相关论文: Compressed Wannier modes found from an $L_1$ regul…

We study existence, unicity and other geometric properties of the minimizers of the energy functional $$ \|u\|^2_{H^s(\Omega)}+\int_\Omega W(u)\,dx, $$ where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the $H^s$…

We have constructed maximally-localized Wannier functions for prototype structures of solid molecular hydrogen under pressure, starting from LDA and tight-binding Bloch wave functions. Each occupied Wannier function can be associated with…

We present an approach to parameterize DFT+$U$+$V$ from hybrid-functional calculations using Wannier-function projections. The method constructs a common localized Wannier basis for both semilocal DFT and hybrid-functional calculations,…

Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…

We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the…

It is proved that for general, not necessarily periodic quasi one dimensional systems, the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial…

Optimal tuning of functional parameters in density functional theory approximations, based on enforcing the ionization potential theorem, has emerged as the method of choice for the non-empirical prediction of the electronic structure of…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…

We introduce a dispersive regularization of the compressible Euler equations in Lagrangian coordinates, in the one-dimensional torus. We assume a Van der Waals pressure law, which presents both hyperbolic and elliptic zones. The dispersive…

A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…

A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state…

In this paper we study ergodicity and mixing property of some measure preserving transformations on the Wiener space (W,H,\mu) which are generated by some random unitary operators defined on the Cameron-Martin space H.

We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…

We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…

Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different…

A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and…

We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…

In a tight-binding lattice model with $n$ orbitals (single-particle states) per site, Wannier functions are $n$-component vector functions of position that fall off rapidly away from some location, and such that a set of them in some sense…