Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Talc is a hydrous magnesium rich layered silicate that is widely disseminated in the Earth from the seafloor to over 100 km depth, in ultra-high pressure metamorphism of oceanic crust. In this paper we determine the single crystal elastic constants at pressures from 0 to 12 GPa of talc triclinic (C 1¯) and monoclinic (C2/c) polytypes using ab initio methods. We find that talc has an extraordinarily high elastic anisotropy at zero pressure that reduces with increasing pressure. The exceptional anisotropy is complemented by a negative Poisson's ratio for many directions in crystal space. Calculations show that talc is not only one of very few common minerals to exhibit auxetic behaviour, but the magnitude of this effect may be the largest reported so far for a mineral. The compression (Vp) and shear (Vs) wave velocity anisotropy is 80% and 85% for the triclinic polytype. At pressures where talc is known be stable in the Earth (up to 5 GPa) the Vp and Vs anisotropy is reduced to about 40% for both velocities, which is still a very high value. Vp is slow parallel to the c-axis and fast perpendicular to it. This remains unchanged with increasing pressure and is observed in both polytypes. The shear wave splitting (difference between fast and slow S-wave velocities) at low pressure has high values in the plane normal to the c-axis, with a maximum near the alow asterisk-axis in the triclinic and the b-axis in the monoclinic polytype. The c-axis is the direction of minimum splitting. The pattern of shear wave splitting does not change significantly with pressure. The volume fraction of talc varies between 11 and 41% for hydrated mantle rocks, but the lack of data on the crystallographic preferred orientation (CPO) precludes a detailed analysis of the impact of talc on seismic anisotropy in subduction zones. However, it is highly likely that CPO can easily develop in zones of deformation due to the platy habit of talc crystals. For random aggregates of talc, the isotropic Vp, Vs and Vp/Vs ratio have significantly lower values than those of antigorite and may explain low-velocity regions in the mantle wedge. Vp/Vs ratios are more complex in anisotropic media because there are fast and slow S-waves, resulting in Vp/Vs1 and Vp/Vs2 ratios for every propagation direction, making interpretation difficult in deformed polycrystalline talc with a CPO. Talc on the subduction plate boundary can strongly influence guided wave velocity as CPO would develop in this region of intense shearing. The very low coefficient of friction (< 0.1) of talc above 100 °C could also explain silent earthquakes at shallow depths (ca 30 km) along the subduction plate boundaries, frequently responsible for tsunami.
ISSN: 0012-821X

hal-00411481
https://hal.archives-ouvertes.fr/hal-00411481
DOI : 10.1016/j.epsl.2008.07.047

