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We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied,…
We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment and investigate the formation of particle clusters. In the presence of a hard-core interaction, cluster sizes exhibit an algebraically…
Droplets coalescing on flat surfaces tend to end up with the smaller droplet migrating into the larger one. We report a counter-intuitive droplet coalescence pattern on a superhydrophilic cylindrical wire, where the larger droplet is pulled…
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…
We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective…
Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to…
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges…
To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter $q$ and we study the time evolution of the network. The…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
We review recent results on the anomalous transport in one-dimensional and quasi-one-dimensional systems with bulk and surface disorder. Main attention is paid to the role of long-range correlations in random potentials for the bulk…
In an increasingly interconnected world, understanding congestion-related phenomena in transportation and their underlying mechanisms is crucial for improving efficiency. As the transportation system becomes denser, different modes of…
We introduce and study a model of percolation with constant freezing (PCF) where edges open at constant rate 1, and clusters freeze at rate \alpha independently of their size. Our main result is that the infinite volume process can be…
We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: By simulating oxides with a mixture of 2-coordinated and…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…
Theoretical studies of coherent atom transport have as yet mainly been restricted to one-dimensional model systems with harmonic trapping potentials. Here we investigate this important phenomenon -- a prerequisite for a variety of…
Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
The asymptotic behavior of the percolation threshold $p_c$ and its dependence upon coordination number $z$ is investigated for both site and bond percolation on four-dimensional lattices with compact extended neighborhoods. Simple…