Gap Independence and Lacunarity in Percolation Clusters

Efficient simulations of epidemic models with tensor networks: Application to the one-dimensional susceptible-infected-susceptible model

The contact process is an emblematic model of a nonequilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible model, and it is widely used to describe contagious spreading. In this work, we demonstrate how accurate and efficient representations of the full probability distribution over all configurations of the contact process on a one-dimensional chain can be obtained by means of matrix product states (MPSs). We modify and adapt MPS methods from many-body quantum systems to study the classical distributions of the driven contact process at late times. We give accurate and efficient results for the distribution of large gaps, and illustrate the advantage of our methods over Monte Carlo simulations. Furthermore, we study the large deviation statistics of the dynamical activity, defined as the total number of configuration changes along a trajectory, and investigate quantum-inspired entropic measures, based on the second Rényi entropy.

No-Enclave Percolation Corresponds to Holes in the Cluster Backbone

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of such holes give the same size-distribution exponent τ=1.82(1) as found for the NEP model. An argument is given that τ=1+d_{B}/2≈1.822 for backbone holes, where d_{B} is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster yields τ=1+d_{f}/2=187/96≈1.948, where d_{f} is the fractal dimension of the cluster, and this value is consistent with the experimental results of gel collapse of Sheinman et al., which give τ=1.91(6). This suggests that the gel clusters are of the universality class of percolation cluster holes. Both models give a discontinuous maximum hole size at p_{c}, signifying explosive percolation behavior.

Directed percolation with long-range interactions: Modeling nonequilibrium wetting

It is argued that some phase transitions observed in models of nonequilibrium wetting phenomena are related to contact processes with long-range interactions. This is investigated by introducing a model where the activation rate of a site at the edge of an inactive island of length l is 1+a l(-sigma) . Mean-field analysis and numerical simulations indicate that for sigma>1 the transition is continuous and belongs to the universality class of directed percolation, while for 0<sigma<1 , the transition becomes first order. This criterion is then applied to discuss critical properties of various models of nonequilibrium wetting.

Characterizing width uniformity by wave propagation

This work describes a different image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wave fronts. The problem of width uniformity is discussed and its importance for the characterization of composite structures normally found in physics and biology highlighted. The methodology involves identifying each cluster (i.e., connected component) of interest, which can correspond to objects or voids, and estimating the respective medial axes by using a recently proposed wave front propagation approach, which is briefly reviewed. The distance values along such axes are identified and their mean and standard deviation values obtained. As illustrated with respect to synthetic and real objects (in vitro cultures of neuronal cells), the combined use of these two features provides a powerful description of the uniformity of the separation between the objects, presenting potential for several applications in material sciences and biology.