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

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

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

Fresh look at randomly branched polymers

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.Comment: 4 page

Management of anterior vaginal prolapse in South Africa : national survey

LetterThe original publication is available at http://www.samj.org.zaTo the Editor: A national survey was done on the management of anterior vaginal prolapse (AVP) by registered gynaecologists and urologists in South Africa. Of 822 questionnaires posted, 30.2% were returned completed (23.2% from gynaecologists and 7.0% from urologists). The information supplied was anonymous and is probably a true reflection of current practice. Of concern were the 36.3% of respondents who did not use a recognised staging system, a low rate of pre-operative urodynamic investigation by gynaecologists (8.4%) and a high rate of synthetic mesh use by urologists (75.9%), even for primary procedures. This first survey among South African prolapse surgeons provides valuable insight into clinical practice.Publishers’ versio

The distribution and spread of the invasive alien common myna, Acridotheres tristis L. (Aves: Sturnidae), in southern Africa

The common myna is an Asian starling that has become established in many parts of the world outside of its native range due to accidental or deliberate introductions by humans. The South African population of this species originated from captive birds that escaped in Durban in 1902. A century later, the common myna has become abundant throughout much of South Africa and is considered to pose a serious threat to indigenous biodiversity. Preliminary observations suggest that the common myna's distribution is closely tied to that of humans, but empirical evidence for this hypothesis is lacking. We have investigated the relationships between common myna distribution, human population size and land-transformation values at a quarter-degree resolution in South Africa. Common mynas were found more frequently than expected by chance in areas with greater human population numbers and land-transformation values. We also investigated the spatial relationship between the bird's range and the locations of South Africa's protected areas at the quarter-degree scale. These results indicate that, although there is some overlap, the common myna distribution is not closely tied to the spatial arrangement of protected areas. We discuss the original introduction, establishment and rate of spread of the common myna in South Africa and neighbouring countries and contrast the current distribution with that presented in The Atlas of Southern African Birds. We also discuss the factors that affect the common myna's success and the consequences that invasion by this species is likely to have, specifically in protected areas

Running dry : assessing the fuel levy as a long term, economically efficient road use fund

The fuel levy, a domestic transport cost component added to the basic fuel price, has long been South Africa?s main source of income to fund the construction and maintenance of roads as well as lend support to public transport (National Treasury, 2014b). During the 2012 / 2013 financial year the fuel levy contributed R40.4 billion to the National Revenue Fund administered by National Treasury (The Citizen, 2013). Of this amount, R17.6 billion (44.0%) and R19.9 billion (49.0%) were allocated to the road and public transport sectors respectively. Recent comments regarding the Gauteng Freeway Improvement Project (e-toll) has raised questions and strong opinions about the continuing use of the fuel levy as the main or only source of income from road users to fund land transport operations and infrastructure in South Africa. The aim of this paper is to assess if a review of the fuel levy is needed, and to be supplemented or replaced by a viable alternative, in order to secure a long term sustainable income source for the country?s aging transport road infrastructure. This paper will provide a historic overview of the South African fuel levy, from its origins in the 1920?s to the present day and will review the current demands on the fund. This will be followed by a comparison between the fuel levy in South Africa and other countries, including selected BRICS nations and selected European countries. Various societal trends will then be considered including alternative fuels, electrical and more fuel efficient vehicles and the impact of these trends on the fuel levy will be assessed. It was found through this assessment that alternative fuels, electrical and more fuel efficient vehicles have had an impact on the fuel levy whereby the registered vehicle population in South Africa grew with 47.2 % between the periods 2003 to 2012. For the same periods the vehicle kilometres driven by the registered vehicle population grew with 38.5 % while the fuel sales only grew by 21.9 %. This had a result where the fuel levy is losing productivity by experiencing declining revenues. The paper concludes that a review of the current fuel levy is needed, as increasing the fuel levy each year will only be a temporary solution. An alternative financing mechanism must be implemented that is not affected by societal trends.Paper presented at the 34th Annual Southern African Transport Conference 6-9 July 2015 "Working Together to Deliver - Sakha Sonke", CSIR International Convention Centre, Pretoria, South Africa.The Minister of Transport, South AfricaTransportation Research Board of the US

A kilometre-based road user charge system : proof of concept study

The South African fuel levy is used to fund government?s general expenditure programmes, including the construction and maintenance of roads and support of public transport. Yet, the continuing reliance of the fuel levy to generate sufficient income is questioned due to a decrease in the average amount of fuel sold per vehicle per annum. The need exists to identify, explore and test a viable and operationally feasible alternative that is not dependant on fuel sales when generating income. The paper undertook a qualitative analysis of transportation financing sources to identify and then explore a viable alternative to the fuel levy. Furthermore, the operational feasibility of the alternative was tested and evaluated through a proof of concept vehicle tracking experiment. A kilometre-based road user charge (KBRUC) system was identified as a viable alternative which addresses many of the problems associated with the fuel levy. The system could entail an on-board global positioning system (GPS) enabled device to be fitted to a road user?s vehicles where vehicle movement data can be collected in order to generate a road use invoice at a set charge per kilometre travelled. The vehicle tracking experiment showed that a suggested configuration of the system is operationally feasible, in small scale, in South African. The paper concludes that further research is needed to assess the operational and technical feasibility of the system on a larger scale as well as policy, social and equity concerns.Paper presented at the 35th Annual Southern African Transport Conference 4-7 July 2016 "Transport ? a catalyst for socio-economic growth and development opportunities to improve quality of life", CSIR International Convention Centre, Pretoria, South Africa.The Minister of Transport, South AfricaTransportation Research Board of the US