Related papers: Low-Order Mathematical Modelling of Electric Doubl…
We analyze a realistic microscopic model for electronic scattering with the neutral differential delay equations of motion of point charges of the Wheeler-Feynman electrodynamics. We propose a microscopic model according to the…
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
We analyze how accurately supervised machine learning techniques can predict the lowest energy levels of one-dimensional noninteracting ultracold atoms subject to the correlated disorder due to an optical speckle field. Deep neural networks…
We propose and discuss a numerical method to model electromagnetic emission from the oscillating relativistic charged particles and its coherent amplification. The developed technique is well suited for free electron laser simulations, but…
The spectral element method constructed by the $Q^k$ ($k\geq 2$) continuous finite element method with $(k+1)$-point Gauss-Lobatto quadrature on rectangular meshes is a popular high order scheme for solving wave equations in various…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
Using molecular dynamics simulations with recently developed importance sampling methods, we show that the differential capacitance of a model ionic liquid based double-layer capacitor exhibits an anomalous dependence on the applied…
Electric double-layer capacitors (EDLCs), consisting of an ionic fluid between two metallic electrodes, are electrochemical energy storage devices complementary to batteries, allowing for a faster charge/discharge. The charging dynamics in…
This study presents a comprehensive analysis of a two-level battery charger for electric vehicles, focusing on modeling, simulation, and performance evaluation. The proposed charger topology employs two switches operating complementarily,…
The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that…
We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous…
Temperature dependence of the capacitance of the electrical double layer (EDL) in concentrated electrolytes/ionic liquids has been under debates for decades. To rationalise the capacitance vs temperature dependence, we run molecular…
We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen--Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method.…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Over the past decade, experimental microscopy and spectroscopy have made significant progress in the study of the morphological, optical, electronic and transport properties of materials. These developments include higher spatial…
We investigate the electric double layer formed between charged walls of a slit-like pore and a solvent primitive model (SPM) for electrolyte solution. The recently developed version of the weighted density functional approach for…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…