Universality, and Computational Algorithms

Nigel Goldenfeld
University of Illinois, Urbana-Champaign

Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will explain that physical predictions, whether analytical or computational, are predicated on the following assumptions: (1) there exists a minimal model that is a caricature of the phenomenon in question; (2) there exists a renormalization group fixed point about which universal quantities can be calculated systematically; and (3) the desired predictions concern quantities that are universal at the appropriate fixed point.  I will give examples where this works and where it fails, and show that in some cases, complex space-time phenomena can be exquisitely captured with simple computational algorithms that not only produce patterns resembling those seen in experiments, but also make accurate predictions about probes of dynamics and spatial organization, such as correlation functions.

Created by Mathematica  (April 20, 2004)