**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.**

**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.**