arXiv subjects

Mohamed Camar-Eddine

Publications and source records attributed to Mohamed Camar-Eddine.

3 recordsLinked to original sources

arXiv2026

Approximation of an optimal control problem on a network with a perturbed problem in the whole space

A classical optimal control problem posed in the whole space R^2 is perturbed by a singular term of magnitude $ε$^{-1} aimed at driving the trajectories to a prescribed network $Γ$. We are interested in the link between the limit problem, as $ε$ $\rightarrow$ 0, and some optimal control problems on networks studied in the literature. We prove that the sequence of trajectories admits a subsequential limit evolving on $Γ$. Moreover, in the case of the Eikonal equation, we show that the sequence of value functions associated with the perturbed optimal control problems converges to a limit which, in particular, coincides with the value function of the expected optimal control problem set on the network $Γ$.

math.AP↗

arXiv2018

Near optimal pentamodes as a tool for guiding stress while minimizing compliance in $3d$-printed materials: a complete solution to the weak $G$-closure problem for $3d$-printed materials

For a composite containing one isotropic elastic material, with positive Lame moduli, and void, with the elastic material occupying a prescribed volume fraction $f$, and with the composite being subject to an average stress, ${ σ}^0$, Gibiansky, Cherkaev, and Allaire provided a sharp lower bound $W_f({ σ}^0)$ on the minimum compliance energy $σ^0:ε^0$, in which ${ ε}^0$ is the average strain. Here we show these bounds also provide sharp bounds on the possible $({ σ}^0,{ ε}^0)$-pairs that can coexist in such composites, and thus solve the weak $G$-closure problem for $3d$-printed materials. The materials we use to achieve the extremal $(σ^0,ε^0)$-pairs are denoted as near optimal pentamodes. We also consider two-phase composites containing this isotropic elasticity material and a rigid phase with the elastic material occupying a prescribed volume fraction $f$, and with the composite being subject to an average strain, $ε^0$. For such composites, Allaire and Kohn provided a sharp lower bound $\widetilde{W}_f({ ε}^0)$ on the minimum elastic energy $σ^0:ε^0$. We show that these bounds also provide sharp bounds on the possible $({ σ}^0,{ ε}^0)$-pairs that can coexist in such composites of the elastic and rigid phases, and thus solve the weak $G$-closure problem in this case too. The materials we use to achieve these extremal $({ σ}^0,{ ε}^0)$-pairs are denoted as near optimal unimodes.

math.AP↗

arXiv2013

Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures

In this paper we determine, in dimension three, the effective conductivities of non periodic high-contrast two-phase cylindrical composites, placed in a constant magnetic field, without any assumption on the geometry of their cross sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is based on a compactness result and the cylindrical nature of the microstructure. The homogenized laws we obtain extend those of the periodic fibre-reinforcing case of [M. Briane and L. Pater. Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three. J. Math. Anal. Appl., 393 (2) (2012), 563 -589] to the case of periodic and non periodic composites with more general transversal geometries.

math.AP↗