Lectures: Self-Organization & Pattern Formation

Self-Organization & Pattern Formation

Can we build predictive theories for self-organizing systems—spanning fluids, diffusion–reaction systems, soft/active matter, and living systems—without tracking every microscopic detail? Yes: by exploiting universality, symmetry, and conservation laws, and coarse-graining to reveal instability mechanisms, mesoscopic laws, and scaling behavior.

Scope

Nonequilibrium, spatially extended systems that spontaneously generate order. Emphasis on the onset of instability, pattern selection, dynamics, and the emergence of mesoscopic laws. Methods include dynamical systems, continuum field theories, statistical physics, weakly nonlinear analysis, and differential geometry.

Themes

• Dynamical systems & bifurcations: linear/nonlinear stability, fixed points/attractors, excitability, synchronization, chaos; normal forms and amplitude equations.
• Instability mechanisms: Turing and Hopf; interfacial (Mullins–Sekerka); hydrodynamic (Rayleigh–Bénard, shear/viscous, Marangoni); morphoelastic buckling and wrinkling; Saffman–Taylor fingering.
• Pattern formation: phase separation & coarsening; interface dynamics; diffusion–reaction patterns and waves; excitable media; fronts, pulses, dendrites; thin-film dewetting and flows.
• Geometry & confinement: curvature and weakly non-flat geometries, boundary conditions, selection by confinement, and heterogeneity.
• Active field theories & broken detailed balance: non-variational couplings and stresses; absence of a free-energy/Lyapunov functional; deterministic circulating fluxes; universality and scaling near nonequilibrium transitions.

Lectures will be updated on YouTube. The first lecture will take place on October 16th.