Nonequilibrium Physics with Interdisciplinary Applications
LATEST:
The lecture notes will get updated in the future (last update: 14.08.13).
A voluntary new excercise has been added.
Time and Location:
Time: Monday, 10:00 - 11:30 Uhr (tutorial: 11:30 - 12:00)
Place: Seminar room Institute for Theoretical Physics
Additional lectures to make up for those that had to be cancelled
are scheduled for
Monday, 22.07.13, 10:00-12:00 and 13:00-15:00
Tuesday, 23.07.13, 14:00-16:00.
Topics:
The course will introduce the basic concepts and methods of
nonequilibrium physics and stochastic systems. These will be
illustrated using examples from interdisciplinary applications.
Examples are:
- Stochastic processes and their description (Master-,
Fokker-Planck equation)
- Basic models (random walk, cellular automata models)
- Analytical and numerical methods
- Phase transitions
- Traffic (jam formation, phases, models)
- Pedestrian dynamics (collective effects, evacuations)
- Biological systems (ant trails, intracellular transport)
- Socio-economic systems (stock market, auctions, supply chains)
- Game theory (chip distribution in Poker, Ebay auctions)
- Pattern formation
Audience, requirements:
The course is part of the master course, e.g. as specialised course
(4 credit points) in "Statistical and Biological Physics"
Knowledge in statistical physics is helpful, but not essential.
Problem sheet 1
Problem sheet 2
Problem sheet 3
Problem sheet 4
Problem sheet 5
Problem sheet 6
Problem sheet 7
Problem sheet 8
Lecture Notes:
Lecture
notes (last update: 14.08.13)
Slides
for traffic lecture
Slides
for biological transport lecture
Slides
for pedestrian dynamics lecture
Materials:
Video
of Brownian motion
Simulation of Brownian motion, another applet
Simulation of
the Nagel-Schreckenberg model
Flashing ratchet
(Java applet)
Brownian motion (Java applet)
Literature:
- A. Schadschneider, D. Chowdhury, K. Nishinari:
Stochastic Transport in Complex Systems (Elsevier, 2010)
- P.L. Krapivsky, S. Redner, E. Ben-Naim: A Kinetic View of Statistical
Physics (Cambridge University Press, 2010)
- V. Privman (Ed.): Nonequilibrium Statistical Mechanics in One
Dimension (Cambridge University Press, 1997)
- N.G. van Kampen: Stochastic Processes in Physics and Chemistry
(North Holland)
- M. Treiber, A. Kesting:
Verkehrsdynamik und -simulation (Springer, 2010);
english translation: Traffic Flow Dynamics (Springer, 2013)
- B. Chopard, M. Droz:
Cellular Automaton Modeling of Physical Systems
(Cambridge University Press)
- R. Mahnke, J. Kaupuzs, I. Lubashevsky:
Physics of Stochastic Processes: How Randomness Acts in Time
(Wiley VCH, 2008)
- N. Boccara:
Modeling Complex Systems (Springer)
- G.M. Schütz: Exactly solvable models for many-body systems
far from equilibrium, in Phase Transitions and Critical Phenomena,
Vol.19, hrsg. von C. Domb and J.L. Lebowitz (Academic Press)
- D. Chowdhury, K. Nishinari, A. Schadschneider:
Physics of transport
and traffic phenomena in biology: from molecular motors and cells
to organisms, Physics of Life Reviews 2, 318 (2005)
PDF
- D. Chowdhury, K. Nishinari, A. Schadschneider:
Self-organized patterns and traffic flow in colonies of organisms:
from bacteria and social insects to vertebrates,
Phase Trans. 77, 601 (2004)
PDF
- D. Chowdhury, L. Santen, A. Schadschneider:
Statistical Physics of Vehicular Traffic and Some Related Systems,
Physics Reports 329, 199 (2000),
PDF
- D. Helbing:
Traffic and related self-driven many-particle systems,
Rev. Mod. Phys. 73, 1067 (2001),
PDF