Related papers: Disorder Induced Limited Path Percolation
The low-energy limits of models with disorder are frequently described by sigma models. In two dimensions, most sigma models admit either a Wess-Zumino-Witten or a theta term. When such a term is present the model can have a stable critical…
Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to…
We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
We investigate electron transport in disordered Hubbard chains contacted to macroscopic leads, via the non-equilibrium Green's functions technique. We observe a cross-over of currents and conductances at finite bias which depends on the…
The turning distance is a well-studied metric for measuring the similarity between two polygons. This metric is constructed by taking an $L^p$ distance between step functions which track each shape's tangent angle of a path tracing its…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…
Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al \cite{PAR10B}). For…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
We study shortest paths and spanning trees of complex networks with random edge weights. Edges which do not belong to the spanning tree are inactive in a transport process within the network. The introduction of quenched disorder modifies…
We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…
Advancements in materials design and manufacturing have allowed for the production of ordered and disordered metamaterials with diverse and novel properties. Hyperuniform two-phase heterogeneous materials, which anomalously suppress density…
Two stochastic models are proposed to generate a system composed of two interdependent scale-free (SF) or Erd\H{o}s-R\'{e}nyi (ER) networks where interdependent nodes are connected with exponential or power-law relation, as well as…
Disordered pinning models are statistical mechanics models built on discrete renewal processes: renewal epochs in this context are called contacts. It is well known that pinning models can undergo a localization/delocalization phase…
The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths $P(g)\simg^{\mu-1}$. Distributions of equivalent conductances are estimated numerically on hierarchical…
The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive…
Modern large network systems normally work in cooperation and incorporate dependencies between their components for purposes of efficiency and regulation. Such dependencies may become a major risk since they can cause small scale failures…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…