Related papers: Scattering functions of knotted ring polymers
We present computer simulations to examine probability distributions of gyration radius for the no-thickness closed polymers of N straight segments of equal length. We are particularly interested in the conditional distributions when the…
It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers…
Stochastic simulations are used to characterize the knotting distributions of random ring polymers confined in spheres of various radii. The approach is based on the use of multiple Markov chains and reweighting techniques, combined with…
Several nontrivial properties are shown for the mean square radius of gyration $R_K^2$ of ring polymers with a fixed knot type K. Through computer simulation, we discuss both finite-size and asymptotic behaviors of the gyration radius under…
By performing Monte Carlo sampling of $N$-steps self-avoiding polygons embedded on different Bravais lattices we explore the robustness of universality in the entropic, metric and geometrical properties of knotted polymer rings. In…
We use deformations and mutations of scattering diagrams to show that the coefficients of a scattering diagram with initial functions $f1 = (1+tx)^{\mu}$ and $f2 = (1+ty)^{\nu}$ are polynomial in ${\mu}$, ${\nu}$ and non-trivial in a…
Anomalously strong finite-size effects have been observed for the mean square radius of gyration $R^2_K$ of Gaussian random polygons with a fixed knot $K$ as a function of the number $N$ of polygonal nodes. Through computer simulations with…
We examine numerically the distribution function $f_K(r)$ of distance $r$ between opposite polygonal nodes for random polygons of $N$ nodes with a fixed knot type $K$. Here we consider three knots such as $\emptyset$, $3_1$ and $3_1 \sharp…
The scattering function and radius of gyration of an ideal polymer network are calculated depending on the strength of the bonds that form the crosslinks. Our calculations are based on an {\it exact} theorem for the characteristic function…
An explicit expression is derived for the scattering function of a self-avoiding polymer chain in a $d$-dimensional space. The effect of strength of segment interactions on the shape of the scattering function and the radius of gyration of…
The freely rotating chain is one of the classic discrete models of a polymer in dilute solution. It consists of a broken line of N straight segments of fixed length such that the angle between adjacent segments is constant and the N-1…
In this work we present scattering functions of conjugates consisting of a colloid particle and a self-avoiding polymer chain. This model is directly derived from the two point correlation function with the inclusion of excluded volume…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…
A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible…
We study numerically scattering and transport statistical properties of tight-binding random networks characterized by the number of nodes $N$ and the average connectivity $\alpha$. We use a scattering approach to electronic transport and…
Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we…
We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and…
The role of the topology and its relation with the geometry of biopolymers under different physical conditions is a nontrivial and interesting problem. Aiming at understanding this issue for a related simpler system, we use Monte Carlo…