PDE-Applied Math Archives for Academic Year 2017

Liquid drops on Rough surfaces

When: Thu, September 14, 2017 - 3:30pm
Where: Kirwan Hall 3206
Speaker: Inwon Kim (UCLA) -

Data-based stochastic model reduction for chaotic systems

When: Thu, October 12, 2017 - 3:30pm
Where: Kirwan Hall 3206
Speaker: Fei Lu (John Hopkins University) - http://www.math.jhu.edu/~feilu/
Abstract: The need to develop reduced nonlinear statistical-dynamical models from time series of partial observations of complex systems arises in many applications such as geophysics, biology and engineering. The challenges come mainly from memory effects due to the nonlinear interactions between resolved and unresolved scales, and from the difficulty in inference from discrete data.

We address these challenges by introducing a discrete-time stochastic parametrization framework, in which we infer nonlinear autoregression moving average (NARMA) type models to take the memory effects into account. We show by examples that the NARMA type stochastic reduced models that can capture the key statistical and dynamical properties, and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the Kuramoto-Sivashinsky equation of spatiotemporally chaotic dynamics.

A free boundary problem with facets

When: Thu, October 19, 2017 - 3:30pm
Where: Kirwan Hall 3206
Speaker: Will Feldman (University of Chicago) -
Abstract: I will discuss a variational problem on the lattice analogous to the Alt-Caffarelli problem. The scaling limit is a free boundary problem for the Laplacian with a discontinuous constraint on the normal derivative at the boundary. The discontinuities cause the formation of facets in the free boundary. The problem is related to models for contact angle hysteresis of liquid drops studied by Caffarelli-Lee and Caffarelli-Mellet.