Topics in Physics of Complex Systems
Selected topics in the research areas of the ``Complexity Lab''
( CATS etc) at the Niels Bohr Institute,
Blegdamsvej. The course can be followed by students at 4-5'th year
and by PhD students. The course is ideal for student who plan to
write their thesis within complex systems and bio-complexity.
The topics that will be covered are:
Burgers equation, shell models for turbulence, scaling analysis
for Navier-Stokes equations, non-equilibrium statistical mechanics,
the motion and scaling behavior of interfaces, hydrodynamics
instabilities, self-organized critical behavior,
evolution in biological systems, proteins, genetic contacts and networks, etc.
Students should preferably have taken the following courses:
Fysik 222/Dynamiske Systemer Fysik222/Dynamiske Systemer , Statistisk Mekanik, evt. Hydrodynamik
Time and place: Niels Bohr Institutet, Blegdamsvej 17, Aud. D,
Thursdays 13.15 - 15 (NOTE: Back to standard time). First time: 5/9.
Two hours exercises per week.
Exam: Oral. About 12-15 questions from a curriculum defined
by material (notes, papers, book chapters) handed out
by the teachers.
Responsible: Mogens Hoegh Jensen , email@example.com, tel.: 35325371
Kim Sneppen (KS), Peter Ditlevsen (PD), Hans Fogedby (HF),
Mogens Hoegh Jensen (MHJ).
1: Introduction: Equilibrium and non-equilibrium statistical mechanics, turbulence, interfaces, etc. Discussion of the topics in the course (MHJ)
2: Ising Model, MFT, Landau Theory, Critical exponents (HF)
3: Scaling, Scaling laws, Kadanoff construction, (Real Space Renormalization) (HF)
4: Simulations, Monte Carlo Methods, Diffusion equation, NOTES for this time is outside my office (NBI, Kb7b) on the post-shelves (from friday noon). The exercise for next time is Problem 7.5 in Yeomans book, is in the notes. You should write your own Monte-Carlo program (MHJ)
5: Burgers equation, conservation laws, exact solutions (MHJ) Exercises 1
6: Conservation laws, Kolmogorov theory, intermittency, discrete models
(MHJ) Exercises 2 Exercises
7,8,9: Navier-Stokes equations (elimination of pressure), Reynolds number, symmetries and conservation laws, closure problems. (PD) Notes of Peter Ditlevsen can be downloaded here
10: SOC, Evolution in Biology (KS)
11: Cells, DNA and proteins (KS).
12,13: Genetic Switches, Genetic Networks, Internet (KS)
14: Interfaces (MHJ)
Spørgetime: Onsdag den 15., kl. 10-12 i Aud. D.
Pensum and exam list for oral exam 6, 16 January:
Questions and pensum