Related papers: Fractal and Statistical Properties of Large Compac…
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…
Topologically stabilized polymer conformations observed in melts of nonconcatenated polymer rings and crumpled globules, are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite…
We study Hamiltonian walks (HWs) on the family of three--dimensional modified Sierpinski gasket fractals, as a model for compact polymers in nonhomogeneous media in three dimensions. Each member of this fractal family is labeled with an…
We present a computer simulation study of the compact self-avoiding loops as regards their length and topological state. We use a Hamiltonian closed path on the cubic-shaped segment of a 3D cubic lattice as a model of a compact polymer. The…
Monte Carlo simulations of coarse-grained polymers provide a useful tool to deepen the understanding of conformational and statistical properties of polymers both in physical as well as in biological systems. In this study we sample compact…
We study the conformational properties of complex Gaussian polymers containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered at $n$ branching points to either a linear polymer backbone (generalized bottlebrush…
We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular…
Predicting the macroscopic mechanical behavior of polymeric materials from the micro-structural features has remained a challenge for decades. Existing theoretical models often fail to accurately capture the experimental data, due to…
Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics, that have allowed both decades of scientific discovery and provided a universal framework to understand a…
Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform…
Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for…
We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e. self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling…
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer,…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
We study Hamiltonian walks (HWs) on Sierpinski and $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ and find the asymptotic behaviour of the…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
Quantum algorithms for simulation of Hamiltonian evolution are often based on product formulae. The fractal methods give a systematic way to find arbitrarily high-order product formulae, but result in a large number of exponentials. On the…
Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyze the size and shape characteristics of complex polymer structures, containing in…
Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a…
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…