Related papers: Charge and currents distribution in graphs
In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This…
We calculate the current cross-correlation for two weakly interacting mesoscopic conductors. Our derivation is based on the two-particle scattering matrix derived in Goorden and B\"uttiker [Phys. Rev. Lett. {\bf 99}, 146801 (2007)]. We…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a…
We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…
Accurate electricity demand forecasting is essential for several reasons, especially as the integration of renewable energy sources and the transition to a decentralized network paradigm introduce greater complexity and uncertainty. The…
We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the connectivity is simple (no parallel…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
The transfer-matrix of U(1) lattice gauge theory is investigated in the field Fourier space, the basis of which consists of the quantized currents on lattice links. Based on a lattice version of the current conservation, the transfer-matrix…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum…
We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial…
We study numerically scattering and transport statistical properties of tight-binding random networks characterized by the number of nodes $N$ and the average connectivity $\alpha$. We use a scattering approach to electronic transport and…
In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…
We evaluate the joint distributions of electron waiting times in coherent conductors described by scattering theory. Successive electron waiting times in a single-channel conductor are found to be correlated due to the fermionic statistics…
We propose and analyze a graph model to study the connectivity of interdependent networks. Two interdependent networks of arbitrary topologies are modeled as two graphs, where every node in one graph is supported by supply nodes in the…
We study the inverse problem of determining the conductivity matrix of an electrical network from the prescribed knowledge of the magnitude of the induced current along the edges coupled with the imposed voltage or injected current on the…