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The presence of small inclusions or of a surface defect modifies the solution of the Laplace equation posed in a reference domain Ω 0. If the characteristic size of the perturbation is small, then one can expect that the solution of the problem posed on the perturbed geometry is close to the solution of the reference shape. Asymptotic expansion with respect(More)
Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to wellposed varia-tional problems under a sign condition of a coefficient. Nevertheless situations where this condition is violated appeared in several works. The wellposedness of such problems was still open.(More)
We consider some singular perturbations of the boundary of a smooth domain. Such domain variations are not differen-tiable within the classical theory of shape calculus. We mimic the topological asymptotic and we derive an asymptotic expansion of the shape function in terms of a size parameter. The two-dimensional case of the Dirichlet energy is treated in(More)
We study the stability of some critical (or equilibrium) shapes in the minimization problem of the energy dissipated by a fluid (i.e. the drag minimization problem) governed by the Stokes equations. We first compute the shape derivative up to the second order, then provide a sufficient condition for the shape Hessian of the energy functional to be coercive(More)
In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the well-posedness except for a(More)
The stability issue of critical shapes for shape optimization problems with the state function given by a solution to the Neumann problem for the Laplace equation is considered. To this end, the properties of the shape Hessian evaluated at critical shapes are analysed. First, it is proved that the stability cannot be expected for the model problem. Then,(More)
Stability of force feedback haptic systems under variable time delays remains a major challenge. This paper presents a theoretical and experimental approach for studying the stability of a haptic interface in interaction with a virtual environment. A novel approach based on Lyapunov theory for assuring the stability of haptic systems under constant and(More)
The stability analysis of haptic systems without time-delay or with constant time-delay using the frequency-domain criteria such as Routh-Hurwitz or Nyquist has been found in many literatures. However, the stability analysis for the discrete-time haptic systems under time-varying delays remains a major challenge in the field of haptics. Based on the(More)