Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.

Liu, X., Ricca, R. (2016). Knots cascade detected by a monotonically decreasing sequence of values. SCIENTIFIC REPORTS, 6, 1-7 [10.1038/srep24118].

Knots cascade detected by a monotonically decreasing sequence of values

RICCA, RENZO
2016

Abstract

Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.
Articolo in rivista - Articolo scientifico
vortex knots, DNA, torus knots, torus links, HOMFLYPT polynomial
English
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Liu, X., Ricca, R. (2016). Knots cascade detected by a monotonically decreasing sequence of values. SCIENTIFIC REPORTS, 6, 1-7 [10.1038/srep24118].
Liu, X; Ricca, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/135483
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