Universal branch statistics of branched flows

Branched flow is a universal phenomenon of particle and wave flows which are subjected to weak, correlated disorder. It has been observed on length scales ranging from a few micrometres, affecting the transport properties of semiconductor devices [1], up to several thousand kilometres, influencing sound propagation through the ocean [2]. It is also responsible for the appearance of large and hazardous freak waves and tsunamis [3]. Here, we address the question of how many branches can be observed on average as a function of distance from an ordered source. We derive a universal curve for this quantity which applies to a wide range of parameters and correlation functions of the underlying disorder [4]. \\[4pt] [1] e.g. M. A. Topinka et al., Nature \textbf{410}, 183 (2001), M. P. Jura et al., Nature Physics \textbf{3}, 841 (2007) \\[0pt] [2] M. Wolfson \& S. J. Tomsovich, Acous. Soc. Am., \textbf{109}, 2693 (2001) \\[0pt] [3] M. V. Berry , New J. Phys. \textbf{7}, 129 (2005); M. V. Berry, Proc. R. Soc. A \textbf{463}, 3055 (2007); E. J. Heller, L. Kaplan \& A. Dahlen, J. Geophys. Res., \textbf{113}, C09023 (2008) \\[0pt] [4] J. J. Metzger, R. Fleischmann and T. Geisel, in preparation