Synopsis:
The goal of this course is to provide a rudimentary introduction to
kinetic theory, which bridges the microscopic theories and the
macroscopic, continuum theories of flows. We will start from a system of
N interacting particles, i.e., the molecular dynamics (MD) of
N particles, and the equivalent Liouville equation for the
N particle distribution function. We then proceed to study the
Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations for
the reduced distribution function, leading to the Boltzmann equation.
We will derive the hydrodynamic equations, i.e., the Navier-Stokes
equations from the Boltzmann equation or its model equations, via the
Chapman-Enskog analysis. In this way the macroscopic theory, i.e., the
hydrodynamics and the relevant transport coefficients, are related to
the underlying microscopic dynamics. The second part of the course
involves numerical methods based on kinetic theory. Applications include
simple and complex fluids, and microfluids.
This course is suitable for the graduate students who are interested
in kinetic theory, mesoscopic methods, nonequilibriam statistical
mechanics, and computational sciences.
There will be no exam for the course, but there will be a set of take-home assignments. The final grade depends the scores of the assignments.