Asymptotics of knotted lattice polygons

Orlandini, Enzo; Tesi, Maria Carla; Rensburg, E J Janse van; Whittington, S G

doi:10.1088/0305-4470/31/28/010

Cited by 105 publications

(214 citation statements)

References 31 publications

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“…Whereas we cannot infer definitive statements on 3D knots from our analysis, the correspondence between figure-eight paraknot and the leading order behaviour of prime knots (and between the Round Table configuration and composite knots) in 2D suggests that similar tightness could be observed in 3D as well. This is consistent with the findings of Janse van Rensburg and Whittington [62], Orlandini et al [63] and Katritch et al [65], and it differs from the conclusions of Quake [53].…”

Section: Discussionsupporting

confidence: 89%

“…These authors conclude that one or more tight knot regions can move along the perimeter of a simply connected ring polymer, each prime component being represented by one knot region [63]. An analogous result was obtained in 2D by Guitter and Orlandini [64].…”

Section: Orlandini Et Al Calculate In a Monte Carlo Study The Numbersupporting

confidence: 55%

“…Each fringe loop, that is, corresponds to a prime component. The additional degrees of freedom coming about by the relative motion of the fringe loops in this configuration correspond to the enhancement of accessible numbers of configurations for knotted chains as measured by Orlandini et al [63,64].…”

Section: The Round-table Configurationmentioning

confidence: 53%

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Tightness of slip-linked polymer chains

et al. 2002

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We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops which can exchange length between each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a sliplinked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip-links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.

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Section: Discussionsupporting

confidence: 89%

Section: Orlandini Et Al Calculate In a Monte Carlo Study The Numbersupporting

confidence: 55%

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Tightness of slip-linked polymer chains

et al. 2002

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“…Furthermore, some dynamical or thermodynamical properties of ring polymers under topological constraints could also be nontrivial. In fact, various computer simulations of ring polymers with fixed topology were performed by several groups [1,2,3,4,5,6,7,8,9,10,11,12]. However, there are still many unsolved problems related to the topological effect, such as the average size of a knotted ring polymer in solution.…”

Section: Introductionmentioning

confidence: 99%

Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical self-avoiding polygons

Shimamura

Deguchi

2002

Phys. Rev. E

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Several nontrivial properties are shown for the mean square radius of gyration R 2 K of ring polymers with a fixed knot type K. Through computer simulation, we discuss both finite-size and asymptotic behaviors of the gyration radius under the topological constraint for self-avoiding polygons consisting of N cylindrical segments with radius r. We find that the average size of ring polymers with a knot K can be much larger than that of no topological constraint. The effective expansion due to the topological constraint depends strongly on the parameter r which is related to the excluded volume. The topological expansion is particularly significant for the small r case, where the simulation result is associated with that of random polygons with the knot K.

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“…For some nontrivial knots (3 1 , 4 1 , 5 1 , 5 2 ), knotting probabilities have been evaluated numerically for several different models of random polygons and self-avoiding polygons. [18][19][20][21][22] . Through the simulations using the Vassiliev-type invariants, it is found that the probability P K (N) as a function of N can be expressed as…”

Section: Introductionmentioning

confidence: 99%

Knot complexity and the probability of random knotting

Shimamura

Deguchi

2002

Phys. Rev. E

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The probability of a random polygon (or a ring polymer) having a knot type K should depend on the complexity of the knot K. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially with respect to knot complexity. Here we assume that some aspects of knot complexity are expressed by the minimal crossing number C and the aspect ratio p of the tube length to the diameter of the ideal knot of K, which is a tubular representation of K in its maximally inflated state.

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Asymptotics of knotted lattice polygons

Cited by 105 publications

References 31 publications

Tightness of slip-linked polymer chains

Tightness of slip-linked polymer chains

Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical self-avoiding polygons

Knot complexity and the probability of random knotting

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