Pattern formation

Prerequisite: An open mind towards complex patterns in living systems. A course in statistical physics. Familiarity with nonlinear dynamics and fluid dynamics. Prior programming experience [preferably in python]

Not-required: Prior biology background.

When: TBA

Where: TBA

First meeting: TBA

In-person course. No online component


Outline

  • What is a pattern? Spatiotemporal patterns in biology.
  • Brief recap of nonlinear dynamics. Phase-space analysis. Numerical tools for pattern formation. Galerkin methods. Amplitude equations. Pattern selection. Vector/Tensor order parameters. Topological defects. Group-theoretic classification of patterns.
  • Patterns driven by free-energy gradients.
  • Self-organized nonequilibrium patterns. Reaction-diffusion systems. Signalling patterns. Turing instabilities. Ecological patterns.
  • Hydrodynamics of active materials. Pattern formation in active matter. Mechanochemical and geometrodynamic patterns in cell & developmental biology. Open problems.

This is an advanced course with emphasis on pattern formation in living systems.

References