Statistical and Biological Physics
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Winter term 2025/2026

Self-Organization and Pattern Formation

[LSF of lectures] [LSF of tutorials] [YouTube]

Tuesday, 10-12 (A348)

Thursdays, 12-14 (A348)

First lecture on 16.10.2025

Homework sheets

    • Sheet 0: Diffusion and Fourier transform, The harmonic oscillator, A model of a laser
    • Sheet 1: Lyapunov functions, Population of fish, Outbreak of an insect in a forest
    • Sheet 2: Bogdanov-Takens bifurcation, Bogdanov-Takens bifurcation: Unfolding the homoclinic orbit, Biochemical Oscillations
    • Sheet 3: Source degradation model, Allen-Cahn equation with external field, Fisher-KPP equation
    • Sheet 4: Cahn-Hilliard equation with an additional reaction term, Cahn-Hilliard equation with active reaction
    • Sheet 5: The LSW theory of Ostwald ripening, The LSW theory in d spatial dimensions, Non-reciprocal Cahn-Hillard equation
    • Sheet 6: Linear Stability of the Keller–Segel Model, Active Model B and Pseudopotentials
    • Sheet 7: Stability of wave solutions of the complex Ginzburg-Landau equation, Phase Equations of the CGLE
    • Sheet 8: Kuramoto models – global synchronization of heterogeneous oscillators, Kuramoto models – spatially coupled identical oscillators, Slow Manifold of Predator-Prey Dynamics
    • Sheet 9: Conceptual Questions

Summer term 2025

Nonequilibrium Field Theories and Stochastic Dynamics

Homework sheets

      • Sheet 0: Binomial Sampling Process (Genetic Drift), Random numbers
      • Sheet 1: One-dimensional Random Walker, One-dimensional Random Walker: Numerics, Cyclic m-step process
      • Sheet 2: The Luria-Delbrück Experiment, Linear Birth-Death Process
      • Sheet 3: Poisson Process on a Ring, Markov processes with infinite state spaces
      • Sheet 4: Brownian particle in a gravitational field, Bistability in an autocatalytic reaction, First passage times
      • Sheet 5: Poisson process on a ring: continuous limit, Fokker–Planck Dynamics for Motility-Induced Phase Separation, Dynamic instability of microtubules
      • Sheet 6: Path integrals and the saddlepoint approximation, Inertial effects for heterogeneous diffusion, Stochastic stock market
      • Sheet 7: Onsager relations and time-irreversibility, Onsager relations for model A and B
      • Sheet 8: Confined semiflexible polymer chain, Dynamics of phase boundaries
      • Sheet 9: State dependent Onsager matrices - Model A, State dependent Onsager matrices - Model B, Path Integral Formulation of Model C
      • Sheet 10: Binodal Construction in Model B, Brownian dynamics of two coupled particles at different temperatures, Linear Stability of the Keller–Segel Model
      • Sheet 11: Pattern Formation in Fluids with Active Stress, Field Theory for Population Dynamics

Summer term 2024

Winter Term 2023/2024

Summer term 2023

Winter term 2022/2023

Summer term 2022

Winter Term 2021/2022

Summer term 2021

Winter term 2020/2021

Summer term 2020

Winter term 2019/2020

Les Houches Lecture Notes

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