English
Related papers

Related papers: Critical exponents for random knots

200 papers

We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both…

Statistical Mechanics · Physics 2009-10-31 J. P. Wittmer , P. van der Schoot , A. Milchev , J. -L. Barrat

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to…

Soft Condensed Matter · Physics 2015-06-17 Angelo Rosa , Ralf Everaers

We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by…

Geometric Topology · Mathematics 2017-06-07 Holger Kammeyer

The statistical mechanics of a non-interacting polymer chain in the limit of a large number of monomers is considered when the total angular momentum, L, is fixed. The radius of gyration for a ring polymer in this situation is derived…

Statistical Mechanics · Physics 2009-11-13 J. M. Deutsch

We employ computer simulations and thermodynamic integration to analyse the effects of bending rigidity and slit confinement on the free energy cost of tying knots, $\Delta F_{\rm knotting}$, on polymer chains under tension. A…

Soft Condensed Matter · Physics 2014-05-15 Peter Poier , Christos N. Likos , Richard Matthews

Using Monte Carlo simulations and advanced knot localization methods, we analyze the length and distribution of prime components in composite knots tied on Freely Jointed Rings (FJRs). For increasing contour length, we observe the…

Statistical Mechanics · Physics 2015-06-18 Luca Tubiana

We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…

Statistical Mechanics · Physics 2015-06-25 H. W. J. Blöte , M. T. Batchelor , B. Nienhuis

The black-hole black-string system is known to exhibit critical dimensions and therefore it is interesting to vary the spacetime dimension $D$, treating it as a parameter of the system. We derive the large $D$ asymptotics of the critical,…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Barak Kol , Evgeny Sorkin

Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the…

Soft Condensed Matter · Physics 2009-11-07 Sandra Barsky , Mark O. Robbins

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N_H (out ofN) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho_H=N_H/N. The average chain…

Statistical Mechanics · Physics 2009-10-28 Carlos J. Camacho , Tone Schanke

The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…

Soft Condensed Matter · Physics 2013-05-29 Matthew Brunner , J. M. Deutsch

One measure of geometrical complexity of a spatial curve is the number of crossings in a planar projection of the curve. For $N$-noded ring polymers with a fixed knot type, we evaluate numerically the average of the crossing number over…

Soft Condensed Matter · Physics 2016-08-31 Miyuki K. Shimamura , Tetsuo Deguchi

The size of rings (also called cyclic polymers) in bidisperse blends of chemically identical rings is analyzed by computer simulations. Data of entangled ring blends and blends of interpenetrating rings are compared and it is shown that the…

Soft Condensed Matter · Physics 2021-03-31 Michael Lang

We use molecular dynamics simulations to study a semidilute, unentangled polymer solution containing well dispersed, weakly attractive nanoparticles (NP) of size ($\sigma_N$) smaller than the polymer radius of gyration $R_g$. We find that…

Soft Condensed Matter · Physics 2018-09-18 Valerio Sorichetti , Virginie Hugouvieux , Walter Kob

The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This…

Probability · Mathematics 2007-05-23 Francesco Caravenna , Giambattista Giacomin , Lorenzo Zambotti

Molecular weight dependence of excluded volume effects is examined. The swollen-to-unperturbed coil transition point shifts to lower concentration range with increasing molecular weight (Mw). It is shown that in the limit of the infinite…

Soft Condensed Matter · Physics 2014-01-28 Kazumi Suematsu

When compressed in a slit of width $D$, a $\Theta$-chain that displays the scaling of size $R_0$ (diameter) with respect to the number of monomers $N$, $R_0\sim aN^{1/2}$, expands in the lateral direction as $R_{\parallel}\sim a…

Soft Condensed Matter · Physics 2022-02-28 Lei Liu , Philip A. Pincus , Changbong Hyeon

We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that…

Soft Condensed Matter · Physics 2009-10-30 Ido Golding , Yacov Kantor

Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single…

Soft Condensed Matter · Physics 2022-12-02 Mattia Alberto Ubertini , Jan Smrek , Angelo Rosa

The scattering function and radius of gyration of an ideal polymer network are calculated depending on the strength of the bonds that form the crosslinks. Our calculations are based on an {\it exact} theorem for the characteristic function…

Condensed Matter · Physics 2016-08-31 M. P. Solf , T. A. Vilgis