Nonlinear Waves Seminar - Patrick Shipman

Patrick Shipman, Department of Mathematics, Colorado State University

Topological measures of order for templated pattern-forming systems

When the surface of a nominally flat binary material is bombarded with a broad, normally incident ion beam, disordered hexagonal arrays of nanodots can form.  Defects, such as dislocations in ripple patterns or penta-hepta pairs in hexagonal arrays, limit the utility of patterns produced by ion bombardment.  Together with D. Pearson, F. Motta, and M. Bradley, we have proposed a method, namely templating the surface, to increase the order in the patterns. To evaluate the efficacy of this method, a means of quantifying the degree of order is needed.  We compare time-honored methods, such as the autocorrelation function, with new topological methods we propose which utilize persistent homology.