Symmetry breaking and pattern formation in soft matter and active fluids
Geometric constraints affect pattern selection and topological defect formation in a wide range of non-equilibrium processes, from crystal growth to morphogenesis. In the first part of this talk, I will summarize recent experimental and theoretical work that aims to understand how curvature controls symmetry breaking and topological defects on the wrinkled surfaces of elastic bilayer materials [1]. Specifically, we will present a higher-order PDE model that captures essential characteristics of the experimental data. In the second part, we will generalize the underlying ideas to obtain an analytically tractable description [2] of bacterial and other active suspensions. The resulting generalized Navier-Stokes equations reveal an unexpected chiral symmetry-breaking mechanism, and offer insight into the triad dynamics of classical turbulence by uncovering a previously unknown cubic invariant [3].
[1] Nature Materials 14, 337 (2015); PRL 116, 104301 (2016) [2] PNAS 114, 2119 (2017); PRL 120, 164503 (2018) [3] J Fluid Mech 841, 701 (2018)
As of July 2018, Jörn Dunkel is Associate Professor of Mathematics. He joined the mathematics faculty as Assistant Professor. He field is in physical applied mathematics. Jörn Dunkel received Diplomas in Physics (2004) and Mathematics (2005) from the Humboldt University Berlin. He completed his PhD in Statistical Physics under Peter Hänggi at the Universität Augsburg in 2008. After two years of postdoctoral research at the Rudolf-Peierls Centre for Theoretical Physics in the University of Oxford, he spent three years as a Research Associate at DAMTP in the University of Cambridge. Working at the intersection of statistical and biological physics, Jörn's current research focuses on how physical properties of individual cells or microorganisms determine self organization, development and biological function in multicellular complexes. To this end, his group is developing and investigating mathematical models that describe dynamical behavior and structure formation in microbial and soft matter systems.