Éditeur(s) : HAL CCSD
Résumé : In this paper we define the $p$-density of a finite subset $Dsubsetma{N}^r$, and show that it gives a good lower bound for the $p$-adic valuation of exponential sums over finite fields of characteristic $p$. We also give an application: when $r=1$, the $p$-density is the first slope of the generic Newton polygon of the family of Artin-Schreier curves associated to polynomials with their exponents in $D$.
https://hal.archives-ouvertes.fr/hal-00551478

hal-00551478
https://hal.archives-ouvertes.fr/hal-00551478
ARXIV : 0812.3382

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We study the geometrical properties of the subgroups of the multiplicative group of a finite extension of a finite field endowed with its vector space structure, and we show that in some cases the associated projective space has a natural groupe structure. We construct some cyclic codes related to Reed-Muller codes by evaluating polynomials on these subgroups. The geometrical properties of these groups give a fairly simple description of these codes of the Reed-Muller kind.
ISSN: 1071-5797

hal-00770256
https://hal.univ-antilles.fr/hal-00770256
DOI : 10.1006/ffta.1999.0268

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We show that, for any finite field Fq , there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial.
ISSN: 0022-314X

hal-00978911
https://hal.archives-ouvertes.fr/hal-00978911
https://hal.archives-ouvertes.fr/hal-00978911/document
https://hal.archives-ouvertes.fr/hal-00978911/file/AubryBlache5_10.pdf
DOI : 10.1016/j.jnt.2007.10.014

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
The outstanding exposure of deformation bands in a multilayer sequence of the Orange quarry, Provence, France, motivates a study investigating the development and controls of deformation band geometries by field mapping combined with finite element modeling. Field mapping yields new insights into angular relations between, and evolution of, the deformation bands as well as provides input parameters for the setup and boundary conditions of the numerical simulations using ADELI 2D. In particular, reverse-sense deformation bands are found to have developed within three of the four exposed layers of the multilayer stack with similar orientations to bedding, indicating layer-parallel contraction. Numerical simulations, carried out as a parametric study to investigate the influence on deformation band development and geometry, successfully reproduce the sequential development of deformation bands in the three layers as seen in the field as well as recreate the observed angular geometries of similar to 39 degrees to the maximum compression. This angular relationship is put into context with observations from other field studies and theoretical values to explore controls of deformation band orientations. Furthermore, band localization is impeded in the model by increased layer cohesive strength, demonstrating the importance of host-rock property variations on where localization of bands within the multilayer sequence. Results from both field investigation and numerical simulations are consistent with regional tectonics, where the strata underwent gentle folding due to thrust faulting at depth, and bring further insight into the development and geometry of deformation bands in both extensional and contractional tectonic regimes.
ISSN: 0148-0227

hal-00639452
https://hal.archives-ouvertes.fr/hal-00639452
DOI : 10.1029/2011JB008365

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The full numerical simulation of turbulent flows in the context of industrial applications remains a very challenging problem. One of the difficulties is the presence of a large number of interacting scales of different orders of magnitude, ranging from the macroscopic scale to the Kolmogorov dissipation scale. In order to better understand and simulate these interactions, new algorithms of incremental type have recently been introduced, stemming from the theory of infinite-dimensional dynamical systems (see, e.g., the algorithms of Foias, Jolly et al. (1988), Foias, Manley and Temam (1988), Laminie et al. (1993, 1994), Marion and Temam (1989, 1990), and Temam (1990)). These algorithms are based on decompositions of the unknown functions into a large- and a small-scale component, one of the underlying ideas being to approximate the corresponding attractor. In the context of finite element methods, the decomposition of a solution into small- and large-scale components appears when we consider hierarchical bases (Yserentant, 1986; Zienkiewicz et al., 1982). In the present article we derive several estimates of the size of the structures for the linear and nonlinear terms which correspond to interactions of different hierarchical components of the velocity field, and also their time variation. The one-step time variation of these terms can be smaller than the expected accuracy of the computation. Using this remark, we implement an adaptive spatial and temporal multilevel algorithm which treats differently the small- and large-scale components of the flow. We derive several a priori estimates in order to study the perturbation introduced into the approximated equations. All the interaction terms between small- and large-scale structures are frozen during several time steps. Finally, we implement the multilevel method in order to simulate a bidimensional flow described by the Burgers equations. We perform a parametric study of the procedure and its efficiency. The gain in CPU time is significant and the trajectories computed by our multi-scale method remain close to the trajectories obtained with the classical Galerkin method.
ISSN: 0168-9274

