Résumé : Cette thèse a pour objet l'étude de la contrôlabilité à zéro de systèmes d'équations aux dérivées partielles paraboliques, que l'on rencontre en physique, chimie ou en biologie. En chimie ou en biologie, ces systèmes modélisent l'évolution au cours du temps d'une concentration chimique ou de la densité d'une population (de bactéries, de cellules). Le but de la contrôlabilité à zéro est d'amener la solution du système à l'état nul à un temps donné T, en agissant sur le système à l'aide d'un contrôle. Nous recherchons donc un contrôle, de norme minimale, tel que la solution associée y vérifie y(T)=O dans le domaine Omega considéré. Les problèmes de contrôlabilité à zéro considérés dans cette thèse sont de trois types. Dans un premier temps, nous nous intéressons à la contrôlabilité à zéro avec un nombre fini de contraintes sur la dérivée normale de l'état, pour l'équation de la chaleur semi-linéaire. Puis, nous analysons la contrôlabilité simultanée à zéro avec contrainte sur le contrôle, pour un système linéaire de deux équations paraboliques couplées. Notre dernière étude concerne la contrôlabilité à zéro d'un système non linéaire de deux équations paraboliques couplées. Nous abordons ces problèmes de contrôlabilité principalement à l'aide d'inégalités de Carleman. En effet, l'étude des problèmes de contrôlabilité à zéro, et plus généralement de contrôlabilité exacte, peut se ramener à l'établissement d'inégalités d'observabilité pour le problème adjoint, conséquences d'inégalités de Carleman. Nous construisons le contrôle optimal en utilisant la méthode variationnelle et nous le caractérisons par un système d'optimalité
This thesis is devoted to the study of the null controllability of systems of parabolic partial differential equations, which we meet in physics, chemistry or in biology. In chemistry or in biology, the se systems model the evolution in time of a chemical concentration or the density of a population (of bacteria, cells). The aim of nu Il controllability is to lead the solution of the system to zero in a given time T, by acting on the system with a control. Thus we are looking for a control, of minimal norm, such as the associated solution y satisfies y(T)=O in the domain Omega under concern. We consider three types of null controllability problems in this thesis. At first, we are interested in the null controllability with afinite number of constraints on the normal derivative of the state, for the serni-Iinear heat equation. Then, we analyze the simultaneous null controllability with constraint on the control, for a linear system of two coupled parabolic equations. Our last study deals with the null controllability ofa non linear system oftwo coupled parabolic equations. We approach these controllability problems mainly by means of Carleman's inequalities. Indeed, the study of null controllability problems, and more generally exact controllability problems, is equivalent to obtain observability inequalities for the adjoint problem, consequences of Carleman's inequalities. We build the optimal controlusing the variationnal method and we characterize it by an optimality system

http://www.theses.fr/2013AGUY0609/document

Éditeur(s) : HAL CCSD European Geosciences Union
Résumé : We propose to assess the error done when temperature is considered as a conservative tracer in fluviokarst studies. As a matter of fact, heat exchanges occur between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) that prevents from using this approximation without caution. The conservative tracer approximation boils down to consider the cooling of CS water by PFM flow in an open thermodynamic system where the CS is bounded by an Adiabatic Wall (AW). The resulting CS water temperature contrasts with the one obtained from more complete models (CW), which also take into account heat conduction within the CS, within the PFM, and from the CS to PFM through CS a Conductive Wall. In order to assess first orders of this error, the dimensionless equations, characteristic of CS cooling by PFM, have been solved thanks to Alternate Finite Difference Implicit methods both in AW and CW configurations. Four groups of dimensionless numbers appear in the various terms of energy and mass equations among which the Peclet and Reynolds numbers depict the large morphologic and hydrologic variability of natural karstic systems. A parametric exploration of the differences between AW and CW models has then been conducted vs. Peclet numbers (Pe numbers varying from 106 to 109, at constant CS Reynolds number) and vs. Reynolds numbers (Red varying from 103 to 107, at constant Peclet number). The error curves bound finite volumes in the Peclet–Reynolds space that converge uniformly to zero for the extreme values of these parameters. However, for Peclet and Reynolds numbers characteristic of realistic fluviokarst configurations, the errors reach finite values, that give first order information assessing the error done by considering temperatures as conservative tracers. Maximum relative errors around 10−2 (in fact 0.0092) have been found varying Pe; while it remained slightly lower than 0.7 × 10−2 varying Red. An illustrative example of the temperature conservative tracer AW approximation is presented with the data obtained from the main morphologic and hydrologic properties of the Cent–Font resurgence (Hérault, France). According to the results, the error reached at the output of the fluviokarst is 0.00613 (for Pe = 1.4993 × 108 and Red = 4.2969 × 104). When rescaled to the physical domain, this error leads to a temperature difference of 1.77 K between the CW and AW configurations.
ISSN: 1812-2108

