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Professor Widom's research focuses on theoretical modeling of novel materials such as quasicrystals,
metallic glass and ferrofluids. Methods of statistical mechanics including mean field
theory, transfer matrices, Monte Carlo simulation and exact solution are employed to
investigate thermodynamic properties.
Quasicrystals
are metal alloys which solidify into structures with the crystallographically forbidden
symmetry of an icosahedron. No spatially periodic lattice may have this symmetry. Rather,
the arrangement of atoms in space is quasiperiodic. Widom's studies of these materials
include geometrical models which tile space with appropriate symmetry and realistic atomic
level modeling of specific alloys. The tilings of space with given symmetry are enumerated
using transfer matrices and exact solution via Bethe Ansatz. Thermodynamics of atomic
models are investigated using Monte Carlo simulation and electronic-structure based total
energy calculations.
Metallic glass forms when a liquid metal alloy cools so quickly that it
solidifies before it crystallizes, freezing into a liquid-like structure.
These materials have unusual and potentially useful physical properties,
especially when they form in bulk solids. Widom employs first-principles
calculations to predict the structure and stability of metallic alloys. As
part of this work he has developed a
database of cohesive energies for crystalline alloys.
Ferrofluids are
colloidal suspensions of 100 Angstrom scale magnetic grains. As a superparamagnet, this
fluid has extraordinary response to applied fields, leading to many useful commercial
applications. The disordered fluid state may contain long chains of grains connected by
their magnetic attraction. At high magnetic strength and volume fraction the fluid may
phase separate or even become spontaneously aligned. Using mean field theory and Monte
Carlo simulation Widom investigates magnetic susceptibility and phase transitions of this
complex fluid. Recent studies examine polarization textures and droplet shapes of
spontaneously magnetized liquids.
Other research interests include hydrodynamic
pattern formation, gel
electrophoresis and reptation of DNA, and the structure of metallic glass.
Selected Publications
(Full listing at
http://euler.phys.cmu.edu/widom/pubs/pubs.html)
Widom, M., "Renormalization
Group Analysis of Quasiperiodicity in Analytic Maps," Comm. Math. Phys.
92, 121 (1983).
Widom, M., D. Bensimon, L.
P. Kadanoff, and S. J. Shenker, "Strange Objects in the Complex Plane," J.
Stat. Phys. 32, 443 (1983).
Widom, M., and L. P.
Kadanoff, "Renormalization Group Analysis of Bifurcations in Area-Preserving
Maps," Physica D 5, 287 (1982)
Mazenko, G. F., and M. Widom,
"Structure Pulses in a Simple Nonequilibrium System," Phys. Rev. B 25,
1860 (1982)
Grest, G. S., and M. Widom,
"N-Color Ashkin-Teller Model," Phys. Rev. B 24, 6508 (1981)
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