmosphere (95 bars at the surface), balloon platforms offer an interesting means to transport and land in-situ measurement instruments. Due to the large Archimede force, a 2 cubic meter He-pressurized balloon floating at 10 km altitude may carry up to 60 kg of payload. LAVOISIER is a project submitted to ESA in 2000, in the follow up and spirit of the balloon deployed at cloud level by the Russian Vega mission in 1986. It is composed of a descent probe, for detailed noble gas and atmosphere composition analysis, and of a network of 3 balloons for geochemical and geophysical investigations at local, regional and global scales

Modelling the effect of air exchange on 222Rn and its progeny concentration in a tunnel atmosphere

The effect of air exchange on the concentration of 222Rn and its progeny in the atmosphere of the Roselend tunnel, in the French Alps, is estimated using a box modelling scheme. In this scheme, the atmosphere is divided into a small number of well mixed zones, separated by flow restricted interfaces, characterized by their exchange rate. A four-box model, representing the three sections of the tunnel present until 2001 and an adjacent inner room, accounts for the spatial variations of the background 222Rn concentration, and for the time structure of transient bursts observed regularly in this tunnel since 1995. A delay of the order of one day, observed during some transient bursts in the inner room with respect to the end of the tunnel, is accounted for if the bursts are assumed to be mainly generated in the end section of the tunnel, and stored temporarily in the inner room via air exchange. The measured radon concentration is reproduced by this model for an air exchange rate of 1.6×10-6 s-1 between the room and the tunnel, in a context of a global ventilation rate of 10-5 s-1 in the tunnel. Gradual onset and decay phases, varying from burst to burst, are also suggested. The equilibrium factor of 222Rn with its progeny, measured in 2002 with values varying from 0.60±0.05 to 0.78±0.06, is interpreted with a five-box model representing the five sections of the tunnel present after 2001. This model indicates that the equilibrium factor does not provide additional constraints on the air exchange rates, but the value of the deposition rate of the unattached short-lived radon progeny can be inferred, with results varying from 0.2 to 6 h-1 in the various sections. This study illustrates the benefits of a simple modelling tool to evaluate the effect of natural ventilation on 222Rn and its progeny concentration in underground cavities, which is important for radioprotection and for a reliable characterization of signatures of hydrogeological or geodynamical processes. Conversely, this study shows that 222Rn and progeny measurements provide a non-invasive method for characterizing natural ventilation conditions in delicate underground cavities, such as painted caves. © 2005 Elsevier B.V. All rights reserved

Temporal variations of radon concentration in the saturated soil of Alpine grassland: The role of groundwater flow

Radon concentration has been monitored from 1995 to 1999 in the soil of the Sur-Frêtes ridge (French Alps), covered with snow from November to April. Measurements were performed at 70 cm depth, with a sampling time of 1 h, at two points: the summit of the ridge, at an altitude of 1792 m, and the bottom of the ridge, at an altitude of 1590 m. On the summit, radon concentration shows a moderate seasonal variation, with a high value from October to April (winter), and a low value from May to September (summer). At the bottom of the ridge, a large and opposite seasonal variation is observed, with a low value in winter and a high value in summer. Fluctuations of the radon concentration seem to be associated with temperature variations, an effect which is largely delusory. Indeed, these variations are actually due to water infiltration. A simplified mixing model is used to show that, at the summit of the ridge, two effects compete in the radon response: a slow infiltration response, rich in radon, with a typical time scale of days, and a fast infiltration of radon-poor rainwater. At the bottom of the ridge, similarly, two groundwater contributions compete: one slow infiltration response, similar to the response seen at the summit, and an additional slower response, with a typical time scale of about a month. This second slower response can be interpreted as the aquifer discharge in response to snow melt. This study shows that, while caution is necessary to properly interpret the various effects, the temporal variations of the radon concentration in soil can be understood reasonably well, and appear to be a sensitive tool to study the subtle interplay of near surface transfer processes of groundwater with different transit times. © 2008 Elsevier B.V. All rights reserved

Diffusive transport of gases in wet porous media. Application to radon

International audienceThe prediction of macroscopic diffusion coefficients in dry and wet porous media still strongly relies on measurements, and numerous semi-empirical correlations have been proposed over the years to replace burdensome experimentations, but the range of validity of these correlations can be limited and is not even well-defined. Here, we present ab initio numerical calculations of the diffusion coefficient of two classes of porous media, namely consolidated and unconsolidated soils, where the water phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. We show that these reconstructed media can well represent two categories of soils generally encountered, namely undisturbed and repacked soils, whose diffusivities, to first order, exhibit two distinct dependencies on porosity under dry conditions, but a similar dependence on the water saturation level. We provide a theoretical support to the popular Buckingham law for dry undisturbed soils in the 0.2 to 0.45 porosity range investigated here. This semi-empirical correlation also compares well with our results on wet consolidated soils, although the dependence of the diffusion coefficient on the water saturation level does not seem to be a simple power law. These results, supported by available experiments on gases such as oxygen, hydrogen, or carbon dioxide, appear to be representative of large classes of porous media. The data and their correlations relative to radon are discussed. Finally, some discrepancy with experimental data regarding the value of the percolation threshold remains, which should be investigated further in the future. © Soil Science Society of America, 5585 Guilford Rd., Madison Wl 53711 USA All rights reserved

Soil gas emanations as precursory indicators of volcanic eruptions

Field measurements conducted on several active volcanoes in Italy, the Lesser Antilles, and Indonesia demonstrate the common Occurrence of diffuse soil gas emanations from the volcanic piles, at distances from active craters or fumarolic zones. These emanations consist essentially of carbon dioxide and rare gases and their genetic link with crater fumaroles and/or magma degassing at depth can be verified both chemically and isotopically. We emphasize here the potential use of these fluids for continuous volcano monitoring and eruption forecasting

Radon emanation and electric potential variations associated with transient deformation near reservoir lakes

Two of the most often cited earthquake precursors are radon emanation and electric potential variations, but these few reported examples have generally been deemed questionable. If a mechanism relating crustal deformation to radon emanation or electrical signals does indeed exist, it is thought to involve fluids. Some preliminary insight has been gained into these processes from the study of natural systems under controlled mechanical and hydrological conditions. Here we report electric potential variations, radon emanation and deformation measurements recorded since 1995 in the French Alps in the vicinity of two artificial lakes which have strong seasonal variations in water level of more than 50 metres. We observe that electric potential variations and radon emanations are repeatedly associated with transient deformation events induced by variations in lake levels. These events are characterized by a change in ground tilt which deviates from the expected elastic response, and are associated with periods of accelerating strain, which suggests that accelerated loading can enhance fluid transport properties. Qualitatively, this behaviour can be accounted for by a model in which straining induces fluid overpressure and dynamic flow in cracks. These observations may shed light on the sensitivity of rock transport properties to deformation

Soil gas emanations as precursory indicators of volcanic eruptions

International audienceField measurements conducted on several active volcanoes in Italy, the Lesser Antilles, and Indonesia demonstrate the common Occurrence of diffuse soil gas emanations from the volcanic piles, at distances from active craters or fumarolic zones. These emanations consist essentially of carbon dioxide and rare gases and their genetic link with crater fumaroles and/or magma degassing at depth can be verified both chemically and isotopically. We emphasize here the potential use of these fluids for continuous volcano monitoring and eruption forecasting