Strukturbildung fernab vom Gleichgewicht
(Pattern formation far from equilibrium), SS 2021

Goal and focus

This lecture and tutorial course provides an introduction to the methods of nonlinear dynamics and mathematical physics used to analyse and explain patterns in Physics, Chemistry, and Biology and is supplemented by few mini-projects. Central tools of applied mathematics are mastered and discussed in details on a number of analytically solvable examples, ranging from conventional to recently discovered phenomena.


Enrolment: If interested in attending the course, please sign up, see the agnes and moodle links below. To access the course via Moodle, use the enrolment key (Einschreibeschlüssel): MusterBild-21.

Time schedule: The lectures (VL) and tutorials (Ü) take place
VL: Wed, 15:15-16:45
Ü: Fri, 9:15-10:45
Currently, the course takes place online. Please, access the link via Moodle.

Contact: In case of any issues, just drop me an email: straube[AT]


Derivation of basic equations of hydrodynamics
- Equations of ideal and real fluids
- Equations of thermal and thermocapillary convection
- Macro- and microfluidic limits. Microflow in a corrugated geometry
- Boundary conditions ar the interface between fluids
Stability theory
- The principle of linear stability
- Weakly nonlinear analysis. Derivation and analysis of amplitude equations
- Stuart-Landau, complex Ginzburg-Landau, Newell-Whitehead-Segel equations
Chemically reacting systems and nonlinear waves
- Activator-inhibitor reaction-diffusion systems. Turing instability
- Front propagation. Pulled and pushed fronts
- Reaction-advection-diffusion. Absolute and convective instabilities. Global mode
Pattern-forming behavior in colloidal soft matter systems
- Equilibrium and nonequilibrium zigzag transitions
- Chaining and propulsion. Realization of colloidal sieve
- Discrete front and kink propagation
- Extra: Dynamic mode locking and directional locking
- Extra: Patterns in colloidal liquid crystals


Agnes link:

Moodle link: