Related papers: Experimental determination of circuit equations
The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…
Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion…
Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a…
In this paper we present a very simple proof of the existence of at least one non trivial solution for a Kirchhoff type equation on $\RN$, for $N\ge 3$. In particular, in the first part of the paper we are interested in studying the…
In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis,…
We consider a general stable flow problem in a directed and capacitated network, where each vertex has a strict preference list over the incoming and outgoing edges. A flow is stable if no group of vertices forming a path can mutually…
Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable…
Transistors are the cornerstone of modern electronics. Yet, their relatively complex characteristics, allied with often observed great parameter variation, remain a challenge for discrete and integrated electronics. Much of transistor…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
We propose a novel method for a solution of a system of linear equations with the non-negativity condition. The method is based on the Tikhonov functional and has better accuracy and stability than other well-known algorithms.
The redistribution of electrical currents in resistor networks after single-bond failures is analyzed in terms of current-redistribution factors that are shown to depend only on the topology of the network and on the values of the bond…
Studying Birkhoff sums of non-integrable functions involves the challenge of large observations depending on the sampled orbit, which prevents pointwise limit theorems. To address this issue, the largest observations are removed, this…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics…
We consider M systems (each an electron in a long square cylinder) uniformly arranged on a ring and with Coulomb interactions. Exact straightforward numerical time-dependent perturbation calculation of a single N-level ($\lesssim 7$)…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem…
We study the asymptotic behavior of the solutions of the mildly degenerate Kirchhoff equation with a dissipative term. We obtain a new estimate on second-in-time derivative of the solution. Moreover we renormalize the solution in such a way…
The analysis of nonlinear interaction of transversal electromagnetic field with quantum collisionless plasma is carried out. Formulas for calculation electric current in quantum collisionless plasma at any temperature are deduced. It has…