Éditeur(s) : HAL CCSD
Résumé : This work is devoted to the theoritical research and to the numerical calculus of weak solutions (in the sens of generalized functions) for the non linear transport equation((∂u)/(∂t))(x,y,t)+a(x,y,t)((∂f(u))/(∂x))(x,y,t)+b(x,y,t)((∂g(u))/(∂y))(x,y,t)=0 pour t>0with the initial condition u(x,y,0)=u₀(x,y) where the functions {(x,y,t)→a(x,y,t)} and {(x,y,t)→b(x,y,t)} belong to L^{∞}(R²×R⁺) (but can be discontinuous), the functions f and g are smooth and monotonous, the function {(x,y)→u₀(x,y)} belongs to L^{∞}(R²). We recall the necessary notions on nonlinear generalized functions for introducing their tensorial product. The main results (to determine the weak solutions) are sufficient conditions so that, when a sum of généralized functions (like Heaviside or Dirac products) is associated with zero, each terms of the sum is equal to zero. Thanks to these theoretical results, we can solve the Riemann problem with the help of a solver written like tensorial product of Heaviside functions (or like a sum of tensorial product of Heaviside functions) in order to obtain the weak solutions. These weak solutions allow to develop two dimensional numerical Godunov type schemes. Then, numerical tests are performed which give a comparison between the results obtained by these 2D schemes and the ones of the splitting method. These tests prove that the 2D numerical schemes are as reliable as the ones obtained by splitting. They are also more simple in their expression. Moreover, a more detailed comparative study of the two types of numerical schemes show that the 2D schemes are far less expensive in the linear case as well as in the non linear case. They are stable for the L^{∞} norm, unlike the splitting schemes. At least some perspectives as well as an existence theorem of a strong solution "almost eveywhere" for linear hyberbolic systems are studied.
Nous nous intéressons à la recherche et au calcul numérique de solutions faibles (au sens des fonctions généralisées) de l'équation de transport non linéaire((∂u)/(∂t))(x,y,t)+a(x,y,t)((∂f(u))/(∂x))(x,y,t)+b(x,y,t)((∂g(u))/(∂y))(x,y,t)=0 pour t>0complétée de la condition initiale : u(x,y,0)=u₀(x,y) où les fonctions {(x,y,t)→a(x,y,t)} et {(x,y,t)→b(x,y,t)} appartiennent à L^{∞}(R²×R⁺) (mais peuvent être discontinues), les fonctions f et g sont lisses et monotones, la fonction {(x,y)→u₀(x,y)} appartient à L^{∞}(R²). Des rappels sur les fonctions généralisées nous permettent d'introduire leur produit tensoriel. Un des résultats clés (pour déterminer ultérieurement les solutions faibles cherchées) donne des conditions suffisantes pour que, lorsqu'une somme de fonctions généralisées (de type produit d'Heaviside ou de Dirac) est associée à 0, chacun des termes de la somme est nul. Grâce à ces résultats théoriques, on résout le problème de Riemann 2D à l'aide d'un solveur s'écrivant comme produit tensoriel de fonctions type Heaviside (ou comme somme de produit tensoriel de fonctions type Heaviside) afin d'obtenir les solutions faibles. Ces solutions faibles permettent la construction des schémas numériques de type Godunov 2D. Nous les validons par des test numériques comparant les résultats obtenus par ces schémas 2D et ceux de la méthode du splitting. Ces tests montrent que les schémas numériques 2D sont aussi fiables que ceux par splitting, alors qu'ils sont plus simples dans leur écriture. Une étude comparative plus complète entre les deux types de schémas numériques montre de plus que les schémas 2D sont nettement moins coûteux à la fois dans les cas linéaire et non linéaire et qu'ils sont stables pour la norme L^{∞}, contrairement aux schémas par splitting. Enfin des perspectives ainsi qu'un théoréme d'existence de solutions fortes "presque partout" pour des systèmes hyperboliques linéaires sont abordés.
https://hal.archives-ouvertes.fr/tel-01487366

Droits : info:eu-repo/semantics/OpenAccess
tel-01487366
https://hal.archives-ouvertes.fr/tel-01487366
https://hal.archives-ouvertes.fr/tel-01487366/document
https://hal.archives-ouvertes.fr/tel-01487366/file/th%C3%A8se_olivier_jouannelle_HAL.pdf

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
Seismic anisotropy has been widely studied this last decade, particularly by measuring splitting of vertically propagating core shear waves. The main interest in this technique is to characterize upper mantle flow beneath seismic stations. On the other hand, the major restriction in this method is that a single station gives a single anisotropy measurement. Alternative methods have been developed in order to avoid this restriction. An accurate determination of upper mantle seismic anisotropy beneath a seismic station may allow one, by doing anisotropy correction, to characterize remote or deeper anisotropy. The Geoscope network is ideal for this purpose because it is composed of a large set (about 26) of high-quality, broadband seismometers globally distributed and because some of these stations have run for more than 10 years and most of them for more than 5 years. We selected about 100 events at each site, generally of magnitude (m b) > 6.0, and we performed systematic measurements of the splitting parameters (fast polarization direction φ and delay time δt) on SKS, SKKS, and PKS phases. Splitting on oceanic islands has been difficult to observe owing to the low quality of the signal but also perhaps owing to complex upper mantle structures beneath the stations. Station KIP (Kipapa, Hawaii) in the Pacific is the only oceanic Geoscope station with a clear anisotropy. We determined well-constrained splitting parameters for 10 of the 17 continental stations that may be explained by a single anisotropic layer. The poor correlation between fast polarization directions and the absolute plate motion together with the apparent incoherence between the plate velocities and the observed delay times suggest that a simple drag-induced asthenospheric flow alone fails to explain most of the observations. For some stations located on or near major lithospheric structures (TAM, Tamanrasset, Algeria, for instance), we observe a good correlation between fast polarization directions and regional structures. At station SCZ (Santa Cruz, California), we found clear variations of the splitting parameters as a function of the event backazimuth, compatible with two layers of anisotropy. Three stations (CAN (Canberra), HYB (Hyderabad, India) and SSB (Saint Sauveur Badole, France)) seem to be devoid of detectable anisotropy.
ISSN: 2169-9313

hal-01388830
http://hal.univ-reunion.fr/hal-01388830
http://hal.univ-reunion.fr/hal-01388830/document
http://hal.univ-reunion.fr/hal-01388830/file/Barruol_anisoGeoscope_JGR1999.pdf
DOI : 10.1029/1999JB900033

