Related papers: On equivalent resistance of electrical circuits
In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the…
The Randles circuit (including a parallel resistor and capacitor in series with another resistor) and its generalised topology have widely been employed in electrochemical energy storage systems such as batteries, fuel cells and…
Let $G=(V,E)$ be a random electronic network with the boundary vertices which is obtained by assigning a resistance of each edge in a random graph in $\mathbb{G}(n,p)$ and the voltages on the boundary vertices. In this paper, we prove that…
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…
Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…
Let $r(u,v)$ be the resistance distance between two vertices $u, v$ of a simple graph $G$, which is the effective resistance between the vertices in the corresponding electrical network constructed from $G$ by replacing each edge of $G$…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
The validity of the comparison principle in variable coefficient fully nonlinear gradient free potential theory is examined and then used to prove the comparison principle for fully nonlinear partial differential equations which determine a…
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…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
An equivalent circuit model for Frequency Selective Surfaces (FSS) comprising anisotropic elements is presented. The periodic surface is initially simulated with an arbitrary azimuthal incidence angle and its surface impedance matrix is…
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 develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to…
The complex ac-response of a quasi-one dimensional electron system in the one-band approximation with an interaction potential of finite range is investigated. It is shown that linear response is exact for this model. The influence of the…
The spatial variation and temporal variation in surface potential are important error sources in various precision experiments and deserved to be considered carefully. In the former case, the theoretical analysis shows that this effect…
Electric vector potential $\Theta(\boldsymbol{r})$ is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential $\Phi(\boldsymbol{r})$…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
An analytical formula for electrical impedance between an adherent living cell and sensor substrate measured using a microelectrode is presented for the first time. Previously-reported formula has been applicable only for the case where…
We show how to describe the coupling of electrons to non-uniform magnetic fields in the framework of the widely used norm-conserving pseudopotential appro ximation for electronic structure calculations. Our derivation applies to magnetic…