Related papers: Conformational statistics of non-equilibrium polym…
We construct two exactly soluble lattice spin models that demonstrate the importance of three-loop braiding statistics for the classification of 3D gapped quantum phases. The two models are superficially similar: both are gapped and both…
Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…
Experiments using nanofluidic devices have proven effective in characterizing the physical properties of polymers confined to small cavities. Two recent studies using such methods examined the organization and dynamics of two DNA molecules…
Active polymers play a central role in many biological systems, from bacterial flagella to cellular cytoskeletons. Minimal models of semiflexible active filaments have been used to study a variety of interesting phenomena in active systems,…
We consider equilibrium relaxation properties of the end-to-end distance and of principal components in a one-dimensional polymer chain model with nonlinear interaction between the beads. While for the single-well potentials these…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
Most of the theoretical models describing the translocation of a polymer chain through a nanopore use the hypothesis that the polymer is always relaxed during the complete process. In other words, models generally assume that 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 study the diffusion process through an ideal polymer network, using numerical methods. Polymers are modeled by random walks on the bonds of a two-dimensional square lattice. Molecules occupy the lattice cells and may jump to the…
The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the…
We present a statistical model of a dilute polymer solution in good solvent in the presence of low-molecular weight cosolvent. We investigate the conformational changes of the polymer induced by a change of the cosolvent concentration and…
The main topic of these lecture notes is the continuum scaling limit of planar lattice models. One reason why this topic occupies an important place in the theory of probability and mathematical statistical physics is that scaling limits…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
While Flory theories provide an extremely useful framework for understanding the behavior of interacting, randomly branching polymers, the approach is inherently limited. Here we use a combination of scaling arguments and computer…
The localization kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface is studied in the limit of strong segregation between hydrophobic and polar segments in the chain. We…
We analyze the conformational properties of polymer macromolecules in solutions in presence of extended structural obstacles of (fractal) dimension $\varepsilon_d$ causing the anisotropy of environment. Applying the pruned-enriched…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions…
While the structure of chromatin has been studied in great detail on length scales below 30 nm, amazingly little is known about the higher-order folding motifs of chromatin in interphase. Recent experiments give evidence that the folding…
In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…
We study the compression and extension dynamics of a DNA-like polymer interacting with non-DNA binding and DNA-binding proteins, by means of computer simulations. The geometry we consider is inspired by recent experiments probing the…