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Algorithms issued from the NonLinear Galerkin method have been used in many situations and with different discretizations for the resolution of evolutionary nonlinear equations. The main idea of these methods is to use a splitting of the solution in order to model the equation. According to the splitting of the solution, a splitting of the equation is obtained. The modeling principle is to freeze terms which have a small time variation. In this work we use wavelet discretizations of the 2-D Burgers equations and compare the results with the hierarchical finite elements method. The numerical tests indicate that wavelets give better results than finite elements
ISSN: 0885-7474

hal-00383423
https://hal.archives-ouvertes.fr/hal-00383423
DOI : 10.1007/s10915-004-4806-4

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We compare a global compilation of shear-wave splitting measurements with azimuthal seismic anisotropy parameters inferred from surface-wave tomography. The currently available splitting dataset is taken from a novel comprehensive collection of available publications that is updated interactively online. The comparison between the two types of data is made by calculating predicted splitting parameters from the anisotropic tomography model. Comparing these predicted splitting parameters with the observed ones, we find a considerable correlation between the two datasets at global scale. This result is noteworthy, since such correlation did not seem to exist in previous studies. The spatial resolution associated with the two types of methods is rather different. While surface waves have good vertical resolution and poor lateral resolution of several hundreds of kilometers, SKS splitting measurements have good lateral, but poor vertical resolution. The correlation can be understood in light of recent propositions that anisotropy seen by SKS splitting constrains mostly the upper mantle, and therefore a similar depth region as surface waves. The correlation also confirms the generally good quality of the shear-wave measurements, as well as that of the anisotropic tomography model.
ISSN: 0031-9201

hal-00429396
https://hal.archives-ouvertes.fr/hal-00429396
https://hal.archives-ouvertes.fr/hal-00429396/document
https://hal.archives-ouvertes.fr/hal-00429396/file/Wuestefeld_SKS_SW_correlation_PEPI2009-hal.pdf
DOI : 10.1016/j.pepi.2009.05.006

Éditeur(s) : HAL CCSD Elsevier
Résumé : The dense hydrous magnesium silicate called the D phase is the most likely candidate to recycle hydrogen into the lower mantle in subduction zones. As seismology represents the preferred method to detect this mineral in subduction zones, the single crystal elastic tensor has been calculated using first principle methods. A triple cell (View the MathML source) was used to account for an ordered ideal composition of the D phase to lower mantle pressures. The elastic tensor of the mineral at ambient conditions is predicted to be C11 = 387.7, C33 = 287.7, C44 = 100.4, C12 = 108.0, C13 = 51.1, C14 = − 14.6 in GPa with bulk modulus at zero pressure Ko = 163 GPa and a statistical error of about 4.0 GPa for all constants. The pressure derivatives of the elastic constants have been determined to pressure of 80 GPa. Our tensor correctly predicts the published experimental measurements of linear compressibility along the a- and c-axes, the logarithmic pressure derivative of the c/a axial ratio and bulk modulus at zero pressure. It contradicts the experimentally measured elastic tensor reported by (Liu, L.-G., Okamoto, K., Yang, Y.-J., Chen, C.-C., Lin, C.-C., 2004. Elasticity of single-crystal phase D (a dense hydrous magnesium silicate) by Brillouin spectroscopy. Solid State Commun. 132, 517–520), which fails to reproduce the experimental compressibility data. Using the elastic constants and density predicted to 85 GPa, the seismic anisotropy of P- and S-waves has been calculated as a function of pressure. The single crystal has high P-wave velocities and shear wave splitting in the basal plane below 20 GPa. At high pressures, the maximum P-wave velocities have threefold symmetry normal to a-axes in the basal plane, whereas the maximum shear wave splitting is parallel to a-axes with twofold symmetry. The D phase has high Vp and Vs anisotropy at ambient pressure, 17.6% for Vp and 19.9% for Vs. The Vp anisotropy decreases with increasing pressure to about 30 GPa, while it remains constant at 8% from 30 to 85 GPa. The Vs anisotropy decreases to 17% at 20 GPa and then increases to 22% at 85 GPa. The isotropic velocity ratios of S to P (Rs/p), bulk sound to S (Rphi/s) and density to S (Rρ/s) are calculated as a function of pressure. The Rs/p shows very little variation with pressure with low value of 0.6, whereas both Rphi/s and Rρ/s increase with pressure to peak values of 2.8 and 2.0 respectively at about 60 GPa. The presence of the D phase in subducted horizontal ‘stagnant' plates in the circum Pacific could contribute to a number of seismic observations, such as the observed velocity heterogeneity at depths between 500 and 1000 km and the fast S-waves travelling horizontally with horizontal polarization in this depth range. Further the lower density of the D phase compared with anhydrous minerals could influence buoyancy of the hydrated ‘stagnant' slabs. The transformation of the D phase to perovskite plus ferripericlase during thermal annealing may be responsible for horizontal slab seismogenesis.
ISSN: 0012-821X

