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Jihene Lagha

Publications and source records attributed to Jihene Lagha.

3 recordsLinked to original sources
arXiv2023

Sensitivity Analysis of the Current, the Electrostatic Capacity, and the Far-Field of the Potential with Respect to Small Perturbations in the Surface of a Conductor

We derive asymptotic expansions of the current, the electrostatic capacity, and the far-field of the electrostatic potential resulting from small perturbations in the shape of an isolated conductor with $\mathcal{C}^2$-surface. Our derivation is rigourous by using systematic way, based on layer potential techniques and the field expansion (FE) method. We then use these results to study the sensibility analysis of the first eigenvector of the $L^2$-adjoint of the Neumann-Poincaré (NP) operator with respect to small perturbations in the surface of its domain.

math.AP↗
arXiv2016

Small Perturbations of an Interface for Elastostatic Problems

We consider solutions to the Lamé system in two dimensions. By using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation), we establish a rigorous asymptotic expansion for the perturbations of the displacement field caused by small perturbations of the shape of an elastic inclusion with C2-boundary. We extend these techniques to determine a relationship between traction-displacement measurements and the shape of the object and derive an asymptotic expansion for the perturbation in the elastic moments tensors (EMTs) due to the presence of small changes in the interface of the inclusion.

math.AP↗