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 , email@example.com, tel.: 35325371
Ken Haste Andersen (KHA), Peter Ditlevsen (PD), Paolo Giuliani (PG),
Kirstine Berg-Soerensen (KBS), Lene Oddershede (LO), ,
Mogens Hoegh Jensen (MHJ).
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.