Master/graduate course 712:

Topics in Physics of Complex Systems

Selected topics in the research areas of the ``Center for Chaos
and Turbulence Studies ( CATS)'' 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 at CATS. The topics that will be covered are:
Burgers equation, shell models for turbulence, scaling analysis
for Navier-Stikes equations, non-equilibrium statistical mechanics,
the motion and scaling behavior of interfaces, hydrodynamics
instabilities, self-organized critical behavior, patterns,
ripple formation in sand, etc.

Students should have taken the following courses:
Fysik 222/Dynamiske Systemer Fysik 222/Dynamiske Systemer , Statistisk Mekanik, evt. Hydrodynamik

Time and place: Niels Bohr Institutet, Blegdamsvej 17, Aud. D,
                Thursdays 13.15 - 15. First time: Thursday 7 September.
                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),   Hans Fogedby  (HF),
      Mogens Hoegh Jensen (MHJ), Kim Sneppen  (KS).

Preliminary program:

7/9:  Introduction: Equilibrium and non-equilibrium statistical
      mechanics, turbulence, interfaces, etc. Discussion of the
      topics in the course (MHJ)
14/9: Ising Model, MFT, Landau Theory, Critical exponents (HF)
21/9: Scaling, Scaling laws, Kadanoff construction,
      (Real Space Renormalization) (HF)
28/9: Random Walk, Dynamical scaling, Diffusion equation,
      Hydrodynamics (HF)
5/10: Burgers equation, conservation laws, Fourier representation. (MHJ)
12/10:
      Navier-Stokes equations (elimination of pressure),
      Reynolds number, symmetries and conservation laws. (PD) Exercises to 12/10  click here to PD's page
26/10,2,9/11:
      Burgers equation, conservation laws, Kolmogorov theory,
      Fourier transform, discrete models, shell models, intermittency
      (MHJ)
16/11: Statistical description, closure problems. (PD)
23,30/11,7/12:
      Interfaces, KPZ equations, pinning effects, SOC models
      (KS,HF)

NOTE: For the lectures 14 and 21 december I have lectures notes.
              You find them on the post shelves outside my office, Kb floor, NBI.    Mogens

14,21-12:
      Instabilities, patterns, sand ripples (KHA)

We have `question hour' (spoergetime) friday 5 january  10 a.m., Aud. D

Exam (oral) is monday  8 january starting 9 a.m.

 pensum and exam list