Related papers: The evaluation of directionally writhing polymers
The rheology of molecular brushes remains challenging to control due to the multiple length scales and relaxation processes involved and the lack of direct observation of molecular conformation during flow. We use molecular dynamics…
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a…
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…
We investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve…
We review statistical-mechanical theories of single-molecule micromanipulation experiments on nucleic acids. First, models for describing polymer elasticity are introduced. We then review how these models are used to interpret…
We demonstrate a variant of the Bond Fluctuation lattice Monte Carlo model in which moves through cis conformations are forbidden. Ring polymers in this model have a conserved quantity that amounts to a topological linking number. Increased…
Genetic information is stored in a linear sequence of base-pairs; however, thermal fluctuations and complex DNA conformations such as folds and loops make it challenging to order genomic material for in vitro analysis. In this work, we…
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…
We present a self-contained theory for the mechanical response of DNA in single molecule experiments. Our model is based on a 1D continuum description of the DNA molecule and accounts both for its elasticity and for DNA-DNA electrostatic…
A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma…
The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double-helix, these numbers are not always straightforward to compute,…
We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary…
In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover,…
One measure of geometrical complexity of a spatial curve is the number of crossings in a planar projection of the curve. For $N$-noded ring polymers with a fixed knot type, we evaluate numerically the average of the crossing number over…
Using molecular dynamics simulations, we determine the linear and nonlinear viscoelastic properties of a model polymer melt in the unentangled regime. Several approaches are compared for the computation of linear moduli, including…
We study the dynamics of a single polymer subject to thermal fluctuations in a linear shear flow. The polymer is modeled as a finitely extendable nonlinear elastic FENE dumbbell. Both orientation and elongation dynamics are investigated…
We consider mechanically generated molecular braids composed of two molecules where long range interactions between them can be considered to be very weak. We describe a model that takes account of the thermal fluctuations of the braid,…
A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincar\'e and naturally appear in…
The theory of elastic rods can be used to describe certain geometric and topological properties of the DNA molecules. A similar effective field theory approach was previously suggested to describe the conformations and dynamics of proteins.…