We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece
changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.
We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence
effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.
A mechanical equilibrium problem for a material consisting of two components with dierent densities is considered. Due to the heterogeneous material densities, the
outer shape of the underlying workpiece can be changed by shifting the interface between
the subdomains. In this paper, the problem is modeled as a shape design problem for optimally compensating unwanted workpiece changes. The associated control variable is
the interface. Regularity results for transmission problems are employed for a rigorous
derivation of suitable first-order optimality conditions based on the speed method. The paper concludes with several numerical results based on a spline approximation of the
interface.
Chance constraints represent a popular tool for finding decisions that enforce a
robust satisfaction of random inequality systems in terms of probability. They
are widely used in optimization problems subject to uncertain parameters as they
arise in many engineering applications. Most structural results of chance constraints (e.g., closedness, convexity, Lipschitz continuity, differentiability etc.) have been formulated in a finite-dimensional
setting. The aim of this paper is to generalize some of these well-known semi-continuity and convexity properties to a setting of control problems
subject to (uniform) state chance constraints.