Nonequilibrium Physics with Interdisciplinary Applications
Time and Location:
Time: Tuesday, 10:00 - 11:30 Uhr (tutorial: 11:30 - 12:00)
Place: Seminar room Institute for Theoretical Physics
Topic:
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 Biologicial Physics"
Knowledge in statistical physics is helpful, but not essential.
Exercises:
Problem sheet 1
Problem sheet 2
Problem sheet 3
Problem sheet 4
Problem sheet 5
Problem sheet 6
Problem sheet 7
Problem sheet 8
Problem sheet 9
Problem sheet 10
Materials:
Simulation of
the Nagel-Schreckenberg model
Universal statistical properties of poker tournaments
Poker
(slides)
Flashing ratchet
(Java applet)
Ratchets (slides)
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)
- 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