Related papers: Gelation in input-driven aggregation
The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly…
A significant fraction of clusters of galaxies are observed to have substructure, which implies that merging between clusters and subclusters is a rather common physical process of cluster formation. It still remains unclear how cluster…
Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most…
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear…
The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange…
A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
We consider the problem of gelation in the cluster coagulation model introduced by Norris [\textit{Comm. Math. Phys.}, 209(2):407-435 (2000)], where pairs of clusters of types $(x,y)$ taking values in a measure space $E$, merge to form a…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a…
Dust coagulation in interstellar space and protoplanetary disks is usually treated as one of 2 extreme cases: Particle-Cluster Aggregation and Cluster-Cluster Aggregation. In this paper we study the process of hierarchical growth, where…
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…
Clustering is often presumed to lead to enhanced agglomeration between cohesive grains due to the reduced relative velocities of particles within a cluster. Our discrete-particle simulations on gravity-driven, gas-solid flows of cohesive…
Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it…
The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from…
We investigate aggregation and fragmentation dynamics of tracers and inertial aggregates in random flows leading to steady state size distributions. Our objective is to elucidate the impact of changes in aggregation rates, due to…
Using numerically exact methods we examine the Fermi-Hubbard model on arbitrary cluster topology. We focus on the question which systems eventually equilibrate or even thermalize after an interaction quench when initially prepared in a…
We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is…