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We propose a tensor-based criterion for benign landscape in phase retrieval and establish boundedness of gradient trajectories. This implies that gradient descent will converge to a global minimum for almost every initial point.
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes…
We present a systematic study that clarifies validity and limitation of current hybrid functionals in density functional theory for structural and electronic properties of various semiconductors and insulators. The three hybrid functionals,…
The Bethe-Salpeter equation (BSE) combined with the Green's function GW method has successfully transformed into a robust computational tool to describe light-matter interactions and excitation spectra for molecules, solids, and materials…
The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…
Relaxed atomic geometries and chemisorption energies have been calculated for the dissociative adsorption of molecular hydrogen on vicinal Si(001) surfaces. We employ density-functional theory, together with a pseudopotential for Si, and…
It is known that the adiabatic approximation in time-dependent density functional theory usually provides a good description of low-lying excitations of molecules. In the present work, the capability of the adiabatic nonempirical…
We introduce a generalization (gLDA) of the traditional Local Density Approximation (LDA) within density functional theory. The gLDA uses both the one-electron Seitz radius $\rs$ and a two-electron hole curvature parameter $\eta$ at each…
The structure, electronic and dynamic properties of the two layered alpha (litharge) and beta (massicot) phases of PbO have been studied by density functional methods. The role of London dispersion interactions as leading component of the…
Smooth, highly accurate analytical representations of Fermi-Dirac (FD) integral combinations important in free-energy density functional calculations are presented. Specific forms include those that occur in the local density approximation…
We have investigated the conditions necessary to achieve stronger Cherenkov-like instability of plasma waves leading to emission in the terahertz (THz) regime for semiconductor quantum wells (QWs). The surface response function is…
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i)…
The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson--Boltzmann equation, which takes into account the finite size of the ions is presented. We obtain analytical expressions…
A revised version of the semilocal exchange-correlation functional [Phys. Rev. Lett. 117, 073001 (2016)] (TM) is proposed by incorporating the modifications to its correlation content obtained from the full high-density second-order…
Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state,…
For the recently developed particle-hole dispersive optical model, weak violations of unitarity due to a phenomenological description of the spreading effect are considered. Methods for unitarity restoration are proposed and implemented for…
The model of point particle in general external fields is considered and the generalized equivalence principle is suggested identifying all backgrounds which give rise to equivalent particle dynamics. The equivalence transformations for…
One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the problem to linear combinations of Dirac deltas and then perform…
This paper presents an extension of the recently introduced planewave density interpolation (PWDI) method to the electric field integral equation (EFIE) formulation of problems of scattering and radiation by perfect electric conducting…
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…