SS 2016: Nonlinear Dynamics and Stochastic Processes 

Nonlinear dynamical systems are studied in many fields of physics, including classical mechanics, thermodynamics, laser physics, and even biological physics and economics. This will be a first course in nonlinear dynamics, with a focus on geometric aspects and applications. In a second part of the lecture, we will give an introduction to stochastic processes and study the dynamics of nonlinear systems in the presence of noise.

 

Content: Stability analysis, bifurcation theory, oscillators and synchronization, pattern formation, introduction to chaos, introduction to stochastic processes, Langevin and Fokker-Planck formalism, application to first passage time problems and Kramer’s escape rate theory.

Prerequisites: Ordinary Differential Equations, Multi-variate calculus.

Reader: Benjamin Friedrich

Time: Every Tuesday 16.40 (6.DS )

Room: PHY/B214 (Häckelstrasse 3 on main campus)

 

Relevant literature

Strogatz: Nonlinear Dynamics and Chaos, Westview, 2001 (gebraucht ab 20€)

Risken: The Fokker-Planck Equation, Springer, 1996

Stratonovich: Topics in the Theory of Random Noise, Martino, 2014

Ott: Chaos in Dynamical Systems, Cambridge University Press, 2002

VanKampen: Stochastic Processes in Physics and Chemistry, North-Holland, 2007

Script
tba
1. Introdution to Dynamical Systems Theory
2. Linear Stability Analysis
3. Bifurcation theory
4. Oscillations
5. Synchronization
6. Pattern formation
7. Numerics
8. Introduction to Chaos Theory
9. Diffusion and Introduction to Stochastic Processes
10. Nonlinear stochastic dynamcis: Ito vs. Stratonovich
11. Fokker-Planck formalism and Kramer's escape rate theory

SS 2015: Continuum Mechanics for Biological Physics

Continuum mechanics describes fluids and solids; thus providing an indispensable toolkit for biological physics: Living cells move in fluids or adhere to elastic substrates, while showing both elastic and fluid-like properties themselves.
Content. Fluid dynamics and elasticity theory with emphasis on foundations and examples: Navier-Stokes equation from mass and force balance. Reynolds number. Fundamental solution and multipole gymnastiques. Blood flow. Elastostatics. Contact mechanics. Beam theory. Elastic rods, shells, and solids. Visco-elasticity. Experimental methods in cell rheology. Outlook on non-linear elasticity and cell rheology.

Reader: Benjamin Friedrich
Tutorial: Alexander Mietke
Supervision: Stephan Grilll

Time for lecture: Tuesday 14.50-16.20
Location: Biotec, Seminar room E06 (map)

Time for tutorial: Tuesday 16.40-18.10
Location for tutorials: Biotec, Seminar room E06 (map)

Contact: benjamin.friedrich(at)pks.mpg.de
amietke@pks.mpg.de

Script:
lecture notes (hydrodynamics)

lecture notes (elasticity theory)
1. Fluid dynamics basics: Navier-Stokes equation
2. Viscous stresses, Reynolds number, examples of Stokes flow
3. Solving Stokes flow using multipoles
4. Swimming at low Reynolds numbers
5. Mini-course: turbulence
6. Hemodynamics: how your blood flows
7. Introduction to elasticity theory
8. Elasticity of rods, spherical shells, spheroids
9. Contact mechanics
10. Visco-elasticity

Relevant literature

Landau-Lifshitz: Elasticity theory

Landau-Lifshitz: Fluid mechanics

Happel-Brenner: Low Reynolds Number Hydrodynamics

Vogel: Life in moving fluids

Batchelor: An introduction to fluid mechanics

Feynman: The Feynman Lectures, vol. 2

Johnson: Contact Mechanics

Berg: Random Walks in Biology

WS 2014/2015: Kinematics of Noisy Motion

This will be a hands-on course on the stochastic differential geometry of space curves, linking abstract mathematics and concrete examples. As a warm-up, we will discuss translational and rotational diffusion in the plane. Coupling translations and rotations, we will naturally encounter multiplicative noise, allowing us to discuss the subtleties of Ito versus Stratonovich calculus. We will then see how active translations and rotations can be conveniently described as a path on a Lie group called SE(3). No prior knowledge of Lie groups needed.

Dates: 28.11.2014, 05.12.2014, 12.12.2014 Friday, 13:00 - 14:30 Location: WIL-C203
Script: click here

SS 2014: Continuum Mechanics for Biological Physics

Continuum mechanics describes fluids and solids; thus providing an indispensable toolkit for biological physics: Living cells move in fluids or adhere to elastic substrates, while showing both elastic and fluid-like properties themselves.
Content. Fluid dynamics and elasticity theory with emphasis on foundations and examples: Navier-Stokes equation from mass and force balance. Reynolds number. Fundamental solution and multipole gymnastiques. Blood flow. Elastostatics. Contact mechanics. Beam theory. Elastic rods, shells, and solids. Visco-elasticity. Experimental methods in cell rheology. Outlook on non-linear elasticity and cell rheology.
Readers: Benjamin M Friedrich, Elisabeth Fischer-Friedrich
supervision: Stephan Grill
Time: Friday 9.20
Location: Physics building on Main campus, room B214
benjamin.friedrich(at)pks.mpg.de
script :
lecture notes (hydrodynamics)

lecture notes (elasticity theory)
1. Fluid dynamics basics: Navier-Stokes equation
2. Viscous stresses, Reynolds number, examples of Stokes flow
3. Solving Stokes flow using multipoles
4. Swimming at low Reynolds numbers
5. Mini-course: turbulence
6. Hemodynamics: how your blood flows
7. Introduction to elasticity theory
8. Elasticity of rods, spherical shells, spheroids
9. Contact mechanics
10. Visco-elasticity

Relevant literature

Landau-Lifshitz: Elasticity theory

Landau-Lifshitz: Fluid mechanics

Happel-Brenner: Low Reynolds Number Hydrodynamics

Vogel: Life in moving fluids

Batchelor: An introduction to fluid mechanics

Feynman: The Feynman Lectures, vol. 2

Johnson: Contact Mechanics

Berg: Random Walks in Biology