Related papers: Effective Impedance over Ordered Fields
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigen-vectors of the graph Laplacian. Graph laplacians are used to find low dimensional structures in high…
Lattices of compatibly embedded finite fields are useful in computer algebra systems for managing many extensions of a finite field $\mathbb{F}_p$ at once. They can also be used to represent the algebraic closure $\bar{\mathbb{F}}_p$, and…
In Refs.[1] and [2], calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on the stratification of the network and Stieltjes function associated with the…
The effective conductivity ($T^{eff}$) of 2D and 3D Random Resistor Networks (RRNs) with random edge conductivity are studied. The combined influence of geometrical disorder, which controls the overall connectivity of the medium, and leads…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
The problem of cascading failures in cyber-physical systems is drawing much attention in lieu of different network models for a diverse range of applications. While many analytic results have been reported for the case of large networks,…
Cascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly…
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…
We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…
We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
Based upon the resistor analogy and using the ideal loop gas approximation(ILGA) it is shown that only pending loops reduce the modulus of an otherwise perfect network made of monodisperse strands and junctions of identical functionality.…
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
The dynamic response of power grids to small disturbances influences their overall stability. This paper examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework…
The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix…
The correct definition of the conductance of finite systems implies a connection to the system of the massive ideal leads. Influence of the latter on the properties of the system appears to be rather essential and is studied below on the…
Here we report a comprehensive analysis of the robustness of five high-quality real-world complex weighted networks to errors and attacks of nodes and links. We analyze C. Elegans, Cargo ship, E. Coli, Us Airports and Human brain real-world…
Effective resistance is a distance between vertices of a graph that is both theoretically interesting and useful in applications. We study a variant of effective resistance called the biharmonic distance. While the effective resistance…
This paper explores whether graph embedding methods can be used as a tool for analysing the robustness of power-grids within the framework of network science. The paper focuses on the strain elevation tension spring embedding (SETSe)…
We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load…