hal-01358348
https://hal.archives-ouvertes.fr/hal-01358348
https://hal.archives-ouvertes.fr/hal-01358348/document
https://hal.archives-ouvertes.fr/hal-01358348/file/hessd-11-169-2014.pdf
DOI : 10.5194/hessd-11-169-2014

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier-Stokes equations. As is well known, the use of staggered grids (e.g., MAC grids [M. Perić, R. Kessler and G. Scheuerer, Comput. & Fluids 16 (1988), no. 4, 389-403; Zbl 0672.76018]) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization [S. Faure, J Laminie and R. Temam, "Colocated finite volume schemes for fluid flows'', submitted; M. Perić, R. Kessler and G. Scheuerer, op. cit.], for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equation; the two- and three-dimensional Navier-Stokes equations, which introduce new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere [see S. Faure, J Laminie and R. Temam, op. cit.; "Finite volume discretization and multilevel methods for the Navier-Stokes equations'', in preparation].
ISSN: 0885-7474

hal-00730193
https://hal.archives-ouvertes.fr/hal-00730193

Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Direct numerical simulations of flow through two millimeter-scale rock samples of limestone and sandstone are performed using three diverse fluid dynamic simulators. The resulting steady-state velocity fields are compared in terms of the associated empirical probability density functions (PDFs) and key statistics of the velocity fields. The pore space geometry of each sample is imaged at 5.06−μm voxel size resolution using X-ray microtomography. The samples offer contrasting characteristics in terms of total connected porosity (about 0.31 for the limestone and 0.07 for the sandstone) and are typical of several applications in hydrogeology and petroleum engineering. The three-dimensional fluid velocity fields within the explicit pore spaces are simulated using ANSYS® FLUENT® ANSYS Inc. (2009), EULAG Prusa et al. (Comput. Fluids 37, 1193–1207 2008), and SSTOKES Sarkar et al. (2002). These computational approaches are highly disperse in terms of algorithmic complexity, differ in terms of their governing equations, the adopted numerical methodologies, the enforcement of internal no-slip boundary conditions at the fluid-solid interface, and the computational mesh structure. As metrics of comparison to probe in a statistical sense the internal similarities/differences across sample populations of velocities obtained through the computational systems, we consider (i) integral quantities, such as the Darcy flux and (ii) main statistical moments of local velocity distributions including local correlations between velocity fields. Comparison of simulation results indicates that mutually consistent estimates of the state of flow are obtained in the analyzed samples of natural pore spaces despite the considerable differences associated with the three computational approaches. We note that in the higher porosity limestone sample, the structures of the velocity fields obtained using ANSYS FLUENT and EULAG are more alike than either compared against the results obtained using SSTOKES. In the low-porosity sample, the structures of the velocity fields obtained by EULAG and SSTOKES are more similar than either is to the fields obtained using ANSYS FLUENT. With respect to macroscopic quantities, ANSYS FLUENT and SSTOKES provide similar results in terms of the average vertical velocity for both of the complex microscale geometries considered, while EULAG tends to render the largest velocity values. The influence of the pore space structure on fluid velocity field characteristics is also discussed.
ISSN: 1420-0597

hal-01174152
https://hal.archives-ouvertes.fr/hal-01174152
DOI : 10.1007/s10596-015-9486-7

