Related papers: Spatial Dependence of Microscopic Percolation Cond…
Many realistic systems such as infrastructures are characterized by spatial structure and anisotropic alignment. Here we propose and study a model for dealing with such characteristics by introducing a parameter that controls the strength…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
Power lines, roadways, pipelines and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of…
We have obtained the universal conductance distribution of two-dimensional disordered systems in the strongly localized limit. This distribution is directly related to the Tracy-Widom distribution, which has recently appeared in many…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
Nonlocal currents, in devices where two normal metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev…
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we…
We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various…
We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size of the…
Network percolation has recently been proposed as a method to characterize the global structure of an urban system form the bottom-up. This paper proposes to extend urban network percolation in a multi-dimensional way, to take into account…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio of the complex conductances of both phases. We propose an algorithm to determine the conductance of a finite network, in…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
Almost all network research has been focused on the properties of a single network that does not interact and depends on other networks. In reality, many real-world networks interact with other networks. Here we develop an analytical…
Using the integral equations of the Noncrossing Approximation, the differential conductance is computed as a function of voltage for scattering from a two channel Kondo impurity in a point contact. The results compare well to experimental…