Related papers: General analytical solutions for DC/AC circuit net…
Average consensus (AC) strategies play a key role in every system that employs cooperation by means of distributed computations. To promote consensus, an $N$-agent network can repeatedly combine certain node estimates until their mean value…
The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such…
Students often have difficulty in understanding qualitatively the behaviour of simple electric circuits. In particular, as different studies have shown, they find multiple batteries connected in multiple loops difficult to analyse. In a…
An explicit formula for the resistance between two nodes in a network with a non-symmetric Laplacian matrix L is obtained. This is of great advantage e.g. in electronic circuit fault analysis, where non-linear systems have to be solved…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
Not only are Deep Neural Networks (DNNs) black box models, but also we frequently conceptualize them as such. We lack good interpretations of the mechanisms linking inputs to outputs. Therefore, we find it difficult to analyze in…
A resistance network is a connected graph $(G,c)$. The conductance function $c_{xy}$ weights the edges, which are then interpreted as conductors of possibly varying strengths. The Dirichlet energy form $\mathcal E$ produces a Hilbert space…
Transmission line failures in power systems propagate non-locally, making the control of the resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes the patterns of line failure propagation…
This brief examines the behavior of DC circuits comprised of resistively interconnected constant power devices, as may arise in DC microgrids containing micro-sources and constant power loads. We derive a sufficient condition for all…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…
We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) resistors. Generalizing work of Curtis, Ingerman, Morrow, Colin de Verdiere, Gitler, and Vertigan, we characterize…
We probe the stability of Watts-Strogatz DC microgrids, in which droop-controlled producers and constant power load consumers are homogeneously distributed and obey Kirchhoff's circuit laws. The concept of survivability is employed to…
We show existence and uniqueness for a linearized water wave problem in a two dimensional domain $G$ with corner, formed by two semi-axis $\Gamma_1$ and $\Gamma_2$ which intersect under an angle $\alpha\in (0,\pi ]$. The existence and…
Impedance is an intuitive and efficient way for dynamic representation of power electronics devices. One of the evident strengths, when compared to other small-signal methods, is the natural association with circuit theory. This makes them…
A theory of nonlinear dynamics of mixed Abrikosov vortices with Josephson cores (AJ vortices) on low-angle grain boundaries (GB) in superconductors is proposed. Dynamics and pinning of AJ vortices determine the in-field current transport…
Digital circuits representation learning has made remarkable progress in the electronic design automation domain, effectively supporting critical tasks such as testability analysis and logic reasoning. However, representation learning for…
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…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the…
Despite the unsettled mechanism of electricity generation from the continuous flow of liquids on a surface, the charge-discharge theory has been widely accepted for alternating current (AC) generation from a moving droplet. It has been…