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The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
The quest to solve hard combinatorial optimization problems efficiently -- still a longstanding challenge for traditional digital computers -- has inspired the exploration of many alternate computing models and platforms. As a case in…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By inclusion of the kinetic…
The effective potential theory is a physically motivated method for extending traditional plasma transport theories to stronger coupling. It is practical in the sense that it is easily incorporated within the framework of the Chapman-Enskog…
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary…
The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In…
The shifted-i expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or 4-vector potentials. A parameter {\lambda}=0,1 is introduced in such a way that one can obtain the Klein-Gordon…
In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic ($B$ field)…
Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve…
Theoretical calculations are contributing a significantly higher proportion of data to contemporary spectroscopic databases, which have traditionally relied on experimental observations and semi-empirical models. It is now a common…
The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small…
Differential cross sections are computed for the title polar molecule using static interaction, exchange forces and correlation-polarisation effects as described in detail in the main text. The dipole effect is also reported via the dipole…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
The energies of the alkali exchange reactions are computed from density functional calculations for a series of alkali silicate minerals. First-principles calculations are compared against (1) experiment; (2) thermodynamic models; (3)…
Recently, a new testing approach for response-adaptive clinical trials was proposed based on the allocation probabilities (AP) rather than the outcome data. While original work on the AP test focused on binary and normal endpoints and…
Perhaps the simplest first-principles approach to electronic structure is to fit the charge distribution of each orbital pair and use those fits wherever they appear in the entire electron-electron (EE) interaction energy. The charge…
This is a follow-up of our recently proposed work on pseudopotential calculation (Ref. [21]) of atoms and molecules within DFT framework, using cartesian coordinate grid. Detailed results are presented to demonstrate the usefulness,…