Éditeur(s) : HAL CCSD European Geosciences Union (EGU)
Résumé : International audience
The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
ISSN: 1023-5809

hal-00331099
https://hal.archives-ouvertes.fr/hal-00331099
https://hal.archives-ouvertes.fr/hal-00331099/document
https://hal.archives-ouvertes.fr/hal-00331099/file/npg-14-247-2007.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A series of two-stage torsion experiments on Carrara marble were conducted to constrain the influence of known prior deformation on rheological response and microstructural evolution. Comparison with previous experimental data on Carrara marble flow and fabric evolution during single-stage torsion deformation experiments provided direct insights into the significance of initial deformation at various conditions. Our experiments were conducted at 727 degrees C temperature and 300 MPa confining pressure, while maintaining a constant strain rate of 3 x 10(-4) s(-1) on the periphery of the cylindrical samples. Under these conditions, the marble is known to deform in power-law (n = 6-10) ductile flow. All torsion experiments were performed with a Paterson type gas-medium testing machine equipped with a torsion actuator module.;Prior (D1) and subsequent (D2) deformation are accomplished by two torsion experiments in sequence on same sample segments. The effect of D1 strain history is investigated during D2 by applying counter-clockwise torsion to a sandwich sample consisting of three segments with different D1 rotation sense. D2 samples experienced continued, first and reversed shearing deformation in top, centre and bottom segments, respectively. D2 bulk strain was chosen equal to D1 strain in top and bottom segments.;D1 experiments followed the typical single-stage deformation behaviour of Carrara marble under the applied experimental conditions. Yielding was followed by strain hardening until a peak stress was reached at a shear strain around 1, after which work softening occurred. Weakening gradually evolved into a constant stress regime. During hardening, a shear microstructure and crystallographic preferred orientation (CPO) developed. Afterwards the volume fraction of smaller dynamic recrystallised grains increased continuously, resulting in a recrystallisation microstructure and CPO at shear strains of 5 and higher. The new D2 experiments displayed a strain variation between homogeneously deformed sample segments that increased with increasing D1 strain. The stress-strain behaviour of the D2 bulk sandwich samples showed less pronounced work-hardening and -softening when compared with single-stage deformation experiments. Furthermore, constant flow stress was attained at increasingly lower strain with increasing D1 strain. In most D2 segments, fabric development is equivalent to single-stage experiments at corresponding absolute strain. The fabrics differed markedly from those in single-stage experiments in the case of reversed two-stage deformation at moderate strain (D1 shear strain 1 and 2.6). Experiments show that grain shape by shearing of relict grains is defined by finite strain and thus affected by strain reversal. Recrystallisation is controlled by absolute strain and not influenced by strain reversal.
ISSN: 0040-1951

hal-00617686
https://hal.archives-ouvertes.fr/hal-00617686
DOI : 10.1016/j.tecto.2010.09.029

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A set of four reactive flow-through experiments at temperature T = 100 degrees C and total pressure P=12 MPa was performed in limestone reservoir samples. By using various ranging from 0.7 to 10 MPa, these experiments mimic mass transfers occurring (1) near the injection well, where the brine is almost saturated with CO2 (i.e. P-CO2 approximate to P), and (2) at increasing distances from the injection well, where the fluid displays lower values and higher divalent cation concentrations due rock dissolution along the fluid pathway. Results for P-CO2 = 10 MPa show non-uniform dissolution features associated with transport-controlled mass transfer, while reaction-controlled uniform dissolution is observed for P-CO2 = 2.5 MPa. The experiment with P-CO2 = 6 MPa allows investigating in detail the transition from transport-to reaction-controlled dissolution. Conversely, the experiment reproducing conditions far from the injection well (P-CO2 = 0.7 MPa), shows a decrease of porosity triggered by the precipitation of Mg-rich calcite. For all the dissolution experiments, the time-resolved porosity phi(t) can be modeled by a simple non-linear equation including parameters that characterise the dissolution regime triggered by the reactivity of the inlet fluid (measured by the Damkohler number, Da). Furthermore, all dissolution experiments display power scaling between permeability (k) and porosity (phi) with distinctly different scaling exponents characterising the reactivity of the fluid percolating the sample, independently from the decrease with time of the reactive surface area. It is shown also that dissolution at moderate positive values of Da seems the most efficient to increase permeability and promote a rapid spreading of the reaction front, while inducing minimal modification of the porosity in the vicinity of the CO2 injection well. These results can be used to parameterize the k-phi function for modeling the earliest dissolution processes occurring in the vicinity of the reaction front.
ISSN: 0009-2541