hal-00406379
https://hal.archives-ouvertes.fr/hal-00406379
DOI : 10.1016/j.epsl.2007.04.053

Éditeur(s) : HAL CCSD Global Science Press
Résumé : International audience
In this paper, the authors present two different time-discretization schemes combined with a finite-volume space discretization for the incompressible Navier-Stokes equations. They show that the collocated space discretization, usually used with a projection method, can also be extended to other time discretizations over previous projection methods, like the splitting methods. The main advantage of this splitting method is that the pressure approximation is truly of second order. In the first and second parts of this article, two different time-discretization schemes are considered with a collocated space discretization and it is explained how the unknown can be correctly coupled. Numerical simulations are presented in the last part. Tests of spatial and time accuracies are made. The numerical results when the Navier-Stokes problem is solved are shown, in the model problem of the driven cavity.
ISSN: 1815-2406

hal-00730191
https://hal.archives-ouvertes.fr/hal-00730191

Éditeur(s) : HAL CCSD Seismological Society of America
Résumé : Shear-wave splitting measurements are widely used to analyze orientations of anisotropy. We compare two different shear-wave splitting techniques, which are generally assumed to give similar results. Using a synthetic test, which covers the whole backazimuthal range, we find characteristic differences, however, in fast-axis and delay-time estimates near Null directions between the rotation correlation and the minimum energy method. We show how this difference can be used to identify Null measurements and to determine the quality of the result. This technique is then applied to teleseismic events recorded at station LVZ in northern Scandinavia, for which our method constrains the fast-axis azimuth to be 15° and the delay time 1.1 sec.
ISSN: 0037-1106

hal-00404493
https://hal.archives-ouvertes.fr/hal-00404493
DOI : 10.1785/0120060190

Éditeur(s) : HAL CCSD
Résumé : The method of shear-wave splitting provides a unique possibility to identify seismic anisotropy, which is a result of the preferred orientations of the anisotropic minerals by deformation. The novel software SplitLab, presented in this thesis, simplifies the data processing. The comparison of three independent techniques makes it possible to associate an objective quality to the results and also to define a criterion to automatically detect events without splitting (“Nulls”). This criterion is applied to shear-wave splitting measurements at 16 stations located on the East European Craton. The results indicate that the fast directions reflect the ancient blocks, which constitute the East European Craton. The fast directions in south-west are aligned with the margin of the craton and continue the general tendency of offcraton stations. The stations in the Ural foredeep show fast directions perpendicular to the general tendency of the mountain chain. Various indicators give reason to assume lithospheric origins of anisotropy
La mesure du déphasage des ondes de cisaillement offre la possibilité de caractériser l'anisotropie sismique présente dans les différentes couches de la Terre, qui résulte généralement des orientations préférentielles des minéraux anisotropes induites par la déformation. Le nouveau logiciel SplitLab présenté dans cette thèse, simplifie le traitement des données depuis la requête des données jusqu'à la masure de déphasage et l'interprétation des résultats. La comparaison de trois techniques indépendantes pour mesurer ce déphasage permet de quantifier la qualité des résultats et de détecter automatiquement les mesures sans déphasage apparent. Ce critère est appliqué aux mesures de déphasages des ondes SKS enregistrées en 16 stations situées sur le Craton Est Européen. Les résultats indiquent que les directions rapides reflètent les structures anciennes, qui constituent le Craton Est Européen. En outre, les directions rapides dans le Sud-ouest s'alignent avec la bordure du craton et sont en continuité avec la tendance générale définie par les stations éloignées du Craton. Les stations dans les unités externes de l'Oural montrent des directions rapides perpendiculaires à la tendance générale de la chaîne de montagne.
https://tel.archives-ouvertes.fr/tel-00539114

