Optimal micropatterns in 2D transport networks and their relation to image inpainting

We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field, we show for a two-dimensional situation that both highly non-convex network optimization tasks can be transformed into a convex variational problem, which may be very useful from analytical and numerical perspectives. As applications of the convex formulation, we use it to perform numerical simulations (to our knowledge this is the first numerical treatment of urban planning), and we prove the lower bound of an energy scaling law which helps better understand optimal networks and their minimal energies

Magnetic field of superconductive in-vacuo undulators in comparison with permanent magnet undulators

During the last few years superconductive undulators with a period length of 3.8 mm and 14 mm have been built. In this paper scaling laws for these novel insertion devices are presented: a simple analytic formula is derived which describes the achievable magnetic field of a superconcuctive undulator as a function of gap-width and period length.Comment: Accepted for publication in Nuclear Instruments and Methods in Physics Research, Section