Related papers: Low-Order Mathematical Modelling of Electric Doubl…
We present the first application of phase field modeling to electrochemistry. A free energy functional that includes the electrostatic effect of charged particles leads to rich interactions between concentration, electrostatic potential,…
This study evaluates numerical discretization methods for the Single Particle Model (SPM) used in electrochemical modeling. The methods include the Finite Difference Method (FDM), spectral methods, Pad\'e approximation, and parabolic…
Modelling electrolytes accurately on both a nanoscale and cell level can contribute to improving battery chemistries.[Armand and Tarascon, Nature, 2008, 451, 652-657] We previously presented a thermodynamic continuum model for…
Understanding the electrical double layer (EDL), i.e, the distribution of electrolyte at an electrified interface, in concentrated electrolytes is important for various technologies, such as supercapacitors, batteries and electrocatalysis.…
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…
The electrical double layer (EDL) is fundamental to the operation of devices for electrochemical energy storage and conversion. Existing models of EDL in solid electrolytes focus predominantly on the space charge layer and lack a complete…
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…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem…
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…
A parallel plate capacitor containing an electrolytic solution is the simplest model of a supercapacitor, or electric double layer capacitor. Using both analytical and numerical techniques, we solve the Poisson-Nernst-Planck equations for…
Continuum solvation models are becoming increasingly relevant in condensed matter simulations, allowing to characterize materials interfaces in the presence of wet electrified environments at a reduced computational cost with respect to all…
The electric double layer is an important structure that appears at charged liquid interfaces, and it determines the performance of various electrochemical devices such as supercapacitors and electrokinetic energy converters. Here the…
Studying time-dependent behavior in lasers is analytically difficult due to the saturating non-linearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time…
The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several…
This paper presents transient numerical simulations of hydraulic systems in engineering applications using the spectral element method (SEM). Along with a detailed description of the underlying numerical method, it is shown that the SEM…
We introduce new numerical integration operators which compose the mass and stiffness matrices of a modified spectral element method for simulation of elastic wave propagation. While these operators use the same quadrature nodes as does the…
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…
We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…
Electron energy loss spectroscopy is consolidating as a powerful tool to explore electronic (as well as vibrational) excitations of matter, including molecules. Performed in a scanning transmission electron microscope, this technique is…