tel-00539114
https://tel.archives-ouvertes.fr/tel-00539114
https://tel.archives-ouvertes.fr/tel-00539114/document
https://tel.archives-ouvertes.fr/tel-00539114/file/thesewustefeld.pdf

Éditeur(s) : HAL CCSD BioMed Central
Résumé : International audience
BACKGROUND: Heat and air pollution are both associated with increases in mortality. However, the interactive effect of temperature and air pollution on mortality remains unsettled. Similarly, the relationship between air pollution, air temperature, and social deprivation has never been explored. METHODS: We used daily mortality data from 2004 to 2009, daily mean temperature variables and relative humidity, for Paris, France. Estimates of chronic exposure to air pollution and social deprivation at a small spatial scale were calculated and split into three strata. We developed a stratified Poisson regression models to assess daily temperature and mortality associations, and tested the heterogeneity of the regression coefficients of the different strata. Deaths due to ambient temperature were calculated from attributable fractions and mortality rates were estimated. RESULTS: We found that chronic air pollution exposure and social deprivation are effect modifiers of the association between daily temperature and mortality. We found a potential interactive effect between social deprivation and chronic exposure with regards to air pollution in the mortality-temperature relationship. CONCLUSION: Our results may have implications in considering chronically polluted areas as vulnerable in heat action plans and in the long-term measures to reduce the burden of heat stress especially in the context of climate change.
ISSN: 1476-069X

hal-01070538
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01070538
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01070538/document
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01070538/file/1476-069X-13-53.pdf
DOI : 10.1186/1476-069X-13-53

Éditeur(s) : HAL CCSD
Résumé : International audience
The purpose of our study is to model a geothermal reservoir. When geothermal reservoir are assumed to be composed of pure water, the transfer of mass and energy is classically described by two balance equations: mass balance equation and the energy balance equation. In addition to those equations, fluid velocity ist classically given by the Darcy law while thermodynamic properties, inferred from theoretical or empirical equations of state, are used to close the mathematical system. Once this system is closed, there exist different solutions. The first one is to solve for pressure and temperature with a variable switch to saturation in the two-phase region (e.g. TOUGH2). The second one is to solve for pressure and enthalpy to increase stability of phase transition between single and two-phase states (e.g. Hydrotherm). We adopted the second option and chose te use a splitting method to get rid of the complexity of coupling equations and a finite volume method for the spatial discretization. Selecting object-oriented languages, we developed a multi-language framework, combining Python, Fortran and a C++ implementation of IAPWS (from the freesteam project) including the supercritical equations, in porous media velocity is given by Darcy law and to close the system physical properties are determined by the IAPWS-IF97 thermodynamic formulation. We resolve the equations in pressure and enthalpy instead of pressure and temperature in order to increase stability and to handle easier the passage from a single-phase to a two-phase system. We solve the system by using a splitting method - to get rid of the complexity of coupling equations - and a finite volume method. We offer some freedom to users thanks to the implementation of several methods like explicit or implicit Euler, Runge-Kutta or BDF2 for time solvers or GMRES and BICGSTAB for the linear solver. We can handle several boundary conditions like no-flow - describing a boundary which can not exchange matter with the exterior - or like a mixed-therm condition - a Dirichlet condition to the pressure and a Dirichlet or an outflow condition to the temperature in order to describe a recharge or a discharge zone - ... We're developing a multi-language framework, combining Python, Fortran and the C++ implementation of IAPWS (from the freesteam project). All these languages are object-oriented. We've applied this simulation model to the dogger in Paris, France, to several one-dimensional systems and a two-dimensional one made by Coumou with the CSMP++ platform. The dogger is a reservoir exploited to produce heat by pumping water at 70 and reinjecting it in the reservoir at 40. In the one-dimensional systems we wanted to observe the process of heat transfer from a higher temperature boundary to a smaller one in a high-energy domain. The last simulation shows the natural convection of water in a fault. For every simulation we compared the solutions we found with an other code (TOUGH2 or CSMP++) and they agreed. The next step will be to model the geothermal plant in Guadeloupe, West Indies. It's the only place in France - and in the West Indies so far - producing electricity with the earth power. The temperature can reach up to 1000 and the pressure range is around a few hundreds MPa. In some surface zones we can see two-phase water at atmospheric pressure. In the 1980s Bouillante was a laboratory for France. Since 1995 Bouillante has given 30GWh electricity a year to the Guadeloupeans.
PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering
Stanford, United States

