相关论文: Characterization of the response maps of alternati…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
The response matrix of a resistor network is the linear map from the potential at the boundary vertices to the net current at the boundary vertices. For circular planar resistor networks, Curtis, Ingerman, and Morrow have given a necessary…
Consider a unit-resistive plate in the shape of a regular polygon with 2n sides, in which even-numbered sides are wired to electrodes and odd-numbered sides are insulated. The response matrix, or Dirichlet-to-Neumann map, allows one to…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
In this paper we deal with the notion of the effective impedance of AC networks consisting of resistances, coils and capacitors. Mathematically such a network is a locally finite graph whose edges are endowed with complex-valued weights…
Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…
The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of…
During routine state space circuit analysis of an arbitrarily connected set of nodes representing a lossless LC network, a matrix was formed that was observed to implicitly capture connectivity of the nodes in a graph similar to the…
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…
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…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
Starting with an experimentally observed networks of actin bundles, we model their network structure in terms of edges and nodes. We then compute and discuss the main electrical parameters, considering the bundles as electrical wires. A set…
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…
Networks constructed out of resistors, inductors, capacitors and transformers form a compelling subclass of simple models. Models constructed out of these basic elements are frequently used to explain phenomena in large-scale applications,…
We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
Resistive electrical networks constitute a beautiful example of open, interconnected, large-scale systems, giving rise to an elegant classical mathematical theory, still posing open problems and suggesting important extensions.
This overview presents a collection of results from classical electrical network theory concerning properties of the network admittance matrix, and the relationship between electrical characteristics of the network and various mathematical…