Related papers: Theory of resistor networks: The two-point resista…
This paper presents an introduction and expository account of a beautiful, current, and active application of recursions to the computation of resistance distance. Resistance distance, also referred to as effective resistance, is a…
The adjacency and Laplacian matrices of complex networks with two species of nodes are studied and the spectral density is evaluated by using the replica method in statistical physics. The network nodes are classified into two species (A…
We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
This tutorial paper shows how to compute the DC (or low-frequency) resistance, inductance and capacitance of a pair of parallel wires using the finite element method. A three-dimensional infinite domain (open boundary) modeling of…
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…
This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights. The definiteness of the weighted Laplacian is studied in terms of certain matrices that are related via congruent and similarity…
We derive a two-terms asymptotics for eigenvalues of the Dirichlet Laplacian in a narrow strip of variable width. The asymptotics is taken with respect to a small paprameter that characterizes the width of the strip.
We study the robustness of interdependent networks where two networks are said to be interdependent if the operation of one network depends on the operation of the other one, and vice versa. In this paper, we propose a model for analyzing…
A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…
This paper addresses the problem of bearing-based network localization, which aims to localize all the nodes in a static network given the locations of a subset of nodes termed anchors and inter-node bearings measured in a common reference…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
The main contribution of this paper is a six-step semi-automatic algorithm that obtains a recursion satisfied by a family of determinants by systematically and iteratively applying Laplace expansion to the underlying matrix family. The…
Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
Pattern formation, arising from systems of autonomous reaction-diffusion equations, on networks has become a common topic of study in the scientific literature. In this work we focus primarily on directed networks. Although some work prior…
In a recent experiment, the out-of-plane surface susceptibility of a single-layer two-dimensional atom crystal in the visible spectrum has been measured. This susceptibility gives a measurable contribution to the reflectivity of…
In heterogeneous system, the correspondence between calculated and measured quantities, such as the conductivity or the resistivity, is not obvious since the former ones are local quantities whereas the latter ones are often average values…
We study electric properties of random resistor networks consisting of resistors of two kinds numerically, focusing on the power loss across each bond. Tuning the ratio of the resistances $r$ and their respective fraction $\alpha$ we find…