Denis Aubry

Spatial patterns of basal drag inferred using control methods from a full-Stokes and simpler models for Pine Island Glacier, West Antarctica

[1] Basal drag is a fundamental control on ice stream dynamics that remains poorly understood or constrained by observations. Here, we apply control methods on ice surfacevelocities ofPine IslandGlacier, WestAntarctica toinfer the spatial pattern of basal drag using a full‐Stokes (FS) model of ice flow and compare the results obtained with two commonly‐used simplified solutions: the MacAyeal shelfy stream model and the Blatter‐Pattyn model. Over most of the model domain, the three models yield similar patterns of basal drag, yet near the glacier grounding‐line, the simplified models yield high basal drag while FS yields almost no basal drag. The simplified models overestimate basal drag because they neglect bridging effects in an ice stream region of rapidly varying ice thickness. This result reinforces theoretical studies that a FS treatment of ice flow is essential near glacier grounding lines. Citation: Morlighem, M., E. Rignot, H. Seroussi, E. Larour, H. Ben Dhia, and D. Aubry (2010), Spatial patterns of basal drag inferred using control methods from a full‐ Stokes and simpler models for Pine Island Glacier, West Antarctica, Geophys. Res. Lett., 37, L14502, doi:10.1029/2010GL043853.

A mass conservation approach for mapping glacier ice thickness

The traditional method for interpolating ice thickness data from airborne radar sounding surveys onto regular grids is to employ geostatistical techniques such as kriging. While this approach provides continuous maps of ice thickness, it generates products that are not consistent with ice flow dynamics and are impractical for high resolution ice flow simulations. Here, we present a novel approach that combines sparse ice thickness data collected by airborne radar sounding profilers with high resolution swath mapping of ice velocity derived from satellite synthetic-aperture interferometry to obtain a high resolution map of ice thickness that conserves mass and minimizes the departure from observations. We apply this approach to the case of Nioghalvfjerdsfjorden (79North) Glacier, a major outlet glacier in northeast Greenland that has been relatively stable in recent decades. The results show that our mass conserving method removes the anomalies in mass flux divergence, yields interpolated data that are within about 5% of the original data, and produces thickness maps that are directly usable in high spatial-resolution, high-order ice flow models. We discuss the application of this method to the broad and detailed radar surveys of ice sheet and glacier thickness. Copyright 2011 by the American Geophysical Union.

Rheology of the Ronne Ice Shelf, Antarctica, Inferred from Satellite Radar Interferometry Data using an Inverse Control Method

[1] The Antarctic Ice Sheet is surrounded by large floating ice shelves that spread under their own weight into the ocean. Ice shelf rigidity depends on ice temperature and fabrics, and is influenced by ice flow and the delicate balance between bottom and surface accumulation. Here, we use an inverse control method to infer the rigidity of the Ronne Ice Shelf that best matches observations of ice velocity from satellite radar interferometry. Ice rigidity, or flow law parameter B, is shown to vary between 300 and 900 kPa a 1/3 . Ice is softer along the side margins due to frictional heating, and harder along the outflow of large glaciers, which advect cold continental ice. Melting at the bottom surface of the ice shelf increases its rigidity, while freezing decreases it. Accurate numerical modelling of ice shelf flow must account for this spatial variability in mechanical characteristics. Citation: Larour, E., E. Rignot, I. Joughin, and D. Aubry (2005), Rheology of the Ronne Ice Shelf, Antarctica, inferred from satellite radar interferometry data using an inverse control method, Geophys. Res. Lett., 32, L05503, doi:10.1029/2004GL021693.

Adaptive strategy for transient/coupled problems applications to thermoelasticity and elastodynamics

Abstract The interest in adaptive strategies for the finite element method is growing at a fast pace. Researchers are now fully convinced that this should be part of any numerical modelling and try to incorporate the methodology to their problems. Even the industry begins to require such an approach to increase the quality of the numerical results and to get more effective analyses to increase the ratio between computer costs and target error level. The adaptive strategy has first been applied to linear elliptic problems, e.g. linear infinitesimal elasticity [1,6,17,11]). It is now enlarged to nonlinear and transient problems [12–16,5,10,17]. It is the aim of this paper to illustrate the application of the technique of residuals to adaptive refinement of coupled problems and to elastic wave propagation. There are many other approaches to a posteriori error estimations. Some of them appear to be difficult to extend to coupled and transient problems. It is believed that the residual approach is versatile enough to be easily applied to more complex problems. The two basic ideas used here rely on a space-time Galerkin formulation which provides a variational formulation of the error with respect to the residual, and the adjoint state which gives an upper bound of the error by the norm of the residuals weighted by some power of h and Δ t , extending the ideas of Eriksson et al. [5].

A constitutive model for cyclic behaviour of interfaces with variable dilatancy

Abstract In the context of numerical approaches such as the finite element method very often body and interface elements whose constitutive models are developed separately are used. However, for a given mass of soil, a relationship between these two constitutive models could be obtained, providing a more satisfactory approach. Actually experimental results show some common features in the behaviour of body and interfaces in geomaterials. The dependancy of the dilatancy to the mean effective pressure is a good example. The purpose of our study is to propose a cyclic interface constitutive model derived on the basis of an elastoplastic body constitutive law. Usually, stick, slip, debonding and rebonding of the interface happen during subsequent loadings and unloadings. Cyclic loading functions with a memory of the last loading reversal are used to model these features. Finally the model is entirely developed with respect to effective stress vectors and is thus especially suited for the analysis of the influence of the pore pressure.