Droits : info:eu-repo/semantics/OpenAccess
hal-00944133
https://hal-brgm.archives-ouvertes.fr/hal-00944133
https://hal-brgm.archives-ouvertes.fr/hal-00944133/document
https://hal-brgm.archives-ouvertes.fr/hal-00944133/file/Copol.pdf

Éditeur(s) : HAL CCSD Institute for Scientific Computing and Information
Résumé : International audience
In this paper, we solve a problem describing the mechanical deformations of a porous medium in the presence of a monophasic linear flow or a two phase nonlinear flow with the purpose of modelizing subsidence of hydrocarbon reservoirs. An essential characteristics of this problem is that the mechanical deformation and the flow have different time scales. In petroleum industry, one uses different very efficient simulators for the flow problem and the mechanical deformations, which enables to handle complex models. Therefore it is necessary to be able to combine as efficiently as possible the exploitation of these simulators. We propose two alternative splitting approaches. The first one is the staggered algorithm used by engineers, which amounts to a Gauss-Seidel method in the one phase linear case. The second approach is based upon the preconditioned conjugate gradient method. We use a numerical multi-scale method in both of these algorithms. We compare these two approaches and we show that the preconditioned conjugate gradient algorithm is faster and more robust than the staggered algorithm. Applying the preconditioned conjugate gradient algorithm therefore seems to compensate for the fact that the inf-sup condition for the mixed discretization method is not satisfied when combining the simulators for the mechanical deformations and for the flow computations.
ISSN: 1705-5105

Droits : http://creativecommons.org/licenses/by/
hal-01449039
https://hal.archives-ouvertes.fr/hal-01449039
https://hal.archives-ouvertes.fr/hal-01449039/document
https://hal.archives-ouvertes.fr/hal-01449039/file/DHLE.pdf

Résumé : Dans cette thèse nous présentons dans un premier temps une nouvelle notion de différentiabilité généralisée pour les applications multivoques, faisant intervenir des applications positivement homogènes: la H-différentiabilité. Nous étudions la stabilité de cette notion en utilisant la convergence de Fischer, d'abord dédiée aux ensembles mais que nous avons adaptée aux applications multivoques. Nous nous intéressons ensuite à l'étude de la dépendance continue des ensembles de points fixes d'une application multivoque contractante par rapport aux données. Finalement nous analysons la convergence d'une méthode d'approximations successives de type forward-backward splitting, des zéros de la somme de deux opérateurs multivoques non monotones, jouissants notamment de propriétés de pseudo H-différentiabilité
In this thesis we present at first a new concept of generalized differentiation for setvalued mappings, involving positively homogeneous applications: the H-differentiability. We study the stability of this notion by using Fischer convergence,firstly dedicated to sets but which we have adapted to set-valued mappings. We establish the continuous dependence of fixed points sets of set-valued contraction and finally we study the convergence of a forward-backward splitting method for approximating the zeros of the sum of two non-monotone set-valued mappings, notably using properties of pseudo H-differentiability.

