Shape optimization for the generalized Graetz problem

We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared

Group Play in Games and the Role of Consent in Network Formation

Abstract: We study games played between groups of players, where a given group decides which strategy it will play through a vote by its members. When groups consist of two voting players, our games can also be interpreted as network-formation games. In experiments on Stag Hunt games, we find that that the structure of the voting rule completely determines which equilibrium is played, independently of the payoff structure. Thus, we find a stark contrast between how groups and individuals play our games, with payoffs playing a much more important role in equilibrium selection in the latter case. We also explore play between groups where one member of each group dictates the play of that group. We find that the dictator tends to play a less risky strategy when choosing for a group than when playing only for him or herself. We develop a new solution concept, robust-belief equilibrium, which explains the data that we observe. We provide results showing that this solution concept has application beyond the particular games in our experiments

Optimal truss and frame design from projected homogenization-based topology optimization

In this article, we propose a novel method to obtain a near-optimal frame structure, based on the solution of a homogenization-based topology optimization model. The presented approach exploits the equivalence between Michell’s problem of least-weight trusses and a compliance minimization problem using optimal rank-2 laminates in the low volume fraction limit. In a fully automated procedure, a discrete structure is extracted from the homogenization-based continuum model. This near-optimal structure is post-optimized as a frame, where the bending stiffness is continuously decreased, to allow for a final design that resembles a truss structure. Numerical experiments show excellent behavior of the method, where the final designs are close to analytical optima, and obtained in less than 10 minutes, for various levels of detail, on a standard PC