Master/graduate course 712:

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 ,  mhjensen@nbi.dk, tel.: 35325371

Teachers:
       Kim Sneppen  (KS),  Peter Ditlevsen  (PD),  Hans Fogedby   (HF),
      Mogens Hoegh Jensen (MHJ).

Preliminary program:

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 3

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