We define a statistic an(w), the size of the atmosphere of a self-avoiding walk, w, of length n, with the property that 〈an(w)〉 → μ as n → ∞, where μ is the growth constant of lattice self-avoiding… (More)

Moloko C Cholo, Ronald Anderson, Medical Research Council Unit for Inflammation and Immunity, Department of Immunology, Faculty of Health Sciences, University of Pretoria and Tshwane Academic… (More)

We show that the classical Rosenbluth method for sampling self-avoiding walks [1, 2] can be extended to a general algorithm for sampling many families of objects, including self-avoiding polygons.… (More)

The maximum of the linking number between two lattice polygons of lengths n1, n2 (with n1 ≤ n2) is proven to be of the order of n1(n2) 1 3 . This result is generalized to smooth links of unit… (More)

A self-avoiding walk adsorbing on a line in the square lattice, and on a plane in the cubic lattice, is studied numerically as a model of an adsorbing polymer in dilute solution. The walk is… (More)

The coil-globule collapse of dilute linear polymers in a poor solvent is generally thought to be a second order phase transition through θ-polymers at the critical point [10]. A common model for the… (More)

Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects… (More)

A constructive proof is given that certain problems in the statistical mechanics of random copolymers are thermodynamically self-averaging. The proof relies on the use of normal numbers, and… (More)

We consider self-avoiding polygons on the simple cubic lattice with a torsion fugacity. We use Monte Carlo methods to generate large samples as a function of the torsion fugacity and the number of… (More)

Let pn denote the number of self-avoiding polygons of length n on a regular three-dimensional lattice, and let pn(K) be the number which have knot type K. The probability that a random polygon of… (More)