Related papers: Cluster, backbone and elastic backbone structures …
Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel…
We announce our recent proof that, for independent bond percolation in high dimensions, the scaling limits of the incipient infinite cluster's two-point and three-point functions are those of integrated super-Brownian excursion (ISE). The…
Interacting proteins coevolve at multiple but interconnected scales, from the residue-residue over the protein-protein up to the family-family level. The recent accumulation of enormous amounts of sequence data allows for the development of…
Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If…
Diseases emerge, persist and vanish in an ongoing battle for available hosts. Hosts, on the other hand, defend themselves by developing immunity that limits the ability of pathogens to reinfect them. We here explore a multi-disease system…
Genome wide comparisons between enteric bacteria yield large sets of conserved putative regulatory sites on a gene by gene basis that need to be clustered into regulons. Using the assumption that regulatory sites can be represented as…
We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system is consists of clusters of various masses whose concentrations evolve according to an…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
We report analytical and numerical modelling of active elastic networks, motivated by experiments on crosslinked actin networks contracted by myosin motors. Within a broad range of parameters, the motor-driven collapse of active elastic…
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as randomly…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
The percolation of Kandel, Ben-Av and Domany clusters for 2d fully frustrated Ising model is extensively studied through numerical simulations. Critical exponents, cluster distribution and fractal dimension of percolative cluster are given.
In a recent article, one of the authors used $c=0$ logarithmic conformal field theory to predict crossing-probability formulas for percolation clusters inside a hexagon with free boundary conditions. In this article, we verify these…
The elastic backbone is the set of all shortest paths. We found a new phase transition at $p_{eb}$ above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in $2d$ its fractal dimension is…
We analyze a simple model for growing tree networks and find that although it never percolates, there is an anomalously large cluster at finite size. We study the growth of both the maximal cluster and the cluster containing the original…
Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial…
We analyze damage nucleation and localization in the random fuse model with strong disorder using numerical simulations. In the initial stages of the fracture process, damage evolves in an uncorrelated manner, resembling percolation.…
We applied the newly developed rose diagram overlay method to detect the layered structure of 88 nearby open clusters ($\leq$500~pc) on the three projections after the distance correction of their member stars, based on the catalog in…
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…