Biomedical subjects

Stephen Whitelam

Publications and source records attributed to Stephen Whitelam.

4 recordsLinked to original sources

PubMed2006

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid.

We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically and verify this prediction numerically. In addition, we predict that the characteristic relaxation time of the model is a nonmonotonic function of attraction strength, again in agreement with numerical results.

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PubMed2005

Renormalization group study of a kinetically constrained model for strong glasses.

We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson-Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d>/=2 , the behavior of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behavior is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.

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PubMed2004

Facilitated spin models in one dimension: a real-space renormalization group study.

We use a real-space renormalization group (RSRG) to study the low-temperature dynamics of kinetically constrained Ising chains (KCICs). We consider the cases of the Fredrickson-Andersen (FA) model, the East model, and the partially asymmetric KCIC. We show that the RSRG allows one to obtain in a unified manner the dynamical properties of these models near their zero-temperature critical points. These properties include the dynamic exponent, the growth of dynamical length scales, and the behavior of the excitation density near criticality. For the partially asymmetric chain, the RG predicts a crossover, on sufficiently large length and time scales, from East-like to FA-like behavior. Our results agree with the known results for KCICs obtained by other methods.

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PubMed2004

Dynamic criticality in glass-forming liquids.

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero-temperature dynamical critical point. To support our proposal, we derive a dynamic field theory for a generic kinetically constrained model, which we expect to describe the dynamics of a supercooled liquid. We study this field theory using the renormalization group (RG). Its long time behavior is dominated by a zero-temperature critical point, which for d>2 belongs to the directed percolation universality class. Molecular dynamics simulations seem to confirm the existence of dynamic scaling behavior consistent with the RG predictions.

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