Upcoming Events

Patterns, Universality and Computational Algorithms

October 11, 2012 11:00AM to 12:00PM
Presenter 
Nigel Goldenfeld, University of Illinois at Urbana-Champaign
Location 
Building 212, Room A157
Type 
Colloquium
Series 
Materials Science Colloquium
Abstract:
Can we use computational algorithms to make accurate predictions of physical phenomena?  In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captured with simple computational algorithms, that not only produce patterns resembling those seen in experiment, but also make accurate predictions about probes of dynamics and spatial organization, such as correlation functions.  I use examples from condensed matter physics, as well as from geophysics.

Because many patterns involve structure on multiple length and time scales, I also discuss how one can develop multiscale methods for real materials processing from the nanoscale on up.  I show that a computationally-efficient multiscale approach can be developed systematically by using renormalization group or equivalent techniques to derive appropriate coupled phase and amplitude equations, which can then be solved by adaptive mesh refinement algorithms.

Work supported by National Science Foundation and NASA.