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 , firstname.lastname@example.org, tel.: 35325371
Ken Haste Andersen (KHA), Peter Ditlevsen (PD), Hans Fogedby (HF),
Mogens Hoegh Jensen (MHJ), Kim Sneppen (KS).
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,
5/10: Burgers equation, conservation laws, Fourier representation. (MHJ)
Navier-Stokes equations (elimination of pressure),
Reynolds number, symmetries and conservation laws. (PD) Exercises to 12/10 click here to PD's page
Burgers equation, conservation laws, Kolmogorov theory,
Fourier transform, discrete models, shell models, intermittency
16/11: Statistical description, closure problems. (PD)
Interfaces, KPZ equations, pinning effects, SOC models
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
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