Knotting and weak knotting in confined, open random walks using virtual knots

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Knotting and weak knotting in confined, open random walks using virtual knots. / Alexander, Keith; Taylor, Alexander J.; Dennis, Mark R.

In: Journal of Physics A: Mathematical and General, Vol. 53, 045001, 24.07.2019.

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@article{a842e9fe73db436eacbd624241cd2ad7,
title = "Knotting and weak knotting in confined, open random walks using virtual knots",
abstract = " We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modelling confined polymers using both lattice walks and ideal chains, we find an ensemble of random, tangled open curves whose knotting is not dominated by any single knot type, a behaviour we call weakly knotted. We compare cubically confined lattice walks and spherically confined ideal chains, finding the weak knotting probability in both families is quite similar and growing with length, despite the overall knotting probability being quite different. In contrast, the probability of weak knotting in unconfined walks is small at all lengths investigated. For spherically confined ideal chains, weak knotting is strongly correlated with the degree of confinement but is almost entirely independent of length. For ideal chains confined to tubes and slits, weak knotting is correlated with an adjusted degree of confinement, again with length having negligible effect. ",
keywords = "cond-mat.soft, math.GT",
author = "Keith Alexander and Taylor, {Alexander J.} and Dennis, {Mark R}",
note = "19 pages, 9 figures, IoP style",
year = "2019",
month = jul,
day = "24",
doi = "https://doi.org/10.1088/1751-8121/ab5a98",
language = "English",
volume = "53",
journal = "Journal of Physics A: Mathematical and General",
issn = "0305-4470",
publisher = "IOP Publishing Ltd.",

}

RIS

TY - JOUR

T1 - Knotting and weak knotting in confined, open random walks using virtual knots

AU - Alexander, Keith

AU - Taylor, Alexander J.

AU - Dennis, Mark R

N1 - 19 pages, 9 figures, IoP style

PY - 2019/7/24

Y1 - 2019/7/24

N2 - We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modelling confined polymers using both lattice walks and ideal chains, we find an ensemble of random, tangled open curves whose knotting is not dominated by any single knot type, a behaviour we call weakly knotted. We compare cubically confined lattice walks and spherically confined ideal chains, finding the weak knotting probability in both families is quite similar and growing with length, despite the overall knotting probability being quite different. In contrast, the probability of weak knotting in unconfined walks is small at all lengths investigated. For spherically confined ideal chains, weak knotting is strongly correlated with the degree of confinement but is almost entirely independent of length. For ideal chains confined to tubes and slits, weak knotting is correlated with an adjusted degree of confinement, again with length having negligible effect.

AB - We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modelling confined polymers using both lattice walks and ideal chains, we find an ensemble of random, tangled open curves whose knotting is not dominated by any single knot type, a behaviour we call weakly knotted. We compare cubically confined lattice walks and spherically confined ideal chains, finding the weak knotting probability in both families is quite similar and growing with length, despite the overall knotting probability being quite different. In contrast, the probability of weak knotting in unconfined walks is small at all lengths investigated. For spherically confined ideal chains, weak knotting is strongly correlated with the degree of confinement but is almost entirely independent of length. For ideal chains confined to tubes and slits, weak knotting is correlated with an adjusted degree of confinement, again with length having negligible effect.

KW - cond-mat.soft

KW - math.GT

U2 - https://doi.org/10.1088/1751-8121/ab5a98

DO - https://doi.org/10.1088/1751-8121/ab5a98

M3 - Article

VL - 53

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

M1 - 045001

ER -