hal-00445277
https://hal.archives-ouvertes.fr/hal-00445277
DOI : 10.1016/j.chemgeo.2009.03.028

Éditeur(s) : HAL CCSD European Geosciences Union
Résumé : We designed a thermo-mechanical numerical model for fast-spreading mid-ocean ridge with variable viscosity, hydrothermal cooling, latent heat release, sheeted dyke layer, and variable melt intrusion possibilities. The model allows for modulating several accretion possibilities such as the "gabbro glacier" (G), the "sheeted sills" (S) or the "mixed shallow and MTZ lenses" (M). These three crustal accretion modes have been explored assuming viscosity contrasts of 2 to 3 orders of magnitude between strong and weak phases and various hydrothermal cooling conditions depending on the cracking temperatures value. Mass conservation (stream-function), momentum (vorticity) and temperature equations are solved in 2-D cartesian geometry using 2-D, alternate direction, implicit and semi-implicit finite-difference scheme. In a first step, an Eulerian approach is used solving iteratively the motion and temperature equations until reaching steady states. With this procedure, the temperature patterns and motions that are obtained for the various crustal intrusion modes and hydrothermal cooling hypotheses display significant differences near the mid-ocean ridge axis. In a second step, a Lagrangian approach is used, recording the thermal histories and cooling rates of tracers travelling from the ridge axis to their final emplacements in the crust far from the mid-ocean ridge axis. The results show that the tracer's thermal histories are depending on the temperature patterns and the crustal accretion modes near the mid-ocean ridge axis. The instantaneous cooling rates obtained from these thermal histories betray these discrepancies and might therefore be used to characterize the crustal accretion mode at the ridge axis. These deciphering effects are even more pronounced if we consider the average cooling rates occurring over a prescribed temperature range. Two situations were tested at 1275-1125 °C and 1050-850 °C. The first temperature range covers mainly the crystallization range that is characteristic of the high temperature areas in the model (i.e. the near-mid-oceanic-ridge axis). The second temperature range corresponds to areas in the model where the motion is mainly laminar and the vertical temperature profiles are closer to conductive. Thus, this situation results in less discriminating efficiency among the crustal accretion modes since the thermal and dynamic properties that are described are common to all the crustal accretion modes far from the ridge axis. The results show that numerical modeling of thermo-mechanical properties of the lower crusts may bring useful information to characterize the ridge accretion structure, hydrothermal cooling and thermal state at the fast-spreading ridges and may open discussions with petrological cooling rate results.
ISSN: 1991-959X

hal-00907012
https://hal.archives-ouvertes.fr/hal-00907012
DOI : 10.5194/gmd-6-1659-2013

