Journal article
Characterising knotting properties of polymers in nanochannels
NR Beaton, JW Eng, K Ishihara, K Shimokawa, CE Soteros
Soft Matter | ROYAL SOC CHEMISTRY | Published : 2018
DOI: 10.1039/c8sm00734a
Abstract
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either “local” or “non-local”, based on a standard approach for measuring the “size” of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength is then the knot-size. If the resulting knot-size is small relative to the whole length of the chain, then the knot is considered to be localised or “local”; otherwise, it is “non-local”. Using this definition, we establish that all but exponentially few sufficiently long self-avoiding polygons (closed c..
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Awarded by Natural Sciences and Engineering Research Council of Canada
Funding Acknowledgements
CES acknowledges support in the form of a Discovery Grant from NSERC (Canada) and a CPU allocation from Compute Canada's WestGrid. KI is partially supported by JSPS KAKENHI Grant Number 17K14190. KS is partially supported by JSPS KAKENHI Grant Numbers 26310206, 16H03928, 16K13751 and 17H06463. NRB received support from the PIMS Collaborative Research Group in Applied Combinatorics, and from Australian Research Council grant DE170100186. CES acknowledges helpful discussions with K. Millett. The authors also acknowledge assistance from Rob Scharein with KnotPlot and that some figures were produced using Rob Scharein's KnotPlot.