**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.**