http://www.theses.fr/2011AGUY0490/document

Éditeur(s) : HAL CCSD Society for Industrial and Applied Mathematics
Résumé : International audience
In this paper, we developed a theoretical study for nonconservative sytems in one dimension in order to construct numerical schemes for solving the Riemann problem. The nonconservative form of our model system required the use of a well-adapted theory in order to give us a sense of our problem. We chose a framework of generalized functions for solving a scalar hyperbolic equation with a discontinuous coefficient $sigma_t +usigma_x approx 0$, where u is the velocity solution of a Burgers's equation. After an explicit solution of the Riemann problem, we derived Godunov split schemes for computing an approximate solution of the Cauchy problem. We applied our study to a system modeling elasticity and a system modeling gas dynamics. Some stability properties of a scheme and its convergence to a generalized solution are proved for the first model. Numerical experiments confirmed this convergence result. For the second model, calculations of flows containing weak-to-moderate shocks showed that conservation errors are reduced when the mesh is refined but were not entirely eliminated.
ISSN: 0036-1429

hal-00770266
https://hal.univ-antilles.fr/hal-00770266
DOI : 10.1137/S0036142900378637

Éditeur(s) : HAL CCSD
Résumé : In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone.
https://hal.univ-antilles.fr/hal-00783905

hal-00783905
https://hal.univ-antilles.fr/hal-00783905
https://hal.univ-antilles.fr/hal-00783905/document
https://hal.univ-antilles.fr/hal-00783905/file/10.1.1.165.7044.pdf

Éditeur(s) : HAL CCSD Elsevier Masson
Résumé : In French Guiana, the population growth will result in an increase in demand for agricultural products and thus, will lead to an increase in the amount of tropical forests converted into cropland or pasture. Impacts of different agricultural systems on greenhouse gas (GHG) fluxes have not been studied in French Guiana. In this context, the fire-free chop-and-mulch method was used to convert a tropical forest site to agriculture. This study focused on soil nitrous oxide (N2O) emissions and we compared four land uses: (1) the undisturbed tropical forest, (2) recently converted grassland and recently converted croplands (fertilized soybean/maize rotation) with either (3) disk tillage or (4) no tillage.N2O measurements were obtained through the chamber technique and conducted over a 1-year period (measurements began 19 months after the forest was cleared). N2O fluxes were related to soil parameters measured at each sampling date: nitrate and ammonium contents, gravimetric water content (GWC) and temperature.Through the entire period, the mean (±standard error) and median N2O fluxes were 3.8 ± 0.5 and 2.7 g N ha−1 day−1, respectively for undisturbed tropical forest and 2.4 ± 0.9 and 0.8 g N ha−1 day−1, respectively for grassland (mowed Brachiaria ruziziensis). For croplands, no significant difference was found for N2O emissions between both agricultural practices. The mean (±standard error) and median N2O fluxes were 8.5 ± 1.2 and 4.0 g N ha−1 day−1, respectively for disk tillage plots and 8.5 ± 1.3 and 3.6 g N ha−1 day−1, respectively for no tillage plots. Nitrogen inputs (due to the application of fertilizer or due to the mineralization of crop residues) led to higher N2O fluxes, resulting in significantly higher mean N2O emissions from croplands compared to the forest, when only considering land use effect on N2O fluxes in a statistical model. The soil nitrate content, GWC and temperature had a significant positive effect on N2O fluxes. Taking into account these soil parameters in another statistical model, N2O emissions from croplands were not higher than the natural N2O emissions from tropical forest soils. Our results suggest that, if more forest will have to be converted in the course of the expected population growth in French Guiana, it could have low impact on the soil N2O fluxes (similar to natural fluxes from forest) with the improving of farming techniques (for example modification of the splitting of N-fertilizer) in the cropping plots.
ISSN: 0167-8809

hal-01204228
https://hal.archives-ouvertes.fr/hal-01204228
DOI : 10.1016/j.agee.2015.04.004
PRODINRA : 307607

Éditeur(s) : HAL CCSD
Résumé : International audience
To solve general variational inequalities considered in Robinson [9], we propose a generalized version of an algorithm introduced by Bermudez and Moreno [3]. Our results extend, improve and develop some known results in this field.
Advanced Modeling and Optimization