hal-00730710
https://hal.archives-ouvertes.fr/hal-00730710

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : This paper presents an inversion method using the interseismic velocity field to determine effective rigidity of the lithosphere. The method is based on the minimization of a cost function defined as the quadratic measure of the difference between measured and modelled velocity fields on a discrete set of points. The continuous mapping of the rigidity is fulfilled with a limited set of parameters and the forward solution is achieved using a plane stress finite element code. The computation of the cost function gradient in the parameters' space allows one to iteratively find the best parameters set through a suitable optimization algorithm.;We first design a benchmark including an abrupt rigidity variation that cannot be described by a continuous function. For such a case, we show that increasing the number of parameters is a way to accurately describe sharp variations of the rigidity map. Then, we use a dense GPS velocity field over the southwestern United States to estimate the corresponding rigidity variations for different spatial resolutions of the parameters' grid. We analyse the conceptual and practical difficulties associated with our methodology. Finally, rigidity maps obtained by our inversion method in southwestern United States and particularly across the San Andreas Fault System are reviewed and compared to current plate rigidity estimates and geophysical data over this area.
ISSN: 0956-540X

hal-00669897
https://hal.archives-ouvertes.fr/hal-00669897
DOI : 10.1111/j.1365-246X.2011.05192.x

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : International audience
We performed forward modelling of seismic anisotropy beneath a migrating strike-slip plate boundary to: (1) test if such a geodynamic context might explain teleseismic shear wave splitting data in the vicinity of the central part of the San Andreas Fault and (2) constrain the power of such data to unravel vertical and lateral variations in deformation patterns in the upper mantle. The modelling involves five steps: (1) thermomechanical modelling, using a finite-element code, of the deformation field, (2) viscoplastic self-consistent modelling of the resulting olivine and pyroxene crystal preferred orientations, (3) calculation of the elasticity tensors for different domains of the finite elements (FEs) model, (4) forward modelling of seismic wave propagation through the model using ray theory, finite-frequency theory and a full-wave approach and (5) performing splitting measurements on the synthetic seismograms. SKS splitting data in central California are best fitted by a model with a hotter geotherm within 60 km of the plate boundary accounting for the opening of an asthenospheric window due to the northward migration of the Mendocino Triple Junction. The westward motion of the plate boundary cannot however explain the rotation of fast polarization directions east of the San Andreas Fault in central California. Comparison between modelled and measured individual shear wave splitting also implies that the homogeneity of the two-layer models accounting for the observations in the vicinity of the San Andreas Fault indicates a sharp transition between lithospheric and asthenospheric deformations beneath this plate boundary. The ability of different synthetic approaches to localize horizontally and vertically the plate boundary-related deformation differs significantly. Splitting in ray theory synthetics closely follow variations in olivine crystallographic preferred orientations in the model. In contrast, splitting analysis on full-wave synthetics, which should be more representative of actual long-period SKS waves, results in smooth apparent lateral variations of anisotropy; the exact location and width of the plate boundary may only be retrieved by comparing fast-polarization profiles obtained using a multichannel analysis on waves with different periods.
ISSN: 0956-540X

hal-01236150
http://hal.univ-reunion.fr/hal-01236150
http://hal.univ-reunion.fr/hal-01236150/document
http://hal.univ-reunion.fr/hal-01236150/file/Bonnin_San_Andreas_modelling_GJI2012.pdf
DOI : 10.1111/j.1365-246X.2012.05650.x