Simulation of multiple morphogenetic movements in the Drosophila embryo by a single 3D finite element model

The present work describes a 3D finite element model of the Drosophila embryo designed to simulate three morphogenetic movements during early gastrulation: ventral furrow invagination, cephalic furrow formation and germ band extension. The embryo is represented by a regular ellipsoid and only the mesoderm is modeled. Additionally, the parametric description of the biological structure in a special curvilinear system provides mesh-independent endogenous strains. A deformation gradient decomposition is used to couple an active deformation, specific for each morphogenetic movement, together with a passive deformation, which is due to the response of the continuous mesoderm. Boundary conditions such as the rigid contact with the external vitelline membrane and the yolk pressure are also taken into account. The results suggest that the number of active strains responsible for the morphogenetic events can be less than that deduced from direct experimental observations. Finally, the estimation of the non-local pressures induced during morphogenetic movements is in good agreement with the experimental data.

Processes involved in the propagation of rifts near Hemmen Ice Rise, Ronne Ice Shelf, Antarctica

Interferometric radar images collected by ERS-1, ERS-2 and RADARSAT-1 are used to observe the rupture tip of rifts that propagate along Hemmen Ice Rise on the Ronne Ice Shelf, Antarctica. Interferograms generated in 1992 and 1997 allow for the observation of ice deformation accumulated over 9 and 24 days respectively. These interferograms are combined, in order to separate the continuous process of creep deformation from the more cyclic motion caused by variations in ocean tide. An examination of local gradients in creep deformation reveals the pattern of ice deformation around and near the rupture tips and rifts with great precision (up to 10 cm a-1). We compare the observations with a deformation model for ice and obtain the following results: (1) The tidal oscillation of the Ronne Ice Shelf only yields small deformations along the rifts and near the rupture tips. (2) Along the ice front, the rifts and at the rupture tips, vertical bending is observed which is well explained by a model of viscous deformation of ice. Furthermore, the model indicates that the deformation pattern observed at the rupture tips is a sensitive indicator of the propagation state of the rifts (i.e. active vs inactive). (3) The viscous adjustment of ice is the dominant mode of deformation, masking the deformation pattern predicted by linear elastic fracture mechanics (LEFM). (4) Yet, at a spatial scale equivalent to the length of a rift, the propagation rate is well predicted by LEFM.

A computational mechanics approach to assess the link between cell morphology and forces during confined migration

Confined migration plays a fundamental role during several biological phenomena such as embryogenesis, immunity and tumorogenesis. Here, we propose a two-dimensional mechanical model to simulate the migration of a HeLa cell through a micro-channel. As in our previous works, the cell is modelled as a continuum and a standard Maxwell model is used to describe the mechanical behaviour of both the cytoplasm (including active strains) and the nucleus. The cell cyclically protrudes and contracts and develops viscous forces to adhere to the substrate. The micro-channel is represented by two rigid walls, and it exerts an additional viscous force on the cell boundaries. We test four channels whose dimensions in terms of width are i) larger than the cell diameter, ii) sub-cellular, ii) sub-nuclear and iv) much smaller than the nucleus diameter. The main objective of the work is to assess the necessary conditions for the cell to enter into the channel and migrate through it. Therefore, we evaluate both the evolution of the cell morphology and the cell-channel and cell-substrate surface forces, and we show that there exists a link between the two, which is the essential parameter determining whether the cell is permeative, invasive or penetrating.

Mechanical link between durotaxis, cell polarity and anisotropy during cell migration

Cell migration, a fundamental mechanobiological process, is highly sensitive to the biochemical and mechanical properties of the environment. Efficient cell migration is ensured by the intrinsic polarity of the cell, which triggers a transition from an isotropic to an anisotropic configuration of the acto-mysion filaments responsible for the protrusion-contraction movement of the cell. Additionally, polarity may be highly influenced by the substrate rigidity, which results in a phenomenon called durotaxis. In the present work, we propose a two-dimensional finite element model able to capture three main features of cell migration: durotaxis, cell polarity and anisotropy. The cell is modelled as a continuum able to develop cyclic active strains regulated by the polymerization and depolymerization of the acto-myosin filaments and synchronized with the adhesion forces between the cell and the substrate underneath. A generalized Maxwell model is used to describe the viscoelastic behaviour of the cell constituted by a solid anisotropic branch with active strains (i.e. the acto-myosin filaments) and a fluid viscoelastic branch (i.e. the cytoplasm). Several types of substrate have been tested which are homogeneously soft or stiff or include both regions. The numerical results have been qualitatively compared with experimental observations showing a good agreement and have allowed us to find the mechanical link between durotaxis, cell polarity and anisotropy.

Stochastic Simulations in Dynamic Soil-Structure Interaction

This paper deals with several numerical techniques that account for random excitations and random material parameters occurring in earthquake engineering. It focuses in sequence on the influence on the structural response of the variability of the incident field using filtering theory, on the soil variability by coupling Stochastic Finite Elements, integral operators and Monte-Carlo simulation, and finally on the influence on the site response of a random building distribution using periodic simulations. In each case, practical examples are given to help illustrate the numerical techniques and to underline the importance of randomness in earthquake engineering problems.