Study Programmes 2015-2016
PHYS0961-1  
Irreversibility, instabilities and chaos
Duration :
30h Th, 30h Pr
Number of credits :
Master in physical engineering (120 ECTS)5
Master in physical engineering (120 ECTS)5
Lecturer :
Pierre Dauby
Language(s) of instruction :
French language
Organisation and examination :
Teaching in the first semester, review in January
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Course contents :
Classical (Onsager-Prigogine) Irreversible Thermodynamics. Coupling of the thermodynamical fluxes and forces
  • Direct effects : viscosity, Fourier's, Fick's, Ohm's laws
  • Crossed effects: thermodiffusion, thermoelectricity
Self-organization far from equilibrium
  • Notion of stability of a flow, transitions in fluids
  • Thermoconvective instability (Rayleigh-Bénard-Marangoni instability), linear and non linear approaches, self-organization in fluids, competition between different geometrical patterns
  • Genericity of self-organization phenomena
  • Reaction-diffusion equations : application in chemistry (Belousov-Zhabotinsky), Turing instability, morphogenesis
Introduction to the study of dynamical systems
  • elementary bifurcations
  • transitions to chaos
Learning outcomes of the course :
At the end of the course, the student will know the basics of Classical Irreversible Thermodynamics as developped by Onsager and Prigogine. He will also have learned how to describe self-organization phenomena in the frame of this theory. Eventually, he will be able to illustrate these phenemena by numerical simulations of the corresponding equations.
Prerequisite knowledge and skills :
Basic knowledge of continuum mechanics is an asset.
Planned learning activities and teaching methods :
Theory is presented in lectures. The exercices consist in a numerical analysis of a self-organizing system.
Mode of delivery (face-to-face ; distance-learning) :
Mainly face-to-face teaching (with exercices partly as home-works).
Recommended or required readings :
Notes available on the web ("MyUlg").
Assessment methods and criteria :
Oral or written exam on theory (60%). Report on the numerical homework (40%).
Work placement(s) :
Organizational remarks :
Contacts :
Pierre C. DAUBY, Chargé de cours Institut de Physique (local 2/57), Bât. B5a, Allée du 6 août 17, B-4000 Liège 1 Tel. : 04/366.23.57 - email: PC.Dauby@ulg.ac.be