Éditeur(s) : HAL CCSD Société géologique de France
Résumé : International audience
In this paper, we provide the first structural map of Les Saintes archipelago (Guadeloupe, Lesser Antilles). The finite strain pattern displays four families of fault systems characterized by their statistical structural orientations: N000-N020, N050-N070, N090-N110 and N130-N140 trending fault systems. Our onshore results thus underline a fault network much more complex than the one depicted by the previous offshore geophysical investigations around Les Saintes archipelago, which show only N120-N150 trending system. According to the available K-Ar dating of the volcanic rocks and the relative chronology of the faults defined in the field, we determine the deformation history in Les Saintes islands since the last 3 Ma. The four highlighted trending fault systems are already active since the Pliocene and are consistent with the present-day extensional tectonics in the Guadeloupe archipelago compatible with the reactiva-tion of inherited structures at the active arc scale. We interpret the tectonic evolution of Les Saintes islands as the result of interplay between subduction of aseismic ridges (Tiburon and Barracuda ridges) and oblique convergence. Furthermore , we recognized an exhumed geothermal paleo-system in Terre-de-Haut island which is a good analogue of the present-day active Bouillante geothermal system. Its duration is estimated at 400 k.y. during the Pliocene.
EISSN: 1777-5817

hal-01625778
https://hal.univ-antilles.fr/hal-01625778
https://hal.univ-antilles.fr/hal-01625778/document
https://hal.univ-antilles.fr/hal-01625778/file/VeratIEtAl_Final.pdf
DOI : 10.2113/gssgfbull.187.1.3

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Field evidence for syn-deformation migmatization and crystallization along the Karakorum fault contradicts the study of Wang et al. (2012). The ages of such magmatic rocks provide minimum ages for the onset of deformation at similar to 23 Ma in North Ayilari and similar to 19 Ma in Tangtse. The onset of deformation at 12 Ma in the Ayilari range inferred by Wang et al. (2012) from a muscovite Ar/Ar age is a cooling age, thus only a minimum age. The similar to 60 Ma granodiorite bodies, the ophiolitic rocks and the south Kailash thrust that are correlated across the fault to provide a 52 +/- 2 km finite offset do not define reliable piercing points. Such observations as well as our previous work concur to show that the Karakorum fault initiated in the Oligo-Miocene, and has a long-term dextral slip-rate between 7.5 and 13 mm/yr, approximately twice that proposed by Wang et al. (2012).
ISSN: 0012-821X

hal-00829469
https://hal.archives-ouvertes.fr/hal-00829469
DOI : 10.1016/j.epsl.2012.12.012

Éditeur(s) : HAL CCSD Elsevier Masson
Résumé : International audience
The seismological study of recent seismic crises near Oleron Island confirms the coexistence of an extensional deformation and a transtensive regime in the Atlantic margin of France, which is different from the general western European stress field corresponding to a strike-slip regime. We argue that the switch of the principal stress axes σ1/σ2 in a NW-SE vertical plane is linked with the existence of crustal heterogeneities. Events of magnitude larger than 5 sometimes occur along the Atlantic margin of France, such as the 7 September 1972 (ML = 5.2) earthquake near Oleron island and the 30 September 2002 (ML = 5.7) Hennebont event in Brittany. To test the mechanism of local strain localization, we model the deformation of the hypocentral area of the Hennebont earthquake using a 3D thermo-mechanical finite element code. We conclude that the occurrence of moderate earthquakes located in limited parts of the Hercynian shear zones (as the often reactivated swarms near Oleron) could be due to local reactivation of pre-existing faults. These sporadic seismic ruptures are favoured by stress concentration due to rheological heterogeneities.
ISSN: 1631-0713

hal-00936220
https://hal.archives-ouvertes.fr/hal-00936220
DOI : 10.1016/j.crte.2013.07.004

