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Fluctuations of charged particle number are studied in the canonical ensemble. In the infinite volume limit the fluctuations in the canonical ensemble are different from the fluctuations in the grand canonical one. Thus, the well-known…
We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system…
We study a model of random colliding particles interacting with an infinite reservoir at fixed temperature and chemical potential. Interaction between the particles is modeled via a Kac master equation \cite{kac}. Moreover, particles can…
Highly accurate methods such as coupled cluster (CC) techniques can be used for periodic systems within the framework of the method of increments. Its extension to low-dimensional conducting system is considered. To demonstrate the…
A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With…
In this work, we develop an extended uniform potential (UP) model for a membrane nanopore by including two different charging mechanisms of the pore walls, namely by electronic charge and by chemical charge. These two charging mechanisms…
We consider a model for a quantum battery consisting of a collection of $N$ two-level atoms driven by a classical field and decaying to a common reservoir. In the extensive regime, where the energy $E$ scales as $N$ and the fluctuations…
The Particle-In-Cell (PIC) and Monte Carlo Collisions (MCC) methods are workhorses of many numerical simulations of physical systems. Recently, it was pointed out that, while the two methods can be exactly - or nearly - energy-conserving…
Motivated by the century-old problem of modeling the electron as a pointlike particle with finite self energy, we develop a new class of nonlinear perturbations of Maxwell's electrodynamics inspired by, but distinct from, the Born--Infeld…
As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to…
We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilizes an expanded ensemble in which the insertion and deletion of large particles…
Understanding the evolution of electrified solid-liquid interfaces during electrochemical reactions is crucial. However, capturing the dynamic behavior of the interfaces with high temporal resolution and accuracy over long timescales…
The grand canonical potential for a static quark-antiquark pair at non-vanishing chemical potential was determined at several temperatures. The dynamical staggered simulations were carried out with 2+1 physical quarks along the Lines of…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
First-principles dynamical CPA (Coherent-Potential Approximation) for electron correlations has been developed further by taking into account higher-order dynamical corrections with use of the asymptotic approximation. The theory is applied…
Part I of this paper embeds the AC power flow problem with voltage control and exponential load model in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in…
This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a…
Platinum step edges dominate electrocatalytic activity in fuel cells and electrolysers, yet their atomistic electrochemical behaviour remains poorly understood. Here, we employ \textit{ab initio} molecular dynamics under controlled…
We study the effect of enforcing exact conservation of charges in statistical models of particle production for systems as large as those relevant to relativistic heavy ion collisions. By using a numerical method developed for small…
Voltage-based battery metrics are ubiquitous and essential in battery manufacturing diagnostics. They enable electrochemical "fingerprinting" of batteries at the end of the manufacturing line and are naturally scalable, since voltage data…