Related papers: A Singularity in the Kirchhoff's Circuit Equations
We consider the mathematical treatment of a system of nonlinear partial differential equations based on a model, proposed in 1972 by J. Newman, in which the coupling between the Lithium concentration, the phase potentials and temperature in…
Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
The following is the very first set of the series in 'Problems and Solutions in a Graduate Course in Classical Electrodynamics'. In each of the sets of the problems we intend to follow a theme, which not only makes it unique but also deals…
We investigate the interfacial wave coupling dynamics in liquid metal batteries and their effects to the battery's operation safety. Similar to aluminum reduction cells, liquid metal batteries can be highly susceptible to…
Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms…
This work resolves the open problem of strong singularity ($\alpha(z)> 1$) in nonlocal Kirchhoff-type equations with variable exponents through five original theorems that collectively establish a comprehensive theory. Beginning with…
We consider the problem of optimal charging/discharging of a bank of heterogenous battery units, driven by stochastic electricity generation and demand processes. The batteries in the battery bank may differ with respect to their…
A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within…
This paper follows up a recent debate as to whether classical electrodynamics is inconsistent. I suggest that disagreements can be managed by disambiguating 'theory' in two different ways.
Electrochemical hybrid battery models have major potential to enable advanced physics-based control, diagnostic, and prognostic features for next-generation lithium-ion battery management systems. This is due to the physical significance of…
A multiply connected system in both its open and closed form variations but in equilibrium is studied using quantum waveguide theory. The system exhibits remarkable features, in its open form variation we see current enhancement, hitherto…
Electric current in semiconductors is considered as a function of time. Nonequilibrium fluctuations of the current are studied for strongly nonuniform samples. It is demonstrated that at special conditions the total electric current through…
Recent advances in power system simulation have included the use of complex rectangular current and voltage (I-V) variables for solving the power flow and three-phase power flow problems. This formulation has demonstrated superior…
In this work we deal with elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a right-hand side that is just locally defined in terms of very mild assumptions. Based on an abstract critical…
Electric power systems are undergoing a major transformation as they integrate intermittent renewable energy sources, and batteries to smooth out variations in renewable energy production. As privately-owned batteries grow from their role…
We present the design of an analog circuit which solves linear programming (LP) problems. In particular, the steady-state circuit voltages are the components of the LP optimal solution. The paper shows how to construct the circuit and…
The persistent current of correlated electrons in a continuous one-dimensional ring with a single scatterer is calculated by solving the many-body Schrodinger equation for several tens of electrons interacting via the electron-electron…
The understanding and optimization of solar energy conversion and light emitting devices can greatly benefit from equivalent circuit models describing their response. However, a general model of electron-hole recombination in semiconductors…
With the importance of Li-ion and emerging alternative batteries to our electric future, predicting new sustainable materials, electrolytes and complete cells that safely provide high performance, long life, energy dense capability is…
This talk is assumed to exhibit an overview of the quantum theory for mesoscopic electric circuits and some of its further developments. In the theory the importance of the discreteness of electronic charge in mesoscopic electric circuit is…