Related papers: On equivalent resistance of electrical circuits
In this work, we have computed electrical conductivities at ambient conditions of aqueous NaCl and KCl solutions by using the Einstein-Helfand equation. Common force fields (charge q = 1 e) do not reproduce the experimental values of…
Graphical models are a succinct way to represent the structure in probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of…
In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale…
We give identities for the voltage and resistance functions on a metrized graph to show how these functions behave under any edge deletion/contraction and the identification of any two vertices. This leads to explicit versions of Rayleigh's…
We propose the notion of {\it resistance of a graph} as an accompanying notion of the structure entropy to measure the force of the graph to resist cascading failure of strategic virus attacks. We show that for any connected network $G$,…
This paper deals with the design of MEMS using piezoresistivity as transduction principle. It is demonstrated that when the sensor topology doesn't allow a perfect matching of strain gauges, the resolution is limited by the ability of the…
The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector…
We derive an explict bias dependent expression for electron transfer reaction rate from a solvated redox to a electrode through a bridged molecule of arbitrary length. The interaction of the solvated redox with the solvent is modelled as a…
Coaxial 2-terminal bridge comparison is a widely used metrological method in the dissemination of value of capacitance up to 1000 pF and $10^4$ rad/s. In this range, capacitance can be measured with uncertainties as small as few parts in…
We present an approach to learn about electricity and dc electric circuits by using real representational models based on the gravitational analogy. The additively manufactured models are deployed in a small-scale teaching intervention on…
This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…
We study by means of Monte-Carlo numerical simulations the resistance of two-dimensional random percolating networks of stick, widthless nanowires. We use the multi-nodal representation (MNR) to model a nanowire network as a graph. We…
Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to…
We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phase-oscillator's natural…
We study the electrostatic potential of a molecular wire bridging two metallic electrodes in the limit of weak contacts. With the use of a tight-binding model including a fully three-dimensional treatment of the electrostatics of the…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
Soft adhesive pads are needed for many robotics applications, and one approach is based on electroadhesion. Here we present a general analytic model and numerical results for electroadhesion for soft solids with arbitrary time-dependent…
Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…