Speaker
Prof.
John Wettlaufer
(Yale University & Nordita)
Description
We derive a generalized description of the ice thickness
distribution in the polar ice pack using concepts from
stochastic dynamics. This geophysical problem can be cast
in terms of a Bessel-like process with a negative constant
drift, described by a Fokker-Planck equation with a
logarithmic potential.The problem belongs to a family of
Fokker-Planck equations with logarithmic potentials closely
related to the Bessel process that has been extensively
studied for its applications in physics, biology, and
finance. The Bessel-like process we consider can be solved
by seeking solutions through an expansion into a complete
set of eigenfunctions. The associated imaginary-time
Schrödinger equation exhibits a mix of discrete and
continuous eigenvalue spectra, corresponding to the quantum
Coulomb potential describing the bound states of the
hydrogen atom. We demonstrate this technique by solving the
Brownian motion problem and the Bessel process both with a
constant negative drift. The use of this approach allows one
to study Earth’s polar climate using a single equation
and/or two equations for each of the seasons.
