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

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

In this paper the elementary moves of the BFACF-algorithm for lattice polygons are generalised to elementary moves of BFACF-style algorithms for lattice polygons in the body-centred (BCC) and face-centred (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice. Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices

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

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

'n Empiriese ondersoek na preekvoorstelle oor Ou-Testamentiese tekste in die Leesrooster van 2005

After examining the basic principles for preaching from the Old Testament in a previous article, this article endeavours to investigate a sample of the current state of preaching from the Old Testament. A phenomenological assessment of sermons from the Lectionary of BUVTON (2005) serves as study example. The aim of the research is to determine whether sermons from the Old Testament deals responsibly with the many pitfalls explained in the first article and so often found in preaching from the Old Testament. (article text in Afrikaans

Speel die Bybel nog ’n rol in die praktiese teologie?

Dat dié vraag hoegenaamd gevra word, behoort vreemd aan te doen. Kan dit wees dat ’n belangrike teologiese vakgebied wat oor die dienswerk van die kerk in al sy fasette handel, nie aan die Bybel ’n betekenisvolle plek toeken nie? Daar is ’n hele aantal veranderlikes wat die beantwoording van hierdie vraag beïnvloed. Daarom is dit die moeite werd om die vraag nader te ondersoek ten einde ’n deeglike antwoord te kan verskaf

Prediking Uit Die Ou Testament

Preaching from the Old Testament has many pitfalls. Besides the danger of moralism, allegory and typology, there is the problem of preaching Christ from the Old Testament. Forcing Christ into Old Testament texts has Old Testament scholars up in arms, to the extent that some believe that Christ is not found in the Old Testament and that there are no Messianic texts. Between reading Christ into the Old Testament and not preaching Christ from the Old Testament, the preacher must find a responsible way of dealing with the many challenges. The article endeavours to provide some guidelines and principles for preaching from the Old Testament to a Christian congregation.Acta Theologica Vol. 2 2007: pp. 105-12

Shouldering the blame for impingement: the rotator cuff continuum

The aim of this article was to summarise recent research on shoulder impingement and rotator cuff pathology. A continuum model of rotator cuff pathology is described, and the challenges of accurate clinical diagnosis, imaging and best management discussed.Keywords: shoulder impingement syndrome, subacromial impingement syndrome, rotator cuff, tendinopathy, rehabilitatio

Adsorbed self-avoiding walks subject to a force

We consider a self-avoiding walk model of polymer adsorption where the adsorbed polymer can be desorbed by the application of a force. In this paper the force is applied normal to the surface at the last vertex of the walk. We prove that the appropriate limiting free energy exists where there is an applied force and a surface potential term, and prove that this free energy is convex in appropriate variables. We then derive an expression for the limiting free energy in terms of the free energy without a force and the free energy with no surface interaction. Finally we show that there is a phase boundary between the adsorbed phase and the desorbed phase in the presence of a force, prove some qualitative properties of this boundary and derive bounds on the location of the boundary