Related papers: Branched Polymers and Percolation
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic…
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure $\nu_\lambda$ for all $\lambda>0$. We follow in part a previous incomplete unpublished work of the first named author with M.…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
We determine the distribution of free ends and the monomer insertion potential in the strongly-stretched limit for regularly and statistically branched polymer brushes. We find that the end density flattens in the limit of very strong…
In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in the $3D$ space at a range of chain lengths $N$. The…
The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic…
Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e. transitions in the…
The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…
The aim of this paper is to explore possible ways of extending Smirnov's proof of Cardy's formula for critical site-percolation on the triangular lattice to other cases (such as bond-percolation on the square lattice); the main question we…
We study simple branched coverings of degree d of the 2- and 3- dimensional sphere branched over oriented links. We demonstrate how to use braid charts to develop embeddings of these into $S^k \times D^2$ for $k=2,3 when $d=2,3$. This is an…
Over the past two decades polymer nanocomposites have received tremendous interest from industry and academia due to their advanced properties comparative to polymer blends. Many computational studies have revealed that the macroscopic…
In this note we give upper bounds for the free energy of discrete polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theory of turbulence. For the polymer model, we…
We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties…
This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A.…
Droplet condensation on surfaces produces patterns, called breath figures. Their evolution into self-similar structures is a classical example of self-organization. It is described by a scaling theory with scaling functions whose…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two-thirds power of the interpolating distance. This…