Daniel L. SteinDaniel L. Stein

Professor of Physics and Mathematics
Ph.D., Princeton University, 1979

My Research

D.L. Stein: Research on Noisy Nonequilibrium Dynamics (for Non-Physicists)

In many physical processes, small random fluctuations can become magnified into very large events. This is what underlies such common phenomena as chemical reactions, phase transitions (for example, when a small bubble, or droplet, of one phase expands explosively within another phase - this is what causes boiling but also many other phenomena), biological speciation, computer network state switching, the formation of spatially localized states (convective cells, turbulent vortices, stripes, spots, zigzags, ...), and many others. In all of these, "noise", i.e., small random fluctuations, eventually drives a physical (or computational, or biological, or ...) system over a barrier, and moves it from one stable state to another.

The vast bulk of research on noise-induced transitions has been on physical systems in thermal equilibrium, where the mathematical techniques are plentiful and the physical understanding is well-developed. However, far less understood is how such transitions occur when a system is very far from thermal, chemical, or other, equilibrium - as many systems are much of the time. My research aims at providing a mathematical and physical foundation for understanding and analyzing these processes.

For some more information on some aspects of this research at a nontechnical level, see Ref. 4 in Nontechnical Publications. My research on these topics is partially supported by the National Science Foundation under Grants No. PHY-06-01179 and PHY-06-51077.

Courtesy of
	 Northwestern University Applied Mathematics Department; www.esam.northwestern.edu.

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