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An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known…
We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve…
Electron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the many-electron wave function. However, invoking a variant of the constrained-search formulation…
A introduction into density-functional theory and electronic structure methods is given, that aims at providing an intuitive understanding of the underlying concepts for the novice as well as an entry point towards the more advanced…
We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…
Electric vector potential $\Theta(\boldsymbol{r})$ is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential $\Phi(\boldsymbol{r})$…
Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…
A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield…
A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…
The effective response depends sensitively on composite microstructure due to large fluctuations in the local electric field. For metallic clusters embedded in a dielectric host, the local field distributions are extremely inhomogeneous in…
Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the…
Fast and accurate computations of the power spectrum of cosmic microwave background fluctuations are essential for comparing current and upcoming data sets with the large parameter space of viable cosmological models. The most efficient…
We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…
We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
Various methods for calculating the capacitance of unloaded rolling elements are compared to improve the electric characterization of rolling element bearings. Semi-analytical approximations and finite element simulations are applied and a…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
For robots that have the capability to interact with the physical environment through their end effectors, understanding the surrounding scenes is not merely a task of image classification or object recognition. To perform actual tasks, it…
We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for…