Related papers: A Monte-Carlo study of meanders
We study the statistics of semi-meanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct…
Pour modeliser le repliement compact d'un polymere, on etudie la statistique des meandres, definis comme configurations d'un circuit automobile traversant n fois une riviere. Grace a une methode Monte-Carlo adaptee a un ordinateur…
The meander problem is a combinatorial problem which provides a toy model of the compact folding of polymer chains. In this paper we study various questions relating to the enumeration of meander diagrams, using diagrammatical methods. By…
We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random lattices as well as the famous meander problem of enumerating…
The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a…
We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
Randomly branching polymers with {\em annealed} connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present…
We study the statistics of branching polymers with excluded-volume interactions, by modeling them as single self-avoiding trees on a generic regular periodic lattice with coordination number $q$. Each lattice site can be occupied at most by…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
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…
We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
The problem of calculating the frequencies of network motifs on three and four nodes in large networks is considered. Telecommunications networks, cell molecular networks are investigated. The sizes of the investigated networks are hundreds…
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: \textit{uniform} stretching by external forces and \textit{non-uniform} stretching by external fields. Many…
We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of $n$ sites for…
Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from…
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…
The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…