**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: **