Computational & Applied Math Seminar

Time: 15:00-17:00 of Aug 3, 5, 7, 10, 12 and 14

Venue: Zoom (ID 6694179735)

Based on the reciprocal symmetry for kinetic coefficients, Onsager’s variational principle is of fundamental importance to non-equilibrium statistical physics and thermodynamics in the linear response regime, where many physical phenomena can be accurately described by various partial differential equations. [For his discovery of the reciprocal relations, Lars Onsager was awarded the 1968 Nobel Prize in Chemistry.] Well known examples include the diffusion equation, the Stokes equation, the Cahn-Hilliard equation for binary systems, the Ericksen-Leslie theory for nematic liquid crystals, and the Poisson–Nernst–Planck model for electro-osmosis, which have been intensively studied by applied mathematicians.

The purpose of this short course is to present Onsager’s variational principle and its applications to graduate students in applied mathematics. The presentation consists of four units:

1. Review of elementary statistical physics and thermodynamics

2. Onsager’s reciprocal symmetry for kinetic coefficients

3. Onsager’s variational principle

4. Applications to the derivation of various partial differential equations