相关论文: On the effective impedance of finite and infinite …
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…
In this paper, we study properties of effective impedance of finite electrical networks and calculate the effective impedance of a finite ladder network over an ordered field. Moreover, we consider two particular examples of infinite ladder…
We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving…
The infinite AC ladder network can exhibit unexpected behavior. Entangling the topology brings even more surprises, found by direct numerical investigation. We consider a simple modification of the ladder topology and explain the numerical…
The effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injected at the first node and extracted at the second node, treating edge…
Cascading failures are the typical reasons of black- outs in power grids. The grid topology plays an important role in determining the dynamics of cascading failures in power grids. Measures for vulnerability analysis are crucial to assure…
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…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
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…
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
Output impedances are inherent elements of power sources in the electrical grids. In this paper, we give an answer to the following question: What is the effect of output impedances on the inductivity of the power network? To address this…
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…
For a given infinite connected graph $G=(V,E)$ and an arbitrary but fixed conductance function $c$, we study an associated graph Laplacian $\Delta_{c}$; it is a generalized difference operator where the differences are measured across the…
Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of…
In this survey, we present the basic facts about conduction in infinite networks. This survey is based on the work of Flanders, Zemanian, and Thomassen, who developed the theory of infinite networks from scratch. Here we show how to get a…
We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's…
We consider infinite weighted graphs $G$, i.e., sets of vertices $V$, and edges $E$ assumed countable infinite. An assignment of weights is a positive symmetric function $c$ on $E$ (the edge-set), conductance. From this, one naturally…
In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective…