Related papers: Ring polymers with topological constraints
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that the their behaviour depends crucially on their size: short rings ($N \lesssim$ 100) are swelled whereas longer rings ($N \gtrsim$…
It has been shown that under high cylindrical confinement, two ring polymers with excluded volume interactions between monomers, segregate to two halves of the cylinder to maximize their entropy. In contrast, two ring polymers remain mixed…
Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations…
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
Polymer entanglements lead to complicated topological constraints and interactions between neighbouring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they…
Several nontrivial properties are shown for the mean square radius of gyration $R_K^2$ 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 interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of…
The class of topological insulator materials is one of the frontier topics of condensed matter physics. The great success of this field is due to the conceptual breakthroughs in theories for topological electronic states and is strongly…
Bridging algorithms are global Monte Carlo moves which allow for an efficient sampling of single polymer chains. In this manuscript we discuss the adaptation of three bridging algorithms from lattice to continuum models, and give details on…
Every smooth closed curve can be represented by a suitable Fourier sum. We show that the ensemble of curves generated by randomly chosen Fourier coefficients with amplitudes inversely proportional to spatial frequency (with a smooth…
The effect of different Monte Carlo move sets on the the folding kinetics of lattice polymer chains is studied from the geometry of the conformation-network. The networks have the characteristics of small- world. The Monte Carlo move, rigid…
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…
Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme elongation…
We study the unfolding of a single polymer chain due to an external force. We use a simplified model which allows to perform all calculations in closed form without assuming a Boltzmann-Gibbs form for the equilibrium distribution.…
We investigated the static and dynamic properties of a Rouse ring polymer modified by introducing an effective, spherically symmetric, attractive potential of entropic nature and a memory function describing the effect of dynamic…
A classical knot is described by a one-stroke trajectory with entanglements of a string. The replica method appears as a powerful tool in statistical mechanics for a polymer or self-avoiding walk. We consider this replica N to 0 limit in…
In this work a field theoretical model is constructed to describe the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. As an application, the effects of the…
We numerically examine the nonlinear rubber elasticity of topologically constrained polymer networks. We propose a simple and effective model based on Graessley and Pearson's topological model (GP model) for describing the topological…
We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational…