相关论文: Universal properties of knotted polymer rings

We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the…

This article is concerned with random holomorphic polynomials and their generalizations to algebraic and symplectic geometry. A natural algebro-geometric generalization studied in our prior work involves random holomorphic sections…

In polymer physics it is typically assumed that excluded volume interactions are effectively screened in polymer melts. Hence, chains could be described by an effective random walk without excluded volume interactions. In this letter, we…

We have examined the behaviors of a knotted linear polymer in narrow tubes using Langevin dynamics simulation to investigate the knot localization property in one-dimensional (1D) geometry. We have found that the knot is strongly localized…

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the…

We present results of Monte Carlo study of the monomer-monomer correlation functions, static structure factor and asphericity characteristics of a single homopolymer in the coil and globular states for three distinct architectures of the…

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…

We study the dynamics of a knot in a semiflexible polymer confined to a narrow channel of width comparable to the polymers' persistence length. Using a combination of Brownian dynamics simulations and a coarse-grained stochastic model, we…

A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice…

We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts (Phys. Rev. Lett. 106, 167802 (2011)). A basic assumption lies in the implementation of the noncatenation constraint via the…

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…

An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported…

We study the entanglement complexity of a system consisting of two simple-closed curves (self-avoiding polygons) that span a lattice tube, referred to as a 2SAP. 2SAPs are of interest as the first known model of confined ring polymers where…

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the…

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N=1600 monomers per chain which…

In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…

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…

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 untangled (i.e. non-concatenated and unknotted) rings,…

We present a semi-analytical approach to the determination of the dynamic properties of randomly branched polymers under the Rouse approximation. The principle procedure is based on examining a spectrum of eigenvalues which represents the…

Self-avoiding polymers in strictly two-dimensional ($d=2$) melts are investigated by means of molecular dynamics simulation of a standard bead-spring model with chain lengths ranging up to N=2048. % The chains adopt compact configurations…