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

Manufacturing challenges for custom made solar vehicles in South Africa

Solar challenges are designed to test the reliability and efficiency of solar powered vehicles in endurance races. In the past these manufactured vehicles were technology drivers and led to advances in electric motors and solar cell efficiency. The speed in relation to power consumption is one of the main design considerations, with the only energy source being solar power. In the design and manufacturing of these vehicles a number of requirements need to be met in order to pass the safety standards. The Sasol Solar Challenge (SSC) created an opportunity for South African universities to design and manufacture custom made solar powered vehicles. This paper explores and discusses the challenges for manufacturing solar vehicles in South Africa. Key elements like the communication gap between design and manufacturing, the cost of lightweight solar encapsulation, the shortage of local suppliers and expertise in composite manufacturing are evaluated. These insights can be used as foundation for strategic decisions by future stakeholders

Paediatric cardiac anaesthesia in sickle cell disease : a case series

Sickle cell disease (SCD) is the most common inherited haematological disorder, producing a mutation of the haemoglobin molecule known as haemoglobin S (HbS). The presence of HbS in the erythrocyte makes it prone to sickling - a process which may lead to vaso-occlusive injury, haemolysis and a hypercoagulable state. Sickling is precipitated by dehydration, hypoxia, hypothermia, acidosis and low flow states. Over time, multi-organ damage develops with significant morbidity and mortality. Paediatric patients with SCD and congenital heart defects may require anaesthesia for corrective cardiac surgery on cardiopulmonary bypass (CPB). During the perioperative period these high-risk patients may suffer significant complications when exposed to the conditions that favour erythrocyte sickling. This case series details our experience of four paediatric patients with SCD patients who underwent corrective cardiac surgery at Red Cross War Memorial Children’s Hospital. The pathophysiology is discussed and the perioperative management of transfusion, cardiopulmonary bypass and temperature regulation is highlighted

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

Evidence-based prescription for cyclo-oxygenase-2 inhibitors in sports injuries

Healthcare professionals are increasingly under pressure to return athletes to play in the shortest possible time. There is limited choice in providing treatment that speeds up tissue repair, while simultaneously maintaining good quality of healing. Inflammation forms a fundamental part in the process of tissue repair. However, excessive inflammation may cause more pain, and limit functional restoration. Although the use of anti-inflammatory treatment in the form of a cyclo-oxygenase-2 inhibitor (coxibs) has been widely recognised as being effective, the potential detrimental effect on tissue repair, as described mainly in animal model studies, needs to be taken into account. The side-effects profile on the gastrointestinal tract favour coxibs over non-traditional NSAIDs. The possible effects on the renal and cardiovascular systems also need to be considered. The prescription of coxibs should be pathology and situation specific. There are no clear guidelines on the correct time of administration and the duration of the course, but it seems that the literature is in agreement that they should be administered for a limited time at the lowest effective dose possible.Keywords: cyclo-oxygenase-2 inhibitors (coxibs), sports injuries, treatmen

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Forcing Adsorption of a Tethered Polymer by Pulling

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled

Incidence of heat-labile enterotoxin-producing Escherichia coli detected by means of polymerase chain reaction amplification

CITATION: Winterbach, R. et al. 1994. Incidence of heat-labile enterotoxin-producing Escherichia coli detected by means of polymerase chain reaction amplification. South African Medical Journal, 84:85-87.The original publication is available at http://www.samj.org.zaDiarrhoea can be caused by many different organisms, some of which are notoriously difficult to identify. One of these is enterotoxin-producing Escherichia coli. Recently a new diagnostic technique that uses polymerase chain reaction DNA amplification was developed for detection of the 'A' subunit of the labile enterotoxin-producing E. coli gene. This technique was used to evaluate the incidence of heat-labile (LT+) enterotoxin-producing E. coli in the causation of diarrhoea. The results from this study showed that LT+ E. coli is a cause of diarrhoea in the western Cape and that 5,3% of non-diagnosed diarrhoea patients in Tygerberg Hospital were infected with this pathogen. This represented less than 1% of the total number of cases of diarrhoea investigated in this hospital. The peak coincides with the wetter months in this locality and the infection rate is lower than that reported in most other countries. Given the low incidence of occurrence of this organism we do not recommend routine implementation of the diagnostic procedure. However, this test may be useful at times, e.g. to ascertain the source of a diarrhoea epidemic.Publisher’s versio

Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl