Related papers: A Finite-field Approach for $GW$ Calculations Beyo…
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…
Applied magnetic fields can couple to atomic displacements via generalized Lorentz forces, which are commonly expressed as gyromagnetic $g$ factors. We develop an efficient first-principles methodology based on density-functional…
We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
The search for new materials, based on computational screening, relies on methods that accurately predict, in an automatic manner, total energy, atomic-scale geometries, and other fundamental characteristics of materials. Many…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…
In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…
GW approximation is one of the most popular parameter-free many-body methods that goes beyond the limitations of the standard density functional theory (DFT) to determine the excitation spectra for moderately correlated materials and in…
Using many-body perturbation theory within the $G_0W_0$ approximation, we explore routes for computing the ionization potential (IP), electron affinity (EA), and fundamental gap of three gas-phase molecules -- benzene, thiophene, and (1,4)…
Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of…
Performing high accuracy hybrid functional calculations for condensed matter systems containing a large number of atoms is at present computationally very demanding - when not out of reach - if high quality basis sets are used. We present a…
We combine the renormalized singles (RS) Green's function with the T-Matrix approximation for the single-particle Green's function to compute quasiparticle energies for valence and core states of molecular systems. The $G_{\text{RS}}T_0$…
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…
The finite-amplitude method (FAM) is one of the most promising methods for optimizing the computational performance of the random-phase approximation (RPA) calculations in deformed nuclei. In this report, we will mainly focus on our recent…
We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a…