arXiv subjects
Publications and source records attributed to Abbasali Mohammadi.
Consider the problem of distributing two conducting materials in a ball with fixed proportion in order to minimize the first eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the material with the highest conductivity in a ball around the center. In this paper, we show that the conjecture is not true for all dimensions $n \geq 2$.
In this paper we investigate a minimization problem related to the principal eigenvalue of the $s$-wave Schrödinger operator. The operator depends nonlinearly on the eigenparameter. We prove the existence of a solution for the optimization problem and the uniqueness will be addressed when the domain is a ball. The optimized solution can be applied to design new electronic and photonic devices based on the quantum dots.
In this paper we propose two numerical algorithms to derive the extremal principal eigenvalue of the bi-Laplacian operator under Navier boundary conditions or Dirichlet boundary conditions. Consider a non-homogeneous hinged or clamped plate $Ω$, the algorithms converge to the density functions on $Ω$ which they yield the maximum or minimum basic frequency of the plate.