Related papers: Analytical results on the polymerisation random gr…
The stretching of brushes of long polymers grafted to a planar surface is investigated byMonte Carlo simulations in the limit of very high grafting densities, as achieved in recent experiments. The monomer density profiles are shown to…
We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let n tend to infinity. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the…
We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering…
In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The…
Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue…
Mono- and poly-disperse melts of oligomers (average length 10 monomers) of trans-1,4-polyisoprene are simulated in full atomistic detail. The force-field is developed by means of a mixture of ab initio quantum-chemistry and an automatic…
A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
We estimate the probability regarding polymerization of a macromolecule which is made of distinct monomers. The lattice model of the random walk has been used to mimic the conformations of an ideal chain in two and three dimensions. It has…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…
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 consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…
It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). Here we show that a…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
Knowing how and when trends are formed is a frequently visited research goal. In our work, we focus on the progression of trends through (social) networks. We use a random graph (RG) model to mimic the progression of a trend through the…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…