Nicholas Guttenberg's Website

Nicholas Guttenberg

Office: 3115 ESB
Department of Physics
University of Illinois at Urbana-Champaign
1110 W. Green St.
Urbana, IL 61801-3080
USA

Contact: ngutten2 AT uiuc.edu

Current Research

Research Interests

Research problems I'm interested in fall into the broad categories of complex systems and pattern formation. The work I do on these problems is theoretical analysis combined with simulation. As such, I am also interested in numerical methods related to solving PDEs on irregular geometries (for instance, conformal mapping)

As a general approach to my research, I try to look for properties that are universal across different physical systems that stem from some simple underlying mechanism that happens to be present in each of those cases. Often a system which is complicated (that is, it has many different physical processes and quantities associated with it) can be pared down to a minimal model which still captures the qualitatively distinct features of that system. For example, the Type-I superconductor simulations which I have done produce a pattern of coarsening regions containing the magnetic field which passes through the superconductor. For small enough fields, the relevant quality are that there is the motion of some conserved quantity which has a positive surface tension. There are simpler ways of simulating systems with that quality than those that were used for the superconductor simulation, though they would fail to capture what happens when the field becomes very small (isolated vortices) or very large (bubbles with intact walls forming).

I also have an interest in data visualization. Most of my simulations end up producing a pretty picture to go with the quantitative data. Sometimes artifacts are very visible when looking at an overview of the simulation state that would be hard to pin down given traces of the interesting measurables.

My research is funded by the University of Illinois Distinguished Fellowship. The work on turbulence has been supported by an NCSA developmental grant of computing time and the work on evolutionary biology has been supported by the computing resources of the Institute for Genomic Biology.