Related papers: Capacitance matrix revisited
A very simple system like a parallel-plate capacitor reveals striking features when we examine the peculiar phenomena appearing when it is moving at low speed in different directions. Both hidden momentum and hidden energy appear and their…
The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and…
Reduced density matrix functional theory for the case of solids is presented and a new exchange correlation functional based on a fractional power of the density matrix is introduced. We show that compared to other functionals, this…
Analyzing rate-performance data in battery electrodes is greatly facilitated by access to simple analytical models. Here we describe a number of simple equations for fitting capacity-rate data. These equations output fit parameters, such as…
Recently, an unconditional advantage has been demonstrated for the process of charging of a quantum battery in a collisional model. Motivated by the question of whether such an advantage could be observed experimentally, we consider a model…
I discuss a proposed phase diagram of the cuprate superconductors as a function of temperature, carrier concentration, and a strong magnetic field perpendicular to the layers. I show how the phase diagram gives a unified interpretation of a…
Charge sensing in quantum-dot structures is studied by an exactly solvable reduced model and numerical density-matrix renormalization group methods. Charge sensing is characterized by the repeated cycling of the occupation of…
The rigidity of a matrix measures how many of its entries need to be changed in order to reduce its rank to some value. Good lower bounds on the rigidity of an explicit matrix would imply good lower bounds for arithmetic circuits as well as…
The transfer matrix formalism is implemented in the form of the multiple collision technique to account for dissipative transmission processes by using complex potentials in several models of atomic chains. The absorption term is rigorously…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and inside the cavities. The field inside a particular cavity is…
We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and…
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…
A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…
Integrating power electronics with batteries can offer many advantages, including load sharing and balancing with parallel connectivity. However, parallel batteries with differing voltages and power profiles can cause large circulating…
The properties of the known superconductors can be explained with the correlations dominated superconducting mechanism (CSM). The correlations have the spin correlation, the charge correlation and the spin-charge correlation, and their…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
The capacitance between two adjacent nodes on an infinite square grid of identical capacitors can easily be found by superposition, and the solution is found by explotting the symmetry of the grid. The mathematical problem presented in this…
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of…
Consider a unit-resistive plate in the shape of a regular polygon with 2n sides, in which even-numbered sides are wired to electrodes and odd-numbered sides are insulated. The response matrix, or Dirichlet-to-Neumann map, allows one to…