Fine Properties of Geodesics and Geodesic -Convexity for the Hellinger-Kantorovich Distance.

We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger-Kantorovich problem (), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new regularity properties for the solution of the Hamilton-Jacobi equation arising in the dual dynamic formulation of , which are sufficiently strong to construct a characteristic transport-growth flow driving the geodesic interpolation between two arbitrary positive measures. These results are applied to study relevant geometric properties of geodesics and to derive the convex behaviour of their Lebesgue density along the transport flow.

Experimental proof of Joule heating-induced switched-back regions in OLEDs.

Organic light-emitting diodes (OLEDs) have become a major pixel technology in the display sector, with products spanning the entire range of current panel sizes. The ability to freely scale the active area to large and random surfaces paired with flexible substrates provides additional application scenarios for OLEDs in the general lighting, automotive, and signage sectors. These applications require higher brightness and, thus, current density operation compared to the specifications needed for general displays.

Gradient structures and geodesic convexity for reaction-diffusion systems.

We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic λ-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory.