E J Janse van Rensburg
York University
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Featured researches published by E J Janse van Rensburg.
Journal of Statistical Physics | 1996
M C Tesi; E J Janse van Rensburg; Enzo Orlandini; S G Whittington
We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.
Journal of Physics A | 1993
E J Janse van Rensburg
The sixth, seventh and eighth virial coefficients of hard discs and hard spheres are evaluated numerically (Monte Carlo integration). I improve on the best previous estimates for the seventh virial coefficients, and the integration of the eighth virial coefficient is new. The best estimates for these coefficients for hard discs are B7 /b6 = 0.114 86(7) and B8/b7 = 0.065 14(8); and for hard spheres B7/b6 = 0.01307(7) and B8/b7 = 0.00432(10). b is the second virial coefficient in each case. Pade approximations to the excess pressure and the excess free energy are computed from these results and compared to data otherwise obtained.
Journal of Physics A | 1992
E J Janse van Rensburg; De Witt Sumners; E Wasserman; S G Whittington
Self-avoiding walks on three-dimensional lattices are flexible linear objects which can be self-entangled. The authors discuss several ways to measure entanglement complexity for n-step walks, and prove that these complexity measures tend to infinity with n. For small n, they use Monte Carlo methods to estimate and compare the n-dependence of two of these complexity measures.
Journal of Physics A | 1998
Enzo Orlandini; M C Tesi; E J Janse van Rensburg; S G Whittington
We use Monte Carlo methods to investigate the asymptotic behaviour of the number and mean-square radius of gyration of polygons in the simple cubic lattice with fixed knot type. Let be the number of n-edge polygons of a fixed knot type in the cubic lattice, and let be the mean square radius of gyration of all the polygons counted by . If we assume that , where is the growth constant of polygons of knot type , and is the entropic exponent of polygons of knot type , then our numerical data are consistent with the relation , where is the unknot and is the number of prime factors of the knot . If we assume that , then our data are consistent with both and being independent of . These results support the claims made in Janse van Rensburg and Whittington (1991a 24 3935) and Orlandini et al (1996 29 L299, 1998 Topology and Geometry in Polymer Science (IMA Volumes in Mathematics and its Applications) (Berlin: Springer)).
Journal of Physics A | 1991
E J Janse van Rensburg; S G Whittington
The BFACF algorithm applied to polygons involves sampling on a Markov chain whose state space is the set of all polygons. In three dimensions, for the simple cubic lattice. The authors prove that the ergodic classes of this Markov chain are the knot classes of the polygons.
Journal of Physics A | 2004
E J Janse van Rensburg; A. R. Rechnitzer
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 simulated by a multiple Markov chain Monte Carlo implementation of the pivot algorithm for self-avoiding walks. Vertices in the walk that are visits in the adsorbing line or plane are weighted by e β .T he critical value of β, where the walk adsorbs on the adsorbing line or adsorbing plane, is determined by considering energy ratios and approximations to the free energy. We determine that the critical values of β are βc = 0.565 ± 0.010 in the square lattice 0.288 ± 0.020 in the cubic lattice. In addition, the value of the crossover exponent is determined: φ = 0.501 ± 0.015 in the square lattice 0.5005 ± 0.0036 in the cubic lattice. Metric quantities, including the mean square radius of gyration, are also considered, as well as rescaling of the specific heat and free energy, as the critical point is approached.
Journal of Physics A | 1996
M C Tesi; E J Janse van Rensburg; Enzo Orlandini; S G Whittington
Self-interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the -point. We consider self-avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon. We prove that these walks and polygons have the same limiting free energy if the interactions between nearest-neighbour vertices are repulsive. The attractive interaction regime is investigated using Monte Carlo methods, and we find evidence that the limiting free energies are also equal here. In particular, this means that these models have the same -point, in the asymptotic limit. The dimensions and shapes of walks and polygons are also examined as a function of the interaction strength.
Journal of Knot Theory and Its Ramifications | 1995
E J Janse van Rensburg; S.D. Promislow
How many edges are necessary and sufficient to construct a knot of type K in the cubic lattice? Define the minimal edge number of a knot to be this number of edges. To what extend does the minimal edge number measure the complexity of a knot? What is the behaviour of the minimal edge number under the connected sum of knots, and what is its limiting behaviour? We consider these questions and show that the minimal edge number may be computed using simulated annealing.
Journal of Physics A | 2009
E J Janse van Rensburg
The numerical simulation of self-avoiding walks remains a significant component in the study of random objects in lattices. In this review, I give a comprehensive overview of the current state of Monte Carlo simulations of models of self-avoiding walks. The self-avoiding walk model is revisited, and the motivations for Monte Carlo simulations of this model are discussed. Efficient sampling of self-avoiding walks remains an elusive objective, but significant progress has been made over the last three decades. The model still poses challenging numerical questions however, and I review specific Monte Carlo methods for improved sampling including general Monte Carlo techniques such as Metropolis sampling, umbrella sampling and multiple Markov Chain sampling. In addition, specific static and dynamic algorithms for walks are presented, and I give an overview of recent innovations in this field, including algorithms such as flatPERM, flatGARM and flatGAS.
Journal of Physics A | 1994
Enzo Orlandini; M C Tesi; S G Whittington; D W Sumners; E J Janse van Rensburg
The writhe of a self-avoiding walk in a three-dimensional space is the average over all projections onto a plane of the sum of the signed crossings. We compute this number using a Monte Carlo simulation. Our results suggest that the average of the absolute value of the writhe of self-avoiding walks increases as nalpha , where n is the length of the walks and alpha approximately=0.5. The mean crossing number of walks is also computed and found to have a power-law dependence on the length of the walks. In addition, we consider the effects of solvent quality on the writhe and mean crossing number of walks.