Related papers: Analytical results for the capacitance of a circul…
A parallel plate capacitor containing an electrolytic solution is the simplest model of a supercapacitor, or electric double layer capacitor. Using both analytical and numerical techniques, we solve the Poisson-Nernst-Planck equations for…
The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonovi\'c et al. [1], is traced back to that of the perturbed Kepler problem. A large class of axially…
Most capacitors do not satisfy the conventional assumption of a constant capacitance. They exhibit memory which is often described by a time-varying capacitance. It is shown that the classical relation, $Q\left(t\right)=CV\left(t\right)$,…
In this work we study a strongly coupled system between the equation of plates with fractional rotational inertial force $\kappa(-\Delta)^\beta u_{tt}$ where the parameter $0 <\beta\leq 1$ and the equation of an electrical network…
The capacitance of arbitrarily shaped objects is reformulated in terms of the Neumann-Poincar\'{e} operator. Capacitance is simply the dielectric permittivity of the surrounding medium multiplied by the area of the object and divided by the…
The capacitance of the electric double layer has potential applications in supercapacitors, and theoretical investigations of the double-layer capacitance in binary mixtures are important. In this work, we develop the theory of the electric…
This study is presented in a series of two papers. The first paper is an analytical study. This is the second paper, and here we numerically study the thermal energy harvesting capability of two electronic circuits. The first circuit…
We study the perfect conductivity problem with closely spaced perfect conductors embedded in a homogeneous matrix where the current-electric field relation is the power law $J=\sigma|E|^{p-2}E$. The gradient of solutions may be arbitrarily…
A general quantitative measure of the tendency towards phase separation is introduced for systems exhibiting phase transitions or crossovers controlled by charge carrier concentration. This measure is devised for the situations when the…
We develop a theory of the conductance of a quantum dot connected to two leads by single-mode quantum point contacts. If the contacts are in the regime of perfect transmission, the conductance shows no Coulomb blockade oscillations as a…
We show how capacitance can be calculated simply and efficiently for electrodes cut in a 2-dimensional ground plane. These results are in good agreement with exact formulas and numerical simulations.
We re-examine a familiar problem given in introductory physics courses, about determining the induced charge distribution on an uncharged ``infinitely-large'' conducting plate when placing parallel to it a uniform charged dielectric plate…
In this article we derive a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying supported boundary conditions. To this end, we combine the use of a suitable conformal mapping which…
In this work we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical Density Functional Theory, and show how this measurable quantity can be used as a probe to better…
Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
We present exact closed-form expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force we confirm that even like-charged…
On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact…
It is shown that the famous paradox of two charged capacitors is successfully resolved if all the energy changes in the system are properly considered when some of the charges are transferred from one capacitor to the other. It happens so…
We study the electrostatics of a thin, finite-length conducting cylindrical shell held at constant potential V0. Exploiting axial symmetry, we recast the problem as a one-dimensional singular integral equation for the axial surface-charge…