Related papers: Finite-amplitude method: An extension to the covar…

The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme…

Complementation of finite automata is a basic operation used in numerous applications. The standard way to complement a nondeterministic finite automaton (NFA) is to transform it into an equivalent deterministic finite automaton (DFA) and…

We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the…

In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system trough a finite element reduction, by composing…

The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA…

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…

Finite resolution analog beamforming (FRAB) has been recognized as an effective approach to reduce hardware costs in massive multiple-input multiple-output (MIMO) and millimeter-wave networks. However, the use of FRAB means that the…

In an effective hadronic theory constructed to describe long-range nuclear physics, the dynamics of the vacuum can be expanded in terms with zero or a finite number of derivatives acting on the fields. Thus vacuum dynamics can always be…

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…

We present an efficient implementation of the random phase approximation (RPA) for molecular systems within the domain-based local pair natural orbital (DLPNO) framework. With optimized parameters, DLPNO-RPA achieves approximately 99.9%…

Recently, random feature attentions (RFAs) are proposed to approximate the softmax attention in linear time and space complexity by linearizing the exponential kernel. In this paper, we first propose a novel perspective to understand the…

We develop a second order correction to commonly used density functional approximations (DFA) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact…

The Hartree-Fock-RPA approach is applied to the 1D anti-ferromagnetic Heisenberg model in the Jordan-Wigner representation. Somewhat contrary to expectation, this leads to reasonable results for spectral functions and sum rules in the…

We extend the capabilities of correlation energy functionals based on the adiabatic-connection fluctuation-dissipation theorem by implementing the analytical atomic forces within the random phase approximation (RPA), in the context of plane…

The focus of the present work is the application of the random phase approximation (RPA), derived for inhomogeneous fluids [Frydel and Ma, Phys. Rev. E 93, 062112 (2016)], to penetrable-spheres. As penetrable-spheres transform into…

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains…

The Monge-Amp\`ere equation is a fundamental fully nonlinear elliptic partial differential equation that finds extensive applications across multiple disciplines. This study proposes a novel physics-informed neural network integrated with…

The paper addresses the problem of optimizing a class of composite functions on Riemannian manifolds and a new first order optimization algorithm (FOA) with a fast convergence rate is proposed. Through the theoretical analysis for FOA, it…

We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using Lanford's map.

The quasistatic approximation (QSA) is an efficient method of simulating laser- and beam-driven plasma wakefield acceleration, but it becomes imprecise if some plasma particles make long longitudinal excursions in a strongly nonlinear wave,…