Related papers: On connecting density functional approximations to…
We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with…
When fitting theory to data in the presence of background uncertainties, the question of whether the spectral shape of the background happens to be similar to that of the theoretical model of physical interest has not generally been…
Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…
The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact…
Model checking and testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, when an…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the…
By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space Gamma,…
We present a brief review of the classical density functional theory of atomic and molecular fluids. We focus on the application of the theory to the determination of the solvation properties of arbitrary molecular solutes in arbitrary…
We combine density-functional theory with density-matrix functional theory to get the best of both worlds. This is achieved by range separation of the electronic interaction which permits to rigorously combine a short-range density…
The analysis of human motion opens up a wide range of possibilities, such as realistic training simulations or authentic motions in robotics or animation. One of the problems underlying motion analysis is the meaningful comparison of…
A spin angular gradient approximation for the exchange correlation magnetic field in the density functional formalism is proposed. The usage of such corrections leads to a consistent spin dynamical approach beyond the local approximation.…
A hard sphere fluid confined by hard, structureless, and parallel walls is investigated using a certain version of weighted density functional theory. The density profile, the excess coverage, the finite size contribution to the free…
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by…
Nuclear mean-field models are briefly reviewed to illustrate its foundation and necessity of state dependence in effective interactions. This state dependence is successfully taken into account by the density dependence, leading to the…
Multiscale and multiphysics applications are now commonplace, and many researchers focus on combining existing models to construct combined multiscale models. Here we present a concise review of multiscale applications and their source…
Nearness theory comes into play in homotopy theory because the notion of closeness between points is essential in determining whether two spaces are homotopy equivalent. While nearness theory and homotopy theory have different focuses and…
Subsystem Density-Functional Theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to…