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
TEM Study of Heavitree quartzite deformed at high temperatures and a pressure of 1.5 GPa with three different preparations: water-added, vacuum dried, and sodium doped show a wide range of dislocation microstructure. The vacuum dried sample has a very heterogeneous dislocation distribution varying from almost no dislocations to very high densities. Dislocation nucleation occurs by cross-slip mechanisms, such as Frank-Read sources and Orowan loops around hard inclusions. Shear bands develop in the basal plane composed of two closely spaced shear planes. Dislocations have straight segments and they are aligned along directions of dense packing, suggesting strong Peierls stress control due to the crystal structure. No voids, bubbles or dislocation walls where observed in the vacuum dried sample. The sodium-doped sample had a homogeneous high dislocation density. The water-added sample has a significantly lower, relatively uniform dislocation density. Bubbles associated with dislocations are seen in every grain. Dislocations were either present in loops around bubbles or as straight dislocations with small bubbles spaced along the dislocation line. Some of the long straight dislocations are aligned parallel to the c-axis. Sub-grains where very frequent, sometimes form cells of about 2 p,m in diameter with straight edges. Analysis of dislocations show 1/3 < a > and [c] dislocations in sub-grain walls and free 1/3 < a > dislocations on prism planes. There is clear evidence for dislocation climb with sub-grain walls, dislocation cells, dislocation junctions and dislocation debris of small loops. The major difference between vacuum dried and water-added samples are the homogeneity of the microstructure and evidence for climb in the water-added sample. Glide is clearly difficult, with a high Peierls stress in the vacuum dried sample as shown by areas of very low and very high dislocation density and the crystallographic control of dislocation line direction. The sodium-doped sample indicates that nucleation was easy by the high homogenous dislocation density, but no climb recovery has taken place. The density is high and the dislocations are strongly interacting causing tangles; no evidence for crystallographic control can be observed at these levels of strain. The activation energy for creep in Heavitree quartzite decreases with inferred water content of the specimens form 185 kJ mol(-1) for vacuum dried to 151 for 0.4 wt% water-added samples. Analysis of diffusion data for oxygen under hydrothermal conditions and inferred diffusion data for the hydrogarnet defect and dislocation velocity suggests activation energies for these processes are similar to the activation energy for the dislocation creep of Heavitree quartzite and other quartz aggregates. For data from the previously published experiments with the highest stress resolution there is a correlation between the A pre-factor in the power law creep equation and the activation energy for creep. It is speculated that the correlation may be due to variable hydrogarnet defect concentrations.
ISSN: 0031-9201

hal-00413112
https://hal.archives-ouvertes.fr/hal-00413112
DOI : 10.1016/j.pepi.2008.07.009

Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : International audience
Recent mathematical calculations allow us to define set fracture intensity (I), i.e., the amount of rock mass affected by fracture sets, independently of the investigation mode. This parameter, characteristic of each rock mass, is of much interest to describe the mechanical response of the rock mass to external influences. The aim of this work is to apply these mathematical equations on one site using measurements of three distinct fracture sets: (1) on a plane surface, (2) along a scanline, and (3) using borehole imaging, in order to evaluate and explain variability in collected data. Even if the three types of measurements give differences on absolute intensity values, they still define similar trends, i.e., the order of the fracturing impact of joint sets is the same from the three measurement methods, irrespective of the fact that obtained values are quite different from one survey method to another. We discuss the possible origins of these biases.
ISSN: 1435-9529

hal-01121556
https://hal.archives-ouvertes.fr/hal-01121556
DOI : 10.1007/s10064-014-0572-1

Éditeur(s) : HAL CCSD Seismological Society of America
Résumé : International audience
We present an improvement of the maximum intersection (MAXI) method in which absolute earthquake location is defined by the maximum intersection number of hyperbolic equal differential time (EDT) volumes (one EDT volume being described as all grid nodes satisfying the arrival‐time differences between two stations, ± a tolerance value known as TERR). This 3D technique is well adapted to a strongly heterogeneous environment, avoids the depth versus origin‐time trade‐off (even using P arrivals alone), and objectively filters possible erroneous arrival times. Improvements consist of introducing an iterative multiscale approach on the TERR parameter and conducting a hierarchy of grid discretization to refine the preliminary solution (multigrid algorithm). The outlier cleaning process is strengthened by conducting statistical analyses based on the number of EDT volume intersections per station, rather than on travel‐time residues. Processing two series of synthetic arrival times computed in the 3D seismological configuration of the southernmost Ryukyu subduction zone, offshore Taiwan, allows us to (1) confirm MAXI robustness, even when arrival times are highly disturbed or azimuthal coverage largely reduced, and (2) show that MAXI, by limiting trade‐offs between origin time and depth and between epicentral position and depth, is less affected by a wrong velocity model than a technique that minimizes travel‐time residues. To conclude, we apply the MAXI method to locate earthquakes recorded by the combined Central Weather Bureau of Taiwan (CWB) and the Japanese Meteorological Agency (JMA) networks (1991-2008) within a georealistic a priori 3D P‐velocity model. Hypocenter determinations are selected based on MAXI confidence factors, and earthquake clustering along well‐known tectonic features witnesses hypocenter determination accuracy.
ISSN: 0037-1106

hal-00725227
https://hal.archives-ouvertes.fr/hal-00725227
DOI : 10.1785/0120100311