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The interseismic velocity field provided by geodetic methods is generally interpreted in the framework of a thick elastic lithosphere with a slipping fault at depth. Because lateral variations of lithospheric rheology play a key role in determining the geological strain distribution, I examine the idea that interseismic strain rate variations also occur in response to lateral variations in the elastic thickness of the lithosphere. Using a stress balance principle and some simplifying assumptions, I show using a 1D model that elastic thickness is inversely proportional to strain rate for the simple case of pure strike-slip faulting. Elastic thickness computed on three profiles crossing the San Andreas fault system (SAFS) suggests that the distribution of interseismic strain rate is compatible with a thick elastic lithosphere in the Great Basin-Sierra Nevada province and on the Pacific plate. Conversely, a thin plate with a shallow asthenosphere is needed on the SAFS to explain its high strain rate. A 2.5D Finite Element model of interseismic strain in the Carrizo Plain region in Central California shows how known vertical and horizontal variations of elastic properties refine 1D model predictions. In a case of a multiple fault system, I point out that the interseismic velocity is not causally tied to faults slip rate. Therefore, analysing the velocity field across the SAFS cannot reliably provide faults slip rate distribution as previously claimed. Rather, the apparent correlation between geologic slip rate and interseismic strain may only indicate that the elastic thickness plays a dominant role in controlling fault strength. Finally, I suggest that interseismic geodetic strain could be a new way to infer effective elastic plate thickness on the continents.
ISSN: 0012-821X

hal-00412155
https://hal.archives-ouvertes.fr/hal-00412155
DOI : 10.1016/j.epsl.2008.01.046

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Numerical programs for simulating flow and reactive transport in porous media is essential for predicting reservoir properties related to CO2 sequestration performance, subsurface storage and risk assessment. In this paper we solve the Navier Stokes' equation using finite difference method, on a simulated porous rock structure, to study the velocity distribution of fluid flowing through it under a constant pressure gradient. A reactive solute carried through the fluid is allowed to interact with the minerals in the rock. This chemical reaction dissolves the mineral which changes the rock structure thus affecting its flow properties. These changes of flow properties are studied with variation in reactive solute concentration and pressure field. The different mechanisms of dissolution responsible for the variation of flow properties for the different parameters is predicted. Before the onset of homogeneous dissolution, variation in porosity follows a power-law behaviour with change in permeability when the latter is scaled by the concentration of the reactive species. The simulation results are compared with available experimental data and found to give a reasonable match.
ISSN: 0022-1694

hal-00757760
https://hal.archives-ouvertes.fr/hal-00757760
DOI : 10.1016/j.jhydrol.2012.05.024

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We are concerned with the three-dimensional magnetostatic problem where the nonhomogeneities and the source are confined to a bounded domain. We derive a mixed formulation of this problem whose unknowns are the magnetic field, a current vector potential which is introduced as an auxiliary unknown, and a boundary unknown which results from the boundary integral method. This formulation is an improvement with respect to previous formulations proposed in the literature in the sense that it leads to an easier implementation using Nédélec's edge elements and boundary elements, and to good numerical accuracy. Some numerical results are described and compared with those obtained by using the classical formulation in a scalar potential.
ISSN: 0168-9274

hal-00730199
https://hal.archives-ouvertes.fr/hal-00730199

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
This article is devoted to the presentation of a multilevel method using finite differences that is well adapted for solving Stokes and Navier-Stokes problems in primitive variables. We use Uzawa type algorithms to solve the saddle point problems arising from spatial discretization by staggered grids and a semi-explicit temporal scheme. By means of a new change of basis operator, the two-dimensional velocity and pressure fields of an M.A.C mesh are gathered in a hierarchical order, into several grids preserving the M.A.C property on each of them. These new hierarchical unknowns, called Staggered Incremental Unknowns (SIU), allow us to develop techniques which reduce the cost of the resolution of either Stokes or generalized Stokes problems. An experimental estimation of the condition number of the inner matrix is given, and justifies the preconditioning effect of the staggered incremental unknowns.
ISSN: 0168-9274

hal-00770268
https://hal.univ-antilles.fr/hal-00770268
DOI : 10.1016/S0168-9274(99)00044-6

