相关论文: First-principles analysis of nanoelectromechanical…
A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wave number. It is proved rigorously that the standard residual type error estimator seriously underestimates…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
Tuning the frequency of a resonant element is of vital importance in both the macroscopic world, such as when tuning a musical instrument, as well as at the nanoscale. In particular, precisely controlling the resonance frequency of isolated…
We develop a first-principles computational method for investigating the dielectric screening in extended systems using the self-consistent Sternheimer equation and localized non-orthogonal basis sets. Our approach does not require the…
We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions…
Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of…
We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…
The FEL gain formulas for non-resonant case are studied. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that…
Ejection fraction (EF) of the left ventricle (LV) is considered as one of the most important measurements for diagnosing acute heart failure and can be estimated during cardiac ultrasound acquisition. While recent successes in deep learning…
Electrical currents in low-dimensional quantum materials can drive electrons far from equilibrium, creating stark imbalance between electron and lattice temperatures. Yet, no existing methods enable simultaneous nanoscale mapping of both…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
The ability to create superlattices in van der Waals (vdW) heterostructures via moir\'e interference heralded a new era in the science and technology of two-dimensional materials. Through precise control of the twist angle, flat bands and…
A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…
This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier-Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain…
Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem…
This study investigates the spatio-temporal evolution of the electric field during the early stages of a nanosecond positive corona discharge in atmospheric-pressure air by combining time-resolved E-FISH measurements,…
The plasmon response of metallic nanostructures is anticipated to exhibit nonlocal dynamics of the electron gas when exploring the true nanoscale. We extend the local-response approximation (based on Ohm's law) to account for a general…
Understanding of bonding is key to modelling materials and predicting properties thereof. A widely adopted indicator of bonds and atomic shells is the electron localization function (ELF). The building blocks of the ELF are also used in the…
A formalism for incorporating electron-phonon scattering into the nonequilibrium Green's function (NEGF) framework that is applicable to planar MOSFETs is presented. Restructuring the NEGF equations in terms of approximate summation of…