Related papers: Experimental determination of circuit equations
We have implemented the linear response approximation of a method proposed to compute the electron transport through correlated molecules based on the time-independent Wigner function [P. Delaney and J. C. Greer, \prl {\bf 93}, 36805…
A system of reduced equations is proposed for the electron motion in the strongly-radiation dominated regime for an arbitrary electromagnetic field configuration. The developed approach is used to analyze various scenarios of an electron…
The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is…
I argue that the validity of the new electrodynamic equations for superconductors proposed in my paper can and should be decided by experiment. Furthermore I show that BCS theory is ambiguous in its prediction of screening of longitudinal…
In this paper we describe a couple of exercises that we developed for our online first-year EM course. The labs that we describe are focused on basic concepts from circuit analysis, namely Ohm's law and charging a capacitor with a constant…
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…
A formulation for transport in an inhomogeneous, interacting electron gas is described. Electronic current is induced by a constraint condition imposed as a vector Lagrange multiplier. Constrained minimization of the total energy functional…
We discuss an earlier application of the Ritz variational method for strongly nonlinear problems. We clearly prove that the results derived for several extremely simple problems of supposedly physical and mathematical interest do not…
Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing…
After a rich history in medicine, randomisation control trials both simple and complex are in increasing use in other areas such as web-based AB testing and planning and design decisions. A main objective is to be able to measure…
Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
The extraction of transition frequencies from a spectrum has conventionally relied on empirical methods, and particularly in complex systems, it is a time-consuming and cumbersome process. To address this challenge, we establish a…
Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena.…
This paper gives a general treatment and proof of the direct conservation law method presented in Part I. In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators the dynamics can be understood in terms of lower dimensional equations This is the case for instance of…
We study here the small time dynamics of $N$ electrons on the circle with Coul;omb repulsive interaction and study the series for the velocities (initially zero). The main result is the estimates of the convergence radius from below. We…
The problem of a conducting checkerboard has recently been solved via an elliptic function whose argument is another elliptic function. The behavior of the fields and currents near a vertex of the checkerboard pattern can be discussed by…
Circuit models involving bulk currents and inductances are often used to estimate the energies of coronal magnetic field configurations, in particular configurations associated with solar flares. The accuracy of circuit models is tested by…