Entropic exponents of lattice polygons with specified knot type

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

doi:10.1088/0305-4470/29/12/003

Cited by 35 publications

(64 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The explanation of this convergent behavior lies, we propose, in the phenomenon of knot localization. 53,59,60 Although the presence of local and global knots occur with probability approaching one as the number of edges goes to infinity, 45,46,61,62 several papers have established that for long chains, on average, knots tend to be localized. [63][64][65][66] This implies that the average length of the knotted portion becomes shorter and shorter in relation to the entire polygon as the number of edges increases.…”

Section: B the Effect Of Topology On The Shape Of Polymersmentioning

confidence: 99%

Effect of knotting on polymer shapes and their enveloping ellipsoids

Millett

Plunkett

Piatek

et al. 2009

The Journal of Chemical Physics

View full text Add to dashboard Cite

Effect of knotting on polymer shapes and their enveloping ellipsoidsWe simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.

show abstract

Section: B the Effect Of Topology On The Shape Of Polymersmentioning

confidence: 99%

Effect of knotting on polymer shapes and their enveloping ellipsoids

Millett

Plunkett

Piatek

et al. 2009

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…[16] shall be discussed in section 4 and also note that the simulation results of Refs. [29,30] seem to contain some information on the characteristic length of the SAP on the cubic lattice. However, we are unable to derive any appropriate estimate from them.…”

Section: The Number Of Unknotted Polygonsmentioning

confidence: 99%

On the dominance of trivial knots among SAPs on a cubic lattice

Yao

Matsuda

Tsukahara

et al. 2001

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

The knotting probability is defined by the probability with which an N -step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum 1 models of the SAP as a function of N . In particular the characteristic length of the trivial knot that corresponds to a 'half-life' of the knotting probability is estimated to be 2.5 × 10 5 on the cubic lattice.

show abstract

“…The change in connective constant of c-animals as the number of cycles per vertex changes from zero to non-zero is discussed -among other results -in [18]. Similarly, in a numerical study of knotted polymers [22], it was conjectured that the exponent α depends on the number of prime knots n p that arise in the knot decomposition of a given SAP via the relation α(n p ) = α(0) + n p .…”

Section: Introductionmentioning

confidence: 97%

Punctured polygons and polyominoes on the square lattice

Guttmann

Jensen

Wong

et al. 2000

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

We use the finite lattice method to count the number of punctured staircase and self-avoiding polygons with up to three holes on the square lattice. New or radically extended series have been derived for both the perimeter and area generating functions. We show that the critical point is unchanged by a finite number of punctures, and that the critical exponent increases by a fixed amount for each puncture. The increase is 1.5 per puncture when enumerating by perimeter and 1.0 when enumerating by area. A refined estimate of the connective constant for polygons by area is given. A similar set of results is obtained for finitely punctured polyominoes. The exponent increase is proved to be 1.0 per puncture for polyominoes.

show abstract

Entropic exponents of lattice polygons with specified knot type

Cited by 35 publications

References 18 publications

Effect of knotting on polymer shapes and their enveloping ellipsoids

Effect of knotting on polymer shapes and their enveloping ellipsoids

On the dominance of trivial knots among SAPs on a cubic lattice

Punctured polygons and polyominoes on the square lattice

Contact Info

Product

Resources

About