Éditeur(s) : HAL CCSD
Résumé : 17 pages
We look at the number of solutions of an equation of the form f_1*f_2*...*f_k=a in a finite field, where each f_i is a multilinear polynomial. We use two methods to construct a solution of this problem for the cases a=0, a<>0, and we generally get a semi-explicit formula. We show that this formula can generate a more efficient algorithm than the traditional algorithm which consists to make a systematic computation. We also give explicit formulas in some special cases, and an application of our main result to the search of the weight hierarchy of the multilinear code with separated variables.
https://hal.univ-antilles.fr/hal-00772478

hal-00772478
https://hal.univ-antilles.fr/hal-00772478
ARXIV : math.NT/0603057

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
We analyze the kinematics of fault tip folding at the front of a fold-and-thrust wedge using a sandbox experiment. The analog model consists of sand layers intercalated with low-friction glass bead layers, deposited in a glass-sided experimental device and with a total thickness h = 4.8 cm. A computerized mobile backstop induces progressive horizontal shortening of the sand layers and therefore thrust fault propagation. Active deformation at the tip of the forward propagating basal décollement is monitored along the cross section with a high-resolution CCD camera, and the displacement field between pairs of images is measured from the optical flow technique. In the early stage, when cumulative shortening is less than about h/10, slip along the décollement tapers gradually to zero and the displacement gradient is absorbed by distributed deformation of the overlying medium. In this stage of detachment tip folding, horizontal displacements decrease linearly with distance toward the foreland. Vertical displacements reflect a nearly symmetrical mode of folding, with displacements varying linearly between relatively well defined axial surfaces. When the cumulative slip on the décollement exceeds about h/10, deformation tends to localize on a few discrete shear bands at the front of the system, until shortening exceeds h/8 and deformation gets fully localized on a single emergent frontal ramp. The fault geometry subsequently evolves to a sigmoid shape and the hanging wall deforms by simple shear as it overthrusts the flat ramp system. As long as strain localization is not fully established, the sand layers experience a combination of thickening and horizontal shortening, which induces gradual limb rotation. The observed kinematics can be reduced to simple analytical expressions that can be used to restore fault tip folds, relate finite deformation to incremental folding, and derive shortening rates from deformed geomorphic markers or growth strata.
ISSN: 2169-9313

hal-00138061
https://hal.archives-ouvertes.fr/hal-00138061
https://hal.archives-ouvertes.fr/hal-00138061/document
https://hal.archives-ouvertes.fr/hal-00138061/file/Bernard_et_al-2007-Journalsur Geophysical_Research__Solid_Earth_%281978-2012%29.pdf
DOI : 10.1029/2005JB004149

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Let C be a smooth curve over a Galois ring R. Let f be a function over C, and Ψ be an additive character of order p^l over R; in this paper we study the exponential sums associated to f and Ψ over C, and their L-functions. We show the rationality of the L-functions in a more general setting, then in the case of curves we express them as products of L-functions associated to polynomials over the affine line, each factor coming from a singularity of f. Finally we show that in the case of Morse functions (i.e. having only simple singularities), the degree of the L-functions are, up to sign, the same as in the case of finite fields, yielding very similar bounds for exponential sums.
ISSN: 1071-5797

hal-00551470
https://hal.archives-ouvertes.fr/hal-00551470
https://hal.archives-ouvertes.fr/hal-00551470/document
https://hal.archives-ouvertes.fr/hal-00551470/file/Charlefinal.pdf
DOI : 10.1016/j.ffa.2009.01.001