Related papers: A Singularity in the Kirchhoff's Circuit Equations
In recent years there has been a major interest in developing all solid state batteries, for the sake of safety (issues due to toxic and flammable organic liquid electrolytes are well known) as well as of high energy density…
Bipartite entanglement entropy is one of the most useful characterizations of universal properties in a many-body quantum system. Far from equilibrium, there exist two highly effective theories describing its dynamics -- the quasiparticle…
We present an alternative one-electron equation for resolving many-electron problem to one-electron approximation and including the exchange and correlation effects in an analytical way, thereby fulfilling the requirements for ab initio…
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…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
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 coupled continuum formulation for the electrostatic, chemical, thermal, mechanical and fluid physics in battery materials. Our treatment is at the particle scale, at which the active particles held together by carbon-binders,…
Batteries are pivotal components in overcoming some of today's greatest technological challenges. Yet to date there is no self-consistent atomistic description of a complete battery. We take first steps toward modeling of a battery as a…
Lithium-ion batteries are used to store energy in electric vehicles. Physical models based on electro-chemistry accurately predict the cell dynamics, in particular the state of charge. However, these models are nonlinear partial…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
Electrochemical and equivalent-circuit modelling are the two most popular approaches to battery simulation, but the former is computationally expensive and the latter provides limited physical insight. A theoretical middle ground would be…
Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion intercalation reactions. Using the recently developed Cahn-Hilliard reaction (CHR) theory, we investigate a simple…
Analogies between mechanical and electrical systems have been developed and applied for almost a century, and they have proved their usefulness in the study of mechanical and electrical systems. The development of new elements such as the…
We outline main challenges for future research in batteries, particularly, addressing the urgent needs of developing new environmentally friendly material solutions to enhance the energy density and safety of these storage devices. This…
A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular…
We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the…
Efficient use of multiple batteries is a practical problem with wide and growing application. The problem can be cast as a planning problem under uncertainty. We describe the approach we have adopted to modelling and solving this problem,…
While the standard (introductory physics) way of computing the equvalent resistance of non-trivial electrical ciruits is based on Kirchhoff's rules, there is a mathematically and conceptually simpler approach, called the method of nodal…
Electric circuits manipulate electric charge and magnetic flux via a small set of discrete components to implement useful functionality over continuous time-varying signals represented by currents and voltages. Much of the same…
This paper showed how a simple lumped parameter model of a circuit can yield correct quantum mechanical predictions of its behavior, even when there is quantum entanglement between components of that circuit. It addresses an important…