Master/graduate course 712:

Topics in Physics of Complex Systems

Selected topics in the research areas of the ``Complex Systems
Group  ( 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, patterns,
ripple formation in sand, proteins in cells, diffusion in biological membranes, 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. First time: Week 37.
                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:
       Ken Haste Andersen  (KHA),  Peter Ditlevsen  (PD),  Paolo Giuliani  (PG),
       Kirstine Berg-Soerensen  (KBS),  Lene Oddershede  (LO), ,
      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 (MHJ)

3: Scaling, Scaling laws, Kadanoff construction, (Real Space Renormalization) (MHJ)

4: Diffusion equation, Burgers equation (maybe Random Walk) (MHJ)

5,6: Navier-Stokes equations (elimination of pressure), Reynolds number, symmetries and conservation laws, closure problems. (PD)  Notes of Peter Ditlevsen can be downloaded  here

7: Conservation laws, Kolmogorov theory, intermittency, discrete models (MHJ).

8: Shell models, Interfaces (maybe SOC) (MHJ)

9,10: Magneto hydrodynamics and shell models (PG)

11,12: Instabilities, patterns, sand ripples (KHA)

13,14: Cells and proteins, membranes, optical tweezer (KBS, LO).
 

Preliminary pensum and exam list. We discuss it thursday 13 and thursday 20.

 pensum and exam list

Exam date: January 18, starting 9 am. Room A107, HCO, Censor: Hans Fogedby (Aarhus).

Question Hour: January 16, 1-3 pm, Aud. A or C or D, NBI (there is repair work). NOTE: All
teachers cannot be present at the question hour.