The dynamics of random interfaces in phase transitions

A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ _N models.Work supported by NSF grant No. DMR-8013700.     

Structural phase transitions of the Si(100) surface

A Monte Carlo study of the structural phase transitions on the Si(100) surface for both the “(2×1)” and “c(2×2)” reconstruction families is carried out using the asymmetric dimer model. A second order phase transition is observed at about 250 K from a p(2×2) (layered antiferromagnetic) to a disordered (paramagnetic) state in the “2×1” family. A similar transition is observed about 800 K from a c(2×2) (ferromagnetic) to a disordered state in the “c(2×2)” family. These results are in agreement with real-space renormalization group results. The variation of the specific heat, susceptability and the absolute value of the order parameter as a function of temperature is obtained in the range 200 to 300 K for the “2×1” family and 750 to 850 K for the “c(2×2)” family. Also, the order parameter correlation function is computed for ten different temperatures in the above ranges.     

Phase diagram for a model of urate oxidase

Urate oxidase from Asperigillus flavus has been shown to be a model protein for studying the effects of polyethylene glycol (PEG) on the crystallization of large proteins. Extensive experimental studies based on small angle x-ray scattering [Vivares and Bonnete, J. Phys. Chem. B 108, 6498 (2004)] have determined the effects of salt, pH, temperature, and most importantly PEG on the crystallization of this protein. Recently, some aspects of the phase diagram have also been determined experimentally. In this paper, we use Monte Carlo techniques to predict the phase diagram for urate oxidase in solution with PEG, including the liquid-liquid and liquid-solid coexistence curves. The model used includes an electrostatic interaction, van der Waals attraction, and a polymer-induced depletion interaction [Vivares et al., Eur. Phys. J. E 9, 15 (2002)]. Results from the simulation are compared with experimental results.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Homogeneous Nucleation

Significant progress has been made in recent years in measuring homogeneous nucleation rates in a variety of liquid–vapor and liquid–solid transitions. These studies have revealed serious shortcomings of classical nucleation theory. New theoretical work and simulation studies of simplified model systems have provided a better understanding of homogeneous nucleation, but many challenges remain. This article summarizes some recent developments, with an emphasis on the field-theoretic approach pioneered by Cahn and Hilliard in their study of nucleation in a two-component incompressible fluid in 1959.