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Short course on kinetic theory

This year’s Onsager professor, Matthieu H. Ernst, will give a short course on kinetic theory, starting Wednesday September 12.

Format: Tuesdays and Wednesdays 1415-1600 during the weeks 37-40.
(only Wednesday the first week).

The first 4 double lectures will present the basics of kinetic theory, whereas the 3 final ones on more specialized topics, the emphasis of which will be chosen in dialogue with the audience. No prior knowledge on kinetic theory is required.

Below is a tentative plan, where the basic part consists of chapter I and a quick sample of later chapters. The scope of the specialized part is indicated by the items under chapters II-IV.

I. Boltzmann equation

  • Non-linear Boltzmann equation (NLBE) for molecular gases:
    A complete theory for the approach to equilibrium on the molecular scale in terms of particle distribution functions (pdf).
  • Homogeneous systems:
    Fast relaxation in velocity space to a Maxwell (Gauss) pdf. H-theorem (growth of entropy).
  • Inhomogeneous systems:
    Local density, temperature and flow fields, hydrodynamics and transport coeffisients.
  • Chapman-Enskog theory:
    Calculation of transport coefficients from intermolecular forces.

II. NLBE for granular/inelastic gases

  • No energy conservation, no steady state without energy input.
  • Freely cooling homogeneous states, and non-equilibrium steady states (NESS) with stretched exponential tails.
  • Inhomogeneous states:
    Hydrodynamic equations, clustering instabilities, inelastic collapse.

III. Kinetic theory at mesoscopic levels

  • Direct Simulation Monte Carlo Method (DSMC) or Bird’s Method
  • Lattice Gas Cellular automata (LGCA) and Lattice Boltzmann Equation (LBE)

IV. Kinetic theory of coagulation (Smoluxhowski’s) and fragmentation

Onsager Professor 2007, Matthieu Ernst
Professor Matthieu Ernst

NTNU, 7491 Trondheim, tlf. 73 59 50 00. Kontakt oss
Ansvarlig redaktør: Informasjonssjef Christian Fossen