2023-2024 / PHYS0961-1

Irreversibility, instabilities and chaos

Duration

30h Th, 30h Pr

Number of credits

 Master of Science (MSc) in Engineering Physics5 crédits 

Lecturer

Pierre Dauby

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit 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 learning unit

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

The theoretical part of the course is presented as lectures. In case of a small audience, lectures are replaced by a tutorship that consists in discussions between the sudents and the instructor. The exercices consist in a numerical analysis of a self-organizing system.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course


Additional information:

Face-to-face teaching (except in the case of problems related to the pandemic); exercices partly as home-works.

Recommended or required readings

Notes available on eCampus.
   

Exam(s) in session

Any session

- In-person

written exam AND oral exam

Written work / report


Additional information:

Oral or written exam on theory (60%). Report (compulsory) on the numerical homework (40%).

Work placement(s)

Organisational remarks and main changes to the course

Practical details will be provided on eCampus.
   

Contacts

Pierre C. DAUBY, Professeur Institut de Physique (local 2/57), Bât. B5a, Allée du 6 août 19, B-4000 Liège Tel. : 04/366.23.57 - email: PC.Dauby@uliege.be

Association of one or more MOOCs