Related papers: Experimental determination of circuit equations
This paper describes an electric circuit lab exercise that offers various ways of comparing the equivalent electrical resistance of three-resistor circuits. It requires the use of two multi-meters, a power supply, cables and connectors, an…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
We build bounded solutions to a linear integral equation. Our functions are built as limit of iterated Birkhoff sums over auto-similar dynamical systems. Nous construisons des solutions born\'ees \`a une \'equation int\'egrale. Notre…
This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…
We design a set of classical macroscopic electric circuits in which charge exhibits the mobility restrictions of fracton quasiparticles. The crucial ingredient in these circuits is a transformer, which induces currents between pairs of…
While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is…
We derive the general circuit equations and system models directly from four Maxwell's equations and develop the electric-charge-based and magnetic-flux-based analysis methodologies to unify the analyses for both phase-independent circuits…
We consider Kirchhoff equations with strong damping, namely with a friction term which depends on a power of the "elastic" operator. We address local and global existence of solutions in two different regimes depending on the exponent in…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
For the first time a method is devised for non-iterative modeling of motion of a radiating, electrified pointlike mass that has an internal structure. New, supplementary kinetic constants of accelerated charged particles are defined, that…
Inaccurate circuits make possible the conservation of limited resources, such as energy. But effective design of such circuits requires an understanding of resulting tradeoffs between accuracy and design parameters, such as voltages and…
Objective: To derive a closed-form analytical solution to the swing equation describing the power system dynamics, which is a nonlinear second order differential equation. Existing challenges: No analytical solution to the swing equation…
The action of certain static magnetic fields on charged test particles is interpreted as a consequence of the interaction of the particles with electric dipole distributions emitted by other charged particles in relative motion. The dipole…
In a recent paper [Phys. Rev. B{\bf57}, 3375 (1998)], we examined in detail the nonlinear (electrical) dc response of a random resistor cum tunneling bond network ($RRTN$, introduced by us elsewhere to explain nonlinear response of…
In this paper we consider a generalized Kirchhoff? equation in a bounded domain under the effect of a sublinear nonlinearity. Under suitable assumptions on the data of the problem we show that, with a simple change of variable, the equation…
A novel dielectric scheme is proposed for strongly coupled electron liquids that handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of…
With the rapid development of renewable and distributed energies, the underlying dynamics of power systems are no longer dominated by large synchronous generators, but by numerous dynamic components with heterogeneous characteristics. In…
Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of…
In this article, we are interested in semilinear, possibly degenerate elliptic equations posed on a general network, with nonlinear Kirchhoff-type conditions for its interior vertices and Dirichlet boundary conditions for the boundary ones.…
We propose a novel, fully explainable neural approach to synthesis of combinatorial logic circuits from input-output examples. The carrying advantage of our method is that it readily extends to inductive scenarios, where the set of examples…