Related papers: Random networks of cross-linked directed polymers
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the…
By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
We have obtained the universal conductance distribution of two-dimensional disordered systems in the strongly localized limit. This distribution is directly related to the Tracy-Widom distribution, which has recently appeared in many…
Randomly crosslinked macromolecules undergo a liquid-to-amorphous solid phase transition at a critical crosslink concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence…
The process of polymer condensation, i.e. the formation of bonds between reactive end-groups, is ubiquitous in both industry and biology. Here we study generic systems undergoing polymer condensation in competition with cyclisation. Using a…
Through extensive Monte Carlo simulations, we systematically study the effect of chain stiffness on the packing ability of linear polymers composed of hard spheres in extremely confined monolayers, corresponding effectively to 2D films.…
Certain polymer models are known to exhibit path localization in the sense that at low temperatures, the average fractional overlap of two independent samples from the Gibbs measure is bounded away from $0$. Nevertheless, the question of…
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to…
We revisit the problem of an elastic line (e.g. a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension $d=1+1$. Upon applying a transverse field, a delocalization transition is expected, beyond…
We propose an explanation of the bands of extended states appearing in random one dimensional models with correlated disorder, focusing on the Continuous Random Dimer model [A.\ S\'{a}nchez, E.\ Maci\'a, and F.\ Dom\'\i nguez-Adame, Phys.\…
The formation of bundles composed of actin filaments and cross-linking proteins is an essential process in the maintenance of the cells' cytoskeleton. It has also been recreated by in-vitro experiments, where actin networks are routinely…
We model the behaviour of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local…
Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions…
We consider a model of a polymer in $\mathbb{Z}^{d+1}$, constrained to join 0 and a hyperplane at distance $N$. The polymer is subject to a quenched nonnegative random environment. Alternatively, the model describes crossing random walks in…
It is a well-known open problem in the literature on random polymers to show that a directed polymer in random environment localizes around a favorite path at low temperature. A precise statement of this conjecture is formulated and proved…
The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through…
Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical…