Faculty
Research Profile |
 Nigel
Goldenfeld
Professor
of Physics
University of
Illinois at Urbana-Champaign
3113 ESB
1110 W. Green
Street, Urbana, IL 61801
217-333-8027
nigel@uiuc.edu
Homepage
Research
Summary
Professor
Goldenfeld has made significant contributions to three distinct areas
of condensed matter physics: the theory of pattern formation (for
example, how do snowflakes grow?); high-temperature superconductivity;
and statistical mechanics. He played a leadership role in the identification
of the pairing state of the high temperature superconductors. He is
perhaps most well-known for his work in pattern formation by nonlinear
systems far from equilibium, especially the application of renormalization
group methods for partial differential equations describing nonequilibrium
processes, turbulence in superfluid helium, phase ordering in superconductors
and liquid crystals, and the dynamics of crystal surfaces.
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Current
Projects
- Equilibrium
and Nonequilibrium Phenomena in Condensed Matter
We are modeling phase transition kinetics, developing large deviation
and fluctuations theories for nonequilibrium systems, and studying
dynamic scaling in high-temperature superconductors. Other ongoing
projects include numerical renormalization group methods for PDEs,
critical scaling in black hole formation and turbulence.
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Adaptive Grid Methods for Phase Field Models of Microstructure
Development
We are developing adaptive grid methods for solving asymptotically
efficient phase field models of microstructure development. Present
applications include free dendritic growth, directional solidification,
and eutectic growth.
- Prediction
of Macroscopic Properties of Liquid Helium from Computer Simulation
We are studying phase separation kinetics in helium-3/helium-4
mixtures by using path integral Monte Carlo methods and cell dynamic
models. Our goal is to predict quantitatively the morphology generated
during phase ordering from quantum mechanics alone, with as little
experimental input as possible.
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