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Shape and Topology Optimization for Elliptic Boundery Value Problems using a Piecewise Constant Level Set Method
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
The aim of this thesis is describes the method a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy...
Molecular Diffusion in the Dynamics Brain Extracellular Space
, Ph.D. Dissertation Sharif University of Technology ; Fotouhi, Morteza (Supervisor) ; Kamali Zare, Padideh (Co-Advisor) ; Vejdani, Kaveh (Co-Advisor)
Abstract
In the thesis , we present a universal model of brain tissue microstructure that dynamically links osmosis and diffusion with geometrical parameters of brain extracellular space (ECS) . In the first part , we investigate the biological aspects of the model , and in the second , we analysis the model in the mathematical framework . The first part : Our model robustly describes and predicts the nonlinear time dependency of tortuosity ($\lambda = \sqrt{D/{D^{*}}}$) changes with very high precision in various media with uniform and nonuniform osmolarity distribution , as demonstrated by previously published experimental data ($D$ = free diffusion coefficient , $D^{*}$ = effective...