Related papers: Critical exponents for random knots
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…