Related papers: Conformational statistics of randomly-branching do…
We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropriate multivariate Gaussian which takes into account the…
We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase…
Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single…
In this paper, we employ Molecular Dynamics computer simulations to study and compare the statics and dynamics of linear and circular (ring) polymer chains in entangled solutions of different densities. While we confirm that linear chain…
Polymer melts undergoing large deformation by uniaxial elongation are studied by molecular dynamics simulations of bead-spring chains in melts. Applying a primitive path analysis to strongly deformed polymer melts, the role of topological…
We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer…
Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of…
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 a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
In the paper we investigate statistical and topological properties of fractional Brownian polymer chains, equipped with the short-range volume interactions. The attention is paid to statistical properties of collapsed conformations with the…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius,…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…