Massimo Vergassola – University of California, San Diego
Wednesday, December 3rd, 2025
Zoom opens: 10:30AM EST
Seminar begins: 10:45AM EST
Defects, Parcellation, and Renormalized Negative Diffusivities in Nonhomogeneous Oscillatory Media
Coupling among oscillators in spatially extended systems often locks their frequency at a common value. In the presence of spatial non-homogeneities, locking of different regions at different frequencies leads to parcellation, i.e., a series of synchronized clusters (plateaus). Peristalsis in the intestine and vasomotion in the brain provide major natural examples of nonhomogeneous oscillatory media where such phenomena are relevant. Motivated by these physiological rhythms, I will discuss the phase diagram of a Ginzburg-Landau (GL) model with a frequency gradient. For large gradients and diffusion, the rest state is stable, and the linear spectrum around it maps onto the classical non-Hermitian Bloch-Torrey equation introduced for nuclear magnetic resonance. When complex pairs of eigenvalues turn unstable, precursors of plateaus grow, separated by defects where the GL amplitude vanishes. Nonlinear effects either saturate the amplitude of plateaus or lead to a phase-locked state, with saddle-node bifurcations separating the two regimes. In the region of plateaus, the formation of defects is traced to a nonlinear renormalization of the diffusivity, and the scaling of their number and length vs dynamical parameters is determined.