Damien P. Foster

Asymmetric exclusion model with two species: Spontaneous symmetry breaking

A simple two-species asymmetric exclusion model is introduced. It consists of two types of oppositely charged particles driven by an electric field and hopping on an open chain. The phase diagram of the model is calculated in the meanfield approximation and by Monte Carlo simulations. Exact solutions are given for special values of the parameters defining its dynamics. The model is found to exhibit two phases in which spontaneous symmetry breaking takes place, where the two currents of the two species are not equal.

Two-dimensional self-avoiding walk with hydrogen-like bonding: phase diagram and critical behaviour

The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model displays a collapse transition. In contrast to the standard θ-point model, the transition is first order. The phase diagram in the full fugacity–temperature plane displays an additional transition line, when compared to the θ-point model, as well as a critical transition at finite temperature in the Hamiltonian walk limit.

A corner transfer matrix renormalization group investigation of the vertex-interacting self-avoiding walk model

Ar ecently introduced extension of the corner transfer matrix renormalization group method useful for the study of self-avoiding walk-type models is presented in detail and applied to a class of interacting self-avoiding walks due to Bl¨ ote and Nienhuis. This model displays two different types of collapse transition depending on model parameters. One is the standard θ -point transition. The other is found to give rise to a first-order collapse transition despite being known to be in other respects critical.

Finite-size effects for phase segregation in a two-dimensional asymmetric exclusion model with two species

We investigate the stationary states of a two-dimensional lattice gas model with exclusion, in the presence of an external field. The lattice is populated by equal numbers of positively and negatively charged particles. An analytical mean-field approach and Monte Carlo simulations give strong evidence of the fact that at any finite density the only relevant stationary state of the system in the thermodynamic limit is inhomogeneous, consisting of a strip of particles transverse to the field. In the inhomogeneous phase, the density profiles and the current measured by Monte Carlo simulations are closely related to those found in mean field. The same is true for the finite-size behavior of the system.

Exact evaluation of the collapse phase boundary for two-dimensional directed polymers

The phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer-monomer interactions is calculated exactly using transfer-matrix techniques. The position of the multicritical point is also identified.

Universality of collapsing two-dimensional self-avoiding trails

Results of a numerically exact transfer matrix calculation for the model of Interacting Self-Avoiding Trails are presented. The results lead to the conclusion that, at the collapse transition, Self-Avoiding Trails are in the same universality class as the O(n=0) model of Blote and Nienhuis (or vertex-interacting self-avoiding walk), which has thermal exponent

Competition between self-attraction and adsorption in directed self-avoiding polymers

\nu=12/23

Translocation of short and long polymers through an interacting pore

, contrary to previous conjectures.

Statistical mechanics of the two-dimensional hydrogen-bonding self-avoiding walk including solvent effects.

The phase diagrams are presented for a model of a self-interacting, directed polymer in the presence of an attractive wall or interface. The scaling of the monomer density with lattice size is also discussed.

Corner-transfer-matrix renormalization-group method for two-dimensional self-avoiding walks and other O(n) models

We perform two-dimensional Langevin dynamics simulations of electric-field driven polymer translocation through an attractive nanopore. We investigate the effect of the location of the attractive region using different pore patterns. This is found to have an impact on both the translocation time as a function of the chain length and on the polymer entry frequency. We qualitatively compare our results to available experimental data.