Prof. Eric Dufresne will describe some experiments on some simple composites of elastomers and droplets. First, we will consider their composite mechanical properties. He will show how simple liquid droplets can counterintuitively stiffen the material, and how magnetorheological fluid droplets can provide elastomers with magnetically switchable shape memory. Second, we consider the nucleation, growth, and ripening of droplets within an elastomer. Here, a variety of interesting phenomena emerge: size-tunable monodisperse droplets, shape-tunable droplets, and ripening of droplets along stiffness gradients. We are exploiting these phenomena to make materials with mechanically switchable structural color.
Organizers: Metin Sitti
Beginning with a seminal paper of Diaconis (1988), the aim of so-called "probabilistic numerics" is to compute probabilistic solutions to deterministic problems arising in numerical analysis by casting them as statistical inference problems. For example, numerical integration of a deterministic function can be seen as the integration of an unknown/random function, with evaluations of the integrand at the integration nodes proving partial information about the integrand. Advantages offered by this viewpoint include: access to the Bayesian representation of prior and posterior uncertainties; better propagation of uncertainty through hierarchical systems than simple worst-case error bounds; and appropriate accounting for numerical truncation and round-off error in inverse problems, so that the replicability of deterministic simulations is not confused with their accuracy, thereby yielding an inappropriately concentrated Bayesian posterior. This talk will describe recent work on probabilistic numerical solvers for ordinary and partial differential equations, including their theoretical construction, convergence rates, and applications to forward and inverse problems. Joint work with Andrew Stuart (Warwick).
Organizers: Philipp Hennig