Related papers: A study of polymer knots using a simple knot invar…
The mechanical properties of polymer knots under stretching in a bad or good solvent are investigated by applying a given force $F$ to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer…
The statistical mechanics of single polymer knots is studied using Monte Carlo simulations. The polymers are considered on a cubic lattice and their conformations are randomly changed with the help of pivot transformations. After each…
In the first part of this work a summary is provided of some recent experiments and theoretical results which are relevant in the research of systems of polymer rings in nontrivial topological conformations. Next, some advances in modeling…
The thermal properties of coarse grained knotted polymers containing two kinds of monomers $A$ and $B$ fluctuating in a solution are investigated on a simple cubic lattice using the Wang-Landau MC algorithm. These knots have a more complex…
The topological effects on the thermal properties of several knot configurations are investigated using Monte Carlo simulations. In order to check if the topology of the knots is preserved during the thermal fluctuations we propose a method…
We investigate the thermal and structural properties of knotted diblock copolymer rings using a coarse-grained lattice model in an implicit solvent. The system is studied by means of the Wang--Landau Monte Carlo algorithm, allowing us to…
An extensive study of single block copolymer knots containing two kinds of monomers $A$ and $B$ is presented. The knots are in a solution and their monomers are subjected to short range interactions that can be attractive or repulsive. In…
Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase…
The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological…
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…
Inspired by recent advances in the chromosome capture techniques, a method is proposed to study the structural organization of systems of polymers rings with topological constraints.To this purpose, the system is divided into compartments…
The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction…
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…
The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random…
Semiflexible polymers are widely used as a paradigm for understanding structural phases in biomolecules including folding of proteins. Here, we compare bead-spring and bead-stick variants of coarse-grained semiflexible polymer models that…
A ring polymer in a confining space may exhibit at least two phases, namely an expanded (or solvent-rich phase) if its concentration is small, or a collapsed (or polymer-rich phase) when it is concentrated and compressed. These phases are…
The interplay between the topological and geometrical properties of a polymer ring can be clarified by establishing the entanglement trapped in any portion (arc) of the ring. The task requires to close the open arcs into a ring, and the…
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic…
Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally…
Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on…