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In this paper I propose very simple statistical "memory model" of one-dimensional directed polymers which is capable to store and retrieve a given random quenched trajectory. The model is defined in terms of the elastic string Hamiltonian…
We study the phase behavior of a classical system of particles interacting through a strictly convex soft-repulsive potential which, at variance with the pairwise softened repulsions considered so far in the literature, lacks a region of…
We consider the overdamped motion of Brownian particles, interacting via particle exclusion, in an external potential that varies with time and space. We show that periodic potentials that maintain specific position-dependent phase…
We study a model describing some aspects of the dynamics of biopolymers. The models involve either one or two finite chains with a number N of sites that represent the "units" of a biophysical system. The mechanical degrees of freedom of…
We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in…
We present a novel and rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modelled by harmonic potentials in the limit when the strength of the…
Based on the analogy with the quantum mechanics of a particle propagating in a {\em complex} potential, we develop a field-theoretical description of the statistical properties of a self-avoiding polymer chain in a random environment. We…
We study the buckling of an idealized, semiflexible filament along whose contour magnetic moments are placed. {We give analytic expressions for the critical stiffness of the filament below which it buckles due to the magnetic compression.…
We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant…
We study the dynamics of a single chain polymer confined to a two dimensional cell. We introduce a kinetically constrained lattice gas model that preserves the connectivity of the chain, and we use this kinetically constrained model to…
The mechanical properties of a polymeric network containing both crosslinks and sliplinks (entanglements) are studied using a multi-chain Brownian dynamics simulation. We coarse-grain at the level of chain segments connecting consecutive…
Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic…
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…
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal…
Forced desorption of a semiflexible polymer chain on a solid substrate is theoretically investigated. The pulling force versus displacement is studied for different adsorption energy and persistence length P. It is found that the…
We study the Brownian dynamics of flexible and semiflexible polymer chains densely grafted on a flat substrate, upon rapid quenching of the system when the quality of solvent becomes poor and chains attempt collapse into a globular state.…
We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through…
We consider the force on the end of a polymer chain being pulled through a network at velocity $v$, using computer simulations. We develop algorithms for measuring the force on the end of the chain using lattice models of polymers. Our…
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…
We report that a dielectric polymer chain, constrained at both ends, sharply collapses when exposed to a high electric field. The chain collapse is driven by nonlocal dipolar interactions and anisotropic polarization of monomers, a…