Topological Entanglement of Polymers and Chern-Simons Field Theory

In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static polymers or in a lattice of obstacles is considered. The extension to the case in which the configurations of two or more polymers become non-static is not straightforward unless their trajectories are severely constrained. In this paper we present another approach, based on Chern--Simons field theory, which is able to describe the topological entanglements of two fluctuating polymers in terms of gauge fields and second quantized replica fields.Comment: 16 pages, corrected some typos, added two new reference

Pleasure and pedagogy: the consumption of DVD add-ons among Irish teenagers

This article addresses the issue of young people and media use in the digital age, more specifically the interconnection between new media pleasures and pedagogy as they relate to the consumption of DVD add-ons. Arguing against the view of new media as having predominantly detrimental effects on young people, the authors claim that new media can enable young people to develop media literacy skills and are of the view that media literacy strategies must be based on an understanding and legitimating of young people's use patterns and pleasures. The discussion is based on a pilot research project on the use patterns and pleasures of use with a sample of Irish teenagers. They found that DVDs were used predominantly in the home context, and that, while there was variability in use between the groups, overall they developed critical literacy skills and competences which were interwoven into their social life and projects of identity construction. The authors suggest that these findings could be used to develop DVDs and their add-on features as a learning resource in the more formal educational setting and they go on to outline the potential teaching benefits of their use across a range of pedagogical areas

Entangled Polymer Rings in 2D and Confinement

The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$.Comment: 17 pages of Latex, 1 ps figure now available upon request, accepted for J.Phys.A:Math.Ge

Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, $p_c \sim N^{-1}$, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as $\sim N$, to a smooth state with $\sim N^2$. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which $\sim N^{3/2}$. For $p>>p_c$ we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.Comment: 9 pages, 8 figure