Éditeur(s) : Gauthier-Villars
Résumé : The wind, temperature and current data collected during the joined French-USA FOCAL/SEQUAL programme carried in the equatorial Atlantic band in 1983 and 1984, allowed for the first time a simultaneous study of both the equatorial and coastal (5-degrees-N) upwellings along 4-degrees-W. At the equator, the decreases of both the surface temperature and the depth of the thermocline in boreal summer are correlated with the zonal component of the local windstress in the period band 1-2 months. This corresponds to the time required by the thermocline to lift up at 0-4-degrees-W in the presence of an easterly wind. The local wind cannot however explain the entire vertical variability of the thermal structure at 0-4-degrees-W. The correlation function shows in addition that the temperature there is highly correlated to the wind recorded at St Peter and St Paul Rocks (SPP) in the period band 0-2 months. This time scale is the one required by the Kelvin and Rossby waves to propagate along the equator through equatorial wave guide dynamics. The influence of these waves seems particularly important when considering the upward displacements of the thermocline both in February-March when the winds abruptly relax and in November-December when the wind at 0-4-degrees-W is southwesterly with no secondary negative maximum in the wind record at 1-degrees-N-29-degrees-W (SPP), contrary to the climatological wind field. The computation of the different terms of the heat equation applied to an homogeneous surface layer shows that the cooling is entirely due to vertical advection and eddy diffusion. The cooling would be more effective without the atmospheric heat flux and the horizontal advection of heat transported both by the South Equatorial Current at the surface and the southward current at the bottom of the mixed layer. At the coast, the amplitude and duration of the upwellings are not constant all along the coast: in boreal summer, they are maximum east of the two capes (Palmas and Three Pointes) while in winter the strength of the cooling is maximum in the east of Cape Palmas and then decreases eastward. The meridional slope of the thermocline off the coast concerns a distance which is much larger than the internal Rossby radius of deformation and is coherent with the latitudinal extension and intensity of the Guinea current both in summer and winter. In addition to this geostrophic adjustment, the upward tilt of the thermocline in summer is enhanced by the intensification of the component of the wind parallel to the coast. The application of a simple linear model forced with an eastward wind at that time explains the surface maximum cooling at the coast and the current distribution in both vertical and meridional directions. The two maxima of the zonal component of the Guinea current, in summer (main one) and in winter are in phase with the intensity of the vertical component of the windcurl. The application of the Sverdrup equations shows that the current speeds computed, for both seasons, are of the same order of magnitude as the speeds observed.
Oceanologica Acta (0399-1784) (Gauthier-Villars), 1991 , Vol. 14 , N. 3 , P. 223-240

Droits : info:eu-repo/semantics/openAccess
http://archimer.ifremer.fr/doc/00101/21252/18865.pdf
http://archimer.ifremer.fr/doc/00101/21252/

