Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing light. studied setting, light interacts with penetrable dimension comparable to wavelength an incoming planar wave. The design objective is maximize scattering efficiency inside target angle window. For this, Helmholtz problem piecewise constant refractive index medium models wa...

We discuss the problem of geometric design of curved ducts with variable crosssection by transfinite interpolation with integro-differential constraints. This work is a contribution to a research program including numerical simulation and preliminary design of an experimental apparatus for studying fluid-dynamics of air in internal combustion engines of new conception. The proposed geometric mo...