hal-00783892
https://hal.univ-antilles.fr/hal-00783892

Résumé : Cette thèse est consacrée à la résolution d'un problème fondamental de l'analyse variationnelle qu'est la recherchede zéros d'opérateurs maximaux monotones dans un espace de Hilbert. Nous nous sommes tout d'abord intéressés au cas de l'opérateur somme étendue de deux opérateurs maximaux monotones; la recherche d'un zéro de cet opérateur est un problème dont la bibliographie est peu fournie: nous proposons une version modifiée de l'algorithme d'éclatement forward-backward utilisant à chaque itération, l'epsilon-élargissement d'un opérateur maximal monotone,afin de construire une solution. Nous avons ensuite étudié la convergence d'un nouvel algorithme de faisceaux pour construire ID zéro d'un opérateur maximal monotone quelconque en dimension finie. Cet algorithme fait intervenir une double approximation polyédrale de l'epsilon-élargissement de l'opérateur considéré
This thesis is devoted to solving a basic problem of variational analysis which is the search of zeros of maximal monotone operators in a Hilbert space. First of aIl, we concentrate on the case of the extended som of two maximal monotone operators; the search of a zero of this operator is a problem for which the bibliography is not abondant: we purpose a modified version of the forward-backward splitting algorithm using at each iteration, the epsilon-enlargement of a maximal monotone operator, in order to construet a solution. Secondly, we study the convergence of a new bondie algorithm to construet a zero of an arbitrary maximal monotone operator in a finite dimensional space. In this algorithm, intervenes a double polyhedral approximation of the epsilon-enlargement of the considered operator

http://www.theses.fr/2012AGUY0548/document

Éditeur(s) : HAL CCSD Lavoisier
Résumé : National audience
Dans cette étude, nous présentons, une méthode permettant de découvrir, par le biais de variables agrégées et d’un algorithme génétique, des informations non connues a priori et utiles pour la prédiction de crues. Cette méthode se prête particulièrement bien aux données dans lesquelles des informations à propos d’un même élément sont dispersées à travers plusieurs lignes du jeu de données initial.
In this paper, we present an heuristic based approach for feature selection in the context of flood prediction. Features are complex variables that represent aggregate values. We apply a preprocessing method on data in order to elicit relevant information that could not be easily accessible initially because it is split through several lines of a dataset. A genetic algorithm is used in order to search for the features that may prove the best performances for flood prediction.
ISSN: 1633-1311

hal-01184510
https://hal.archives-ouvertes.fr/hal-01184510

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Imaging deep active volcanic areas remains a challenge in our understanding of their activity and evolution, especially in subduction zones. Study of magnetic anomalies is appropriate to access such dynamics in depth. The magnetic anomaly pattern of the Lesser Antilles Arc (LAA) subduction is studied through Curie Point Depth (CPD), interpreted as the depth of the 580 °C isotherm, and developed to better assess the deep thermal structure of the arc. The depth of the estimated CPD exhibits a complex topography. Keeping in mind the overall uncertainty associated with this method, a main doming is evidenced below the Guadeloupe archipelago. Its apex is shifted towards the ancient arc, suggesting a very hot state of the fore-arc/arc domain. To better understand the LAA thermal state, we perform 2D thermo-mechanical simulations of the subduction zone. Recalling that magnetite is a serpentinization by-product, we simulate water transfer triggered by slab dehydration to test the assumption of fore-arc serpentinization suggested by the positive magnetic anomaly in the vicinity of the Guadeloupe archipelago. In this area, the subduction-induced arc lithosphere hydration and related weakening trigger a fast heating of the upper plate by basal convective removal. This process of fast arc lithosphere thinning may apply where simultaneously the volcanic arc is split in two and normal convergence is high enough. As serpentinization strongly decreases P-wave velocity, we propose a new interpretation of a published seismic profile below Guadeloupe. The seismic layer previously interpreted as the arc lower crust may rather be a layer of serpentinized mantle, as supported by spatial correlations between gravimetric and magnetic anomalies. Consequently, at the scale of Guadeloupe Island, the fore-arc Moho would be shallower than initially assumed, with a dome shape more consistent with both the extensive deformation active since the Oligocene in the inner fore-arc and the CPD doming.
ISSN: 0040-1951

Droits : http://creativecommons.org/licenses/by-nc-nd/
insu-01505300
https://hal-insu.archives-ouvertes.fr/insu-01505300
https://hal-insu.archives-ouvertes.fr/insu-01505300/document
https://hal-insu.archives-ouvertes.fr/insu-01505300/file/Gailler-2017.pdf
DOI : 10.1016/j.tecto.2017.03.014