Éditeur(s) : Wiley-blackwell
Résumé : 1. Approximately 300 pelagic fish species naturally aggregate around floating objects (FOBs) at the surface of the oceans. Currently, more than 50% of the world catch of tropical tuna comes from the industrial tuna fisheries around drifting FOBs. Greater understanding of the complex decision-making processes leading to this aggregation pattern and the impact of the massive release of artificial FOBs by fishermen on the spatial distribution and management of tuna is needed. 2. We analyse how the interplay between social (relationships between individuals) and non-social (responses to the environment) behaviours may affect the spatial distribution of a population in a multi-FOB environment. Taking the example of tropical tunas associating with FOBs and using differential equations and stochastic simulations, we examine how, when increasing the number of FOBs, fish aggregation dynamics and the distribution of the population among patches are affected by the population size, level of sociality and the natural retentive and/or attractive forces of FOBs on individual tuna. 3. Our model predicts that, depending on the species' level of sociality, fish will be scattered among FOBs or aggregated around a single FOB based on the number of FOBs deployed in a homogeneous oceanic region. 4. For social species, we demonstrated that the total fish catch is reduced with increasing FOBs number. Indeed, for each size of population, there are a number of FOBs minimizing the total population of fish associated with FOBs and another number of FOBs maximizing the total population of associated fish. 5. Synthesis and applications. In terms of fisheries management, the total catch volume is directly linked to the total number of floating objects (FOBs) for non-social species, and any limit on the number of sets would then result in a limit on the total catch. For social species (e.g. tuna), however, increasing the number of FOBs does not necessarily lead to an increase in the total catch, which is a non-intuitive result. Indeed, our model shows that, for specific values of the parameters, deploying a greater number of FOBs in the water (all other parameters being constant) does not necessarily help fishermen to catch more tuna, but does increase the level of fishing effort and bycatch.
Journal Of Applied Ecology (0021-8901) (Wiley-blackwell), 2013-10 , Vol. 50 , N. 5 , P. 1081-1092

Droits : 2013 The Authors. Journal of Applied Ecology, 2013 British Ecological Society
http://archimer.ifremer.fr/doc/00151/26275/24439.pdf
DOI:10.1111/1365-2664.12140
http://archimer.ifremer.fr/doc/00151/26275/

Résumé : Dans cette thèse, nous présentons deux modèles mathèmatiques qui simulent la dynamique d'une épidémie de dengue à Cuba. Le premier modèle est décrit par un système d'équations différentielles ordinaires dans le but d'estimer certains paramètres essentiels dans l'évolution de l'èpidérnie. Le deuxième modèle utilise une inclusion différentielle afin de simuler la dynamique sous incertitudes. Nous passons aussi en revue une famille de modèles d'équations différentielles pour l'épidémie de VIH/SIDA à Cuba et nous reformulons l'un de ces modèles en une inclusion différentielle. En outre, pour analyser le comportement de ces deux épidémies et l'effet de l'intervention nous développons un algorithme pratique pour le calcul des ensembles atteignables des inclusions différentielles, qui fournit un cadre mathématique nous permettant de faire des prédictions appropriées de toutes les variables d'état des modèles
Ln this work we present two mathematical models that simulate the dynamics of an epidemic outbreak of dengue disease in Cuba. The i first model is described by a system of ordinary differential equations with the purpose of estimaling some essential parameters in the evolution of the epidemie. The second model uses a differential inclusion in order to simulate the dynamic under uncertainties. Also, we review a family of ordinary differential equations models of HIV/AIDS epidemic in Cuba and one of these models is reformulated as a differential inclusion. In addition, to analyze the behavior of these two epidemies and the effect of intervention, we develop a practical algorithm for the computation of the reachable sets of the differential inclusions, providing a mathematical framework allowing us to make suitable predictions of aII state variables of the models at a future time.

http://www.theses.fr/2011AGUY0413

Éditeur(s) : HAL CCSD
Résumé : International audience
In this note we study the convergence of a descent-proximal method for finding critical points of a DC function. From a practical point of view, we propose an algorithmic pattern obtained by coupling the latter with cutting plane approximations.
Journal of Applied Functional Analysis

hal-00815499
https://hal.univ-antilles.fr/hal-00815499

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
This study demonstrates that 20-100 GHz range can be used for spatially-accurate focusing of heating inside the skin achieved by varying frequency and exposure beam size, as well as by enforcing air convection. The latter is also used to reduce overheating of skin surface. Heating at different skin depths depending on these parameters is investigated in detail using the hybrid bio-heat equation. In particular, it is shown that decreasing frequency and/or increasing exposure beam size at forced airflow result in elevation of heating of deeper layers of tissue and decrease of skin surface temperature. Changes of water content within 15%, which exceed those due to aging and presence of tumors, only slightly affect heating. Exposure intensity necessary to reach a target temperature significantly increases in different areas of body with elevated blood flow. Dependence on exposure intensity and hyperthermia treatment duration is also investigated and discussed. Results of this study suggest that the lower part of the millimeter-wave range is an attractive alternative for non-invasive thermal treatment of skin cancer with a high spatial resolution. Bioelectromagnetics. 36:464-475, 2015. © 2015 Wiley Periodicals, Inc
ISSN: 0197-8462

hal-01187403
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01187403
DOI : 10.1002/bem.21929
PUBMED : 26179286

