Lattice Knots in a Slab

In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case, where an improvement is found. From our data we construct two models of grafted knotted ring polymers squeezed between hard walls, or by an external force. In each model, we determine the entropic forces arising when the lattice polygon is squeezed by externally applied forces. The profile of forces and compressibility of several knot types are presented and compared, and in addition, the total work done on the lattice knots when it is squeezed to a minimal state is determined

Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

Reproductive cycle, nutrition and growth of captive blue spotted stingray, Dasyatis kuhlii (Dasyatidae)

At Burgers' Ocean 7 male and 3 female blue spotted stingrays, Dasyatis kuhlii were born over a period of 4.5 years. This paper describes the experiences of the captive breeding results of this species. The first two young died within 2 days of birth. One of them had an internal yolk sac, which may feed the young in the first few days. The other eight animals started to feed after 4 to 9 days on a variety of food types. Birth size of the young increased with increasing age of the parents. Mating occurred directly after parturition, so no seasonality could be defined. Gestation length ranged between 138 and 169 days, with a mean of 144.9±9.0 days (N = 11). Litter size was one, possibly caused by only one active ovarium. Sexual maturity of the two parent animals is approximately 3.5 years. The average feeding rations for the adults ranged between 10.1% BW week-1 (131 kcal kg BW-1 week-1) and 11.3% BW week-1 (172 kcal kg BW-1 week-1), with a feeding frequency of 4 times per week. The relationship between body weight (BW) and wingspan (WS) is given as BW = 3.6 × 10-5* WS2.940 (R2 = 0.9645; N = 45) (Received December 10 2007) (Accepted April 17 2009) (Online publication August 06 2009

The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

A simple model of a vesicle drop in a confined geometry

We present the exact solution of a two-dimensional directed walk model of a drop, or half vesicle, confined between two walls, and attached to one wall. This model is also a generalisation of a polymer model of steric stabilisation recently investigated. We explore the competition between a sticky potential on the two walls and the effect of a pressure-like term in the system. We show that a negative pressure ensures the drop/polymer is unaffected by confinement when the walls are a macroscopic distance apart

On trivial words in finitely presented groups

We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of such groups by finding the cogrowth series for Baumslag-Solitar groups $\mathrm{BS}(N,N) =$ and prove that their cogrowth rates are algebraic numbers.Comment: This article has been rewritten as two separate papers, with improved exposition. The new papers are arXiv:1309.4184 and arXiv:1312.572