Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, November 30, 2018
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Failing elastically and succeeding stochastically

Abstract:   The mechanical processes that deform pack ice at high latitudes are governed by thin plate theory. One can show that the associated patterns are associated with the elastic failures. Whilst we understand that such failures underlie the constitutive law of the aggregate as embodied in the momentum equation deriving such from thin plate theory has been an intransigent task. On the other hand, we can derive a generalized description of ice thickness distribution (the pdf of ice thickness) using concepts from stochastic dynamics. The full problem can be forced by atmospheric and oceanic fluxes and produce the observed climatology of the ice pack through the numerical solution of a single Fokker-Planck equation (FPE). As such, it provides a far simpler framework for climate modeling than does the typical approach. Further insight is provided by analysis of the FPE. For example, it can be cast in terms of a Bessel-like process described by an FPE with a logarithmic potential and 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.

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Speaker:  John Wettlaufer
Institution:  Yale University

Event Organizer:   Shravan Veerapaneni    shravan@umich.edu

 

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