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper proposes Chebyshev-dependent inhomogeneous second order differential equation for the m-Boubaker polynomials (or Boubaker-Turki polynomials). This differential equation is also presented as a guide to applied physics studies. A concrete example is given through an attempt to solve the Bloch NMR flow equation inside blood vessels.
Applications and Applied Mathematics: An International Journal

hal-00766227
https://hal.univ-antilles.fr/hal-00766227

Éditeur(s) : HAL CCSD
Résumé : International audience
We consider a second-order differential system with Hessian-driven damping . An interesting property of this system is that, after introduction of an auxiliary variable y , it can be equivalently written as a first-order system in time and space. This allows us to extend the analysis to the case of a convex lower semicontinuous potential and so to introduce constraints in the model. When considering the indicator function of a closed convex set, the subdifferential operator takes account of the contact forces. In this setting, by playing with the geometrical damping parameter, we can describe nonelastic shock laws with restitution coefficient. Taking advantage of the infinite dimensional framework, we introduce a nonlinear hyperbolic PDE describing a damped oscillating system with obstacle. The system is dissipative; in the convex case each trajectory weakly converges to a minimizer of the global potential energy function. Exponential stabilization is obtained under strong convexity assumptions.
Differential Equations & Applications

hal-00803214
https://hal.archives-ouvertes.fr/hal-00803214
https://hal.archives-ouvertes.fr/hal-00803214/document
https://hal.archives-ouvertes.fr/hal-00803214/file/Attouch-Mainge-Redont-30August2011.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
This paper is concerned with weighted pseudo almost automorphic functions, which are more general and complicated than weighted pseudo almost periodic functions. Using these properties, we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a Banach spaces which extends known results.
ISSN: 0362-546X

hal-00617634
https://hal.archives-ouvertes.fr/hal-00617634

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
While vertical motion induced by long-term geological loads is often used to estimate the flexural rigidity of the lithosphere, we intend to evaluate the shear rigidity of the lithosphere using horizontal motion. Our approach considers that the rigidity of the lithosphere may be defined as its resistance to horizontal tectonic lateral forces. In this case, a spatial distribution of an effective shear rigidity can be estimated from the analysis of the interseismic velocity fields. We consider the Western United States zone where weakly strained areas (e.g., the Sierra Nevada) are connected with areas of large strain rate (e.g. San Andreas Fault system). By inverting interseismic strain distribution measured by geodetic methods, we infer the effective shear rigidity of the lithosphere. The forward problem is defined using the equations of linear elasticity. The inversion relies on the minimization of the sum of a quadratic measure of the differences between measured and modelled velocity fields. The functional also includes regularization terms for the parameters of the model. The gradient of the functional with respect to the minimization parameters is computed using an adjoint formulation. This permits the treatment of large dimensional minimization problems. Finally, a measure of the uncertainty of our inversion is illustrated through the covariance matrix of the parameters at the optimum. The optimization chart is validated on two synthetic velocity distributions. Then, the effective shear rigidity variations of the Western United States are estimated using the CMM3 interseismic velocities. The inversion displays low effective rigidities along the San Andreas Fault system, the Mojave Desert and in the Eastern California Shear Zone, while rigid areas are found in the Sierra Nevada and in the South Basin and Range. Finally, we discuss the differences between our strain rate and rigidity maps with previously published results for the Western United States.
ISSN: 0040-1951

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hal-01505024
https://hal.archives-ouvertes.fr/hal-01505024
https://hal.archives-ouvertes.fr/hal-01505024/document
https://hal.archives-ouvertes.fr/hal-01505024/file/Paper_tectophysics.pdf
DOI : 10.1016/j.tecto.2017.03.015