Reaching large lengths and long times in polymer dynamics simulations

A lattice model is presented for the simulation of dynamics in polymeric systems. Each polymer is represented as a chain of monomers, residing on a sequence of nearest-neighbor sites of a face-centered-cubic lattice. The polymers are self- and mutually avoiding walks: no lattice site is visited by more than one polymer, nor revisited by the same polymer after leaving it. The dynamics occurs through single-monomer displacements over one lattice spacing. To demonstrate the high computational efficiency of the model, we simulate a dense binary polymer mixture with repelling nearest-neighbor interactions between the two types of polymers, and observe the phase separation over a long period of time. The simulations consist of a total of 46,080 polymers, 100 monomers each, on a lattice with 13,824,000 sites, and an interaction strength of 0.1 kT. In the final two decades of time, the domain-growth is found to be d(t) ~ t^1/3, as expected for a so-called "Model B" system.Comment: 6 pages, 4 eps figure

Electrophoresis simulated with the cage model for reptation

The cage model for polymer reptation is extended to simulate DC electrophoresis. The drift velocity v of a polymer with length L in an electric field with strength E shows three different regions: if the strength of field is small, the drift velocity scales as E/L; for slightly larger strengths, it scales as E^2, independent of length; for high fields, but still E much smaller than 1, the drift velocity decreases exponentially to zero. The behaviour of the first two regions are in agreement with earlier reports on simulations of the Duke-Rubinstein model and with experimental work on DNA polymers in agarose gel.Comment: 14 pages, 9 pictures, 2 table

DNA electrophoresis studied with the cage model

The cage model for polymer reptation, proposed by Evans and Edwards, and its recent extension to model DNA electrophoresis, are studied by numerically exact computation of the drift velocities for polymers with a length L of up to 15 monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by a regime where the velocity decreases exponentially with the applied electric field strength. In agreement with de Gennes' reptation arguments, we find that asymptotically for large polymers the diffusion coefficient D decreases quadratically with polymer length; for the cage model, the proportionality coefficient is DL^2=0.175(2). Additionally we find that the leading correction term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of kink representation approac

Multiple timescales in a model for DNA denaturation dynamics

The denaturation dynamics of a long double-stranded DNA is studied by means of a model of the Poland-Scheraga type. We note that the linking of the two strands is a locally conserved quantity, hence we introduce local updates that respect this symmetry. Linking dissipation via untwist is allowed only at the two ends of the double strand. The result is a slow denaturation characterized by two time scales that depend on the chain length $L$. In a regime up to a first characteristic time $\tau_1\sim L^{2.15}$ the chain embodies an increasing number of small bubbles. Then, in a second regime, bubbles coalesce and form entropic barriers that effectively trap residual double-stranded segments within the chain, slowing down the relaxation to fully molten configurations, which takes place at $\tau_2\sim L^3$. This scenario is different from the picture in which the helical constraints are neglected.Comment: 9 pages, 5 figure

Simulation of Polymer Dynamics in Gels and Melts

I have worked on computer simulations of lattice polymer models. Those models describe a polymer as a long chain of segments, connecting neighboring lattice sites. Polymers show interesting behavior if their freedom of movement is restricted, for example if the polymers move through a gel. The gel forms a three-dimensional structure that blocks sideways movements of the polymers. The polymer can only move by diffusion of "stored length" from one end of the chain to the other end. This is called reptation. We have extended an existing model for a polymer in a gel to simulate a DNA fragment in a gel under the influence of an applied electric field. In weak fields, long fragments move slower than short ones. In this way, fragments of different length can be separated. If the field strength is increased, the fragments orientate themselves parallel to the field, and shorter and longer fragments move with the same velocity. In strong fields, fragments can get trapped in a U-shape, in which the applied field pulls on both ends of the fragment, while the middle cannot move in the direction of the field because of the gel. We also introduce a new lattice polymer model for polymer solutions (melts). In this model, we simulate many polymers, mutually restricting their freedom of motion. We have investigated a mixture of two mutually repelling polymer types. At high temperatures the polymers are homogeneously distributed but if the temperature is lowered, phase separation sets in. The polymer model turns out to be highly efficient, and is the first where the growth of the phase domains can be directly observed. We have also investigated the composition of the two phases after full phase separation. Each phase consists mostly of one type of polymer, but there is always a small contamination with the other polymer type. If the polymers of one type are not all of equal length, then the shorter polymers will occur more often in the rare phase than the long ones. This is called fractionation

Stochastic lattice models for the dynamics of linear polymers

Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal properties as function of polymer length. More than the static properties, the dynamics depends on the rules of motion. Small changes in the hopping probabilities can result in different universal behavior. In particular the cross-over between Rouse dynamics and reptation is controlled by the types and strength of the hoppings that are allowed. The properties are analyzed using a calculational scheme based on an analogy with one-dimensional spin systems. It leads to accurate data for intermediately long polymers. These are extrapolated to arbitrarily long polymers, by means of finite-size-scaling analysis. Exponents and cross-over functions for the renewal time and the diffusion coefficient are discussed for various types of motion.Comment: 60 pages, 19 figure

Predictive variables in lifelong bilingualism: An exploratory study probing the effects of L2 English on L1 Afrikaans syntax

General Linguistic

Intercultural communicative competence is essential for students of international business - but can it be taught? The case of third-year BCom students

Intercultural communicative competence is essential for graduates wishing to work in the business sector. Such competence has become desirable for graduates who see themselves working in “demanding and highly-challenging international environments” (Sain, Kužnin and Roje 2017, 55‒56). In spite of the need for well-developed intercultural competence in the workplace, students of Economic and Business Science are rarely deliberately equipped with an understanding of what language, culture and communication entail. Against this background, we investigated if an intervention, in the form of a 28-lecture undergraduate course, can develop third-year BCom students’ intercultural competence so as to prepare them to deal with the heterogeneity that they will encounter in the workplace (and elsewhere), both in multilingual and multi-cultural South Africa and abroad.Based on eight of the skills and attributes identified by Deardorff (2004) as being markers of interculturally competent individuals (such as knowledge of self and others, respect, critical thinking skills, and an awareness of the importance of being interculturally competent), students (n=18) were assessed prior to the commencement of the course and again upon completion thereof. Pre- and post-course questionnaires were analysed qualitatively and quantitatively, and data were coded according to the eight Deardorff (2004) markers of intercultural competence. Additionally, a focus group discussion (n = 5) was held at the end of the course. The data showed that development took place in the students’ attitudes, knowledge and skills related to intercultural communicative competence. Certain markers of intercultural communicative competence, however, showed more substantial development than others, the notable marker showing such development being critical thinking skills.The finding is that skills indicative of intercultural competence can indeed be developed by means of a curriculum in such a way that students think more critically about (i) cultural and linguistic diversity and (ii) their responsibility as future leaders to communicate optimally in diverse cultural settings. Deliberately including courses on intercultural communication in programmes for students (not only students in Humanities and Social Sciences) could contribute to personal and professional development of students and lead to graduates who are better prepared for a career in multicultural national and international business sectors. Likewise, the introduction of in-service training in intercultural communicative competence can be considered for those who are no longer students, thereby contributing to improved intercultural communication in the workplace