Professor Bassam Bamieh (UCSB): Fragility in Large-scale Dynamics: From Shear-flow transition to Anderson Localization to Networked Dynamical Systems

Fragility phenomena appear to be more ubiquitous than is generally believed. Hydrodynamic stability of wall-bounded shear flows is one striking example where flow fluctuations are highly susceptible to even small irregularities. The well-known phenomenon of Anderson localization is another one where small amounts of material disorder can radically alter the nature of dynamical modes. Recent work has shown that such localization phenomena can also occur without the presence of medium disorder, but rather due to complex geometry such as in vibrational modes of several naturally occurring biomolecules. The common thread between these seemingly disparate phenomena is the fragility of eigenvalues/vectors of large-scale matrices and operators when perturbed in various ways.