Julia Hauser | Searcharxiv

arXiv2026

Convergence of a discrete-in-time Approximation to a Degenerate Parabolic-Hyperbolic System

In this paper we consider an implicit semi-discrete approximation of a degenerate reaction-cross-diffusion system. Due to the symmetry in the parabolic part, this system is known to preserve segregation of densities -- initially non-overlapping densities belonging to different species remain segregated for all times, which leads to internal layers between different species. We show that time-discrete approximations exist and converge to a weak solution, as the timestep goes to zero.

math.AP↗

arXiv2017

Atomic discreteness and the nature of structural equilibrium in conductance histograms of electromigrated Cu-nanocontacts

We investigate the histograms of conductance values obtained during controlled electromigration thinning of Cu thin films. We focus on the question whether the most frequently observed conductance values, apparent as peaks in conductance histograms, can be attributed to the atomic structure of the wire. To this end we calculate the Fourier transform of the conductance histograms. We find all the frequencies matching the highly symmetric crystallographic directions of fcc-Cu. In addition, there are other frequencies explainable by oxidation and possibly formation of hcp-Cu. With these structures we can explain all peaks occurring in the Fourier transform within the relevant range. The results remain the same if only a third of the samples are included. By comparing our results to the ones available in the literature on work-hardened nanowires we find indications that even at low temperatures of the environment, metallic nanocontacts could show enhanced electromigration at low current densities due to defects enhancing electron scattering.

cond-mat.mes-hall↗