Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Artisanal mining's democratizing directions and deviations

Artisanal miners have tended to be portrayed in the literature and media as people who work hard and play hard, not infrequently depicted as ‘rough diamonds’ likely to cross the boundaries of appropriate behaviour through pursuit of wealth and flamboyant living, often at the cost of local environmental damage. A popular alternative image is that of marginalised labourers, driven by poverty to toil in harsh conditions and pursuing mining livelihoods in the face of national governments and large-scale mining companies’ subversion of their land and mineral rights. Both views reflect partial realities, but are inclined to exaggerate the position of miners as mischief-making rogues or victims. Through documentation of the multi-faceted nature of Tanzanian artisanal miners’ work and home lives during the country’s on-going economic mineralisation, we endeavour to convey a balanced rendering of their aspirations, occupational identity and social ties. Our emphasis is on their working lives as artisans, how they organise themselves and contend with the risks of their occupation, including their engagement with government policy and large-scale mining interests.