Symmetry and asymmetry in oscillatory patterns

Event Sponsor: 
Mathmatics and Computer Science - LANS Seminar
Start Date: 
Sep 18 2019 - 10:30am
Building/Room: 
Building 240/Room 1404-1405
Location: 
Argonne National Laboratory
Speaker(s): 
Zachary Nicolaou
Speaker(s) Title: 
Northwestern University
After centuries of scientific study, nonlinear dynamical systems still pose seemingly insurmountable challenges to analysts today.  Chaotic and complex
phenomena, even in the simplest nonlinear systems, bring the reductionist approach into question.  Surprisingly, however, microscopic disorder often
underlies collective macroscopic order, and system symmetry dictates universal routes to pattern formation.  While complexity is currently intractable in
general, some understanding can be gleaned from a few, often idealized, paradigmatic models. Yet, the impact of asymmetries and heterogeneities in
these models is still largely unknown.
 
In this seminar, I will discuss our recent studies on symmetry breaking and asymmetry-induced symmetry in several classical oscillatory systems. First, I
will detail the emergence massively multistable chimera states in networks of Janus oscillators with antiferromagnetic network structure as well as the
enhanced synchronization observed when this structure is perturbed. Next, I will describe the appearance of localized analogs of chimera states in
oscillating chemical reactions and emphasize open questions about the transport of related topological defects.  Finally, I will note surprising new features
of instabilities in media driven by vibrations in heterogeneous geometries, including heterogeneity-stabilized homogeneous states in fluid surfaces and
anharmonic instabilities in coupled pendulum arrays.
Miscellaneous Information: 

This seminar will be streamed. See details at https://anlpress.cels.anl.gov/cels-seminars/