Related papers: Experimental determination of circuit equations
In this article, we consider nonlocal Hamilton-Jacobi Equations on networks with Kirchhoff type conditions for the interior vertices and Dirichlet boundary conditions for the boundary ones: our aim is to provide general existence and…
Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Although we will consider various shapes (e.g. we find all the…
The modified nodal analysis (MNA) is probably the most widely used formulation for the modeling and simulation of electric circuits. Its conventional form uses electric node potentials and currents across inductors and voltage sources as…
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…
The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The…
New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another…
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's…
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…
Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes,…
Over the past decade, Rydberg atom electric field sensors have been under investigation as potential alternatives or complements to conventional antenna-based receivers for select applications in RF communications, remote sensing, and…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
Exact eigendecomposition of large matrices is very expensive, and it is practically impossible to compute exact eigenvalues. Instead, one may set a more modest goal of approaching the empirical distribution of the eigenvalues, recovering…
We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the…
In 1857, Kirchhoff published two seminal papers on the motion of electricity in wires. In that work, he was the first to derive what we now call the telegrapher`s equations, which describes the propagation of electromagnetic signals along a…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…
To be practically useful, modern static analyzers must precisely model the effect of both, statements in the programming language as well as frameworks used by the program under analysis. While important, manually addressing these…
We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in. e.g., first-principles-based simulations of…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…