Denis Mercier

The Höfðahólar rock avalanche (sturzström): Chronological constraint of paraglacial landsliding on an Icelandic hillslope

The Höfðahólar rock avalanche, in the Skagafjörður area of northern Iceland, was investigated on the basis of a geomorphological analysis of its landforms and close surrounding environment. Thanks to sound chronological constraints (14C dating from birch remnants in peat areas that developed within depressions over the chaotic rock-avalanche deposit, tephrochronological sequences resulting from subsequent ash fallouts over the deposit, calibration of an age–depth model of peats and previously dated raised beaches), we define the rock-avalanche implementation with a wider timeframe between 10,200 and 7975 cal. yr BP and with a narrower frame between 9000 and 8195 ± 45 cal. yr BP. Such a well constrained timing proposes one of the most precise datings of an early-Holocene major slope failure in Iceland. This result fits well in the known chronology of the deglaciation in this area and in the prevailing Icelandic theory of a generalized phase of landsliding that occurred shortly after the deglaciation of the area. The main driver for the rock-avalanche occurrence is associated to a paraglacial origin; glacio-isostatic rebound, associated to rockwall debuttressing, is thought to be the main factor in the genesis of this Boreal major disequilibrium.

Existence, uniqueness, and regularity results for piezoelectric systems

We investigate the time-harmonic piezoelectric system (a system coupling the elasticity system with the full Maxwells equations) in polyhedral domains of the space. Existence and uniqueness results of weak solutions are proved in different cases. We describe the corner and edge singularities of that system and deduce some regularity results.

Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses

The aim is to study the boundary controllability of a system modelling the vibrations of a network ofN Euler-Bernoulli beams serially connected by (N − 1) vibrating interior point masses. Using the classical Hilbert Uniqueness Method, the control problem is reduced to the obtention of an observability inequality. The solution is then expressed in terms of Fourier series so that one of the sufficient conditions for the observability inequality is that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value. This property called spectral gap holds. It is proved using the exterior matrix method due to W.H. Paulsen. Two more asymptotic estimates involving the eigenfunctions are required for the observability inequality to hold. They are established using an adequate basis.

Exponential stability of a network of serially connected Euler–Bernoulli beams

The aim is to prove the exponential stability of a system modelling the vibrations of a network of N Euler–Bernoulli beams serially connected. Using a result given by K. Ammari and M. Tucsnak, the problem is reduced to the estimate of a transfer function and the obtention of an observability inequality. The solution is then expressed in terms of Fourier series so that one of the sufficient conditions for both the estimate of the transfer function and the observability inequality is that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value. This property called spectral gap holds. It is proved using the exterior matrix method due to W. H. Paulsen. Two more asymptotic estimates involving the eigenfunctions are required. They are established using an adequate basis.