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Multiple types of Nyquist-like impedance-based criteria are utilized for the small-signal stability analysis of converter-based AC systems. It is usually considered that the determinant-based criterion can determine the overall stability of…
An $SO(3,3)$ BF-type gauge theory is formulated on a six-dimensional spacetime of split signature $(3,3)$, interpreted as the pre-electroweak-symmetry-breaking phase. A MacDowell--Mansouri-type symmetry breaking to $SU(2)\times SU(2)$ is…
This study presents a finite element analysis approach to non-linear and linearized tensegrity dynamics based on the Lagrangian method with nodal coordinate vectors as the generalized coordinates. In this paper, nonlinear tensegrity…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
Inelastic effects in electron transport through nano-sized devices are addressed with a method based on nonequilibrium Green's functions (NEGF) and perturbation theory to infinite order in the electron-vibration coupling. We discuss the…
In this paper, we modeled and simulated uneven current distribution for on-die interconnect structure. We show significant difference when considering uneven current distribution. Finite Element Method approach is used to analyze various…
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 density functional theory is used to study the electronic structure of a quantum wire in a magnetic field. The Kohn-Sham equations are solved numerically for different values of electron densities and filling factors. The critical…
This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is…
In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…
Systems involving nematic liquid crystals subjected to magnetic fields or electric fields are modeled using the Oseen-Frank macroscopic continuum theory, and general criteria are developed to assess the local stability of equilibrium…
We describe an ab initio method for calculating the electronic structure, electronic transport, and forces acting on the atoms, for atomic scale systems connected to semi-infinite electrodes and with an applied voltage bias. Our method is…
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…
To address the challenges that the decarbonization of the energy sector is bringing about, advanced distribution network management and operation strategies are being developed. Many of these strategies require accurate network models to…
Stacked Intelligent Metasurfaces (SIM) have emerged as a revolutionary architecture for next-generation wireless communications, offering wave-domain signal processing capabilities with significantly reduced hardware complexity compared to…
Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework…
We explore the possibility of using free (as opposed to driven) oscillations to verify wire tension in large, open-frame multiwire planes. Using finite-element simulation we predict the signal when two wires are set in motion by applying…
In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…
In electronic structure calculations, various material properties can be obtained by means of computing the total energy of a system as well as derivatives of the total energy w.r.t. atomic positions. The derivatives, also known as…