We apply the Poisson equation to the quantum mechanical Coulomb problem for many-particle systems. By introducing a suitable basis set, the two-electron Coulomb integrals become simple overlaps. This offers the possibility of very rapid linear-scaling treatment of the Coulomb contribution to Kohn-Sham theory.

This paper presents two-dimensional (2D) and three-dimensional (3D) numerical simulations of a half-scale geosynthetic reinforced soil (GRS) bridge abutment during construction load application. The backfill was characterized using nonlinear elastoplastic model that incorporates hyperbolic stress–strain relationship the Mohr–Coulomb failure criterion. Geogrid reinforcements were linearly elasti...

To clarify the factors affecting stability of deep-buried hydraulic tunnels containing pore water, elastoplastic theory and Mogi-Coulomb strength criterion were used to derive analytical solutions stress on surrounding rock-lining structure, tunnel wall displacement, plastic zone radius in rock under different operating conditions. During this process, seepage effect interaction considered. The...

The influence of long-range Coulomb interactions on the properties of onedimensional (1D) strongly correlated electron systems in vicinity of the metalinsulator phase transition is considered. It is shown that unscreened repulsive Coulomb forces lead to the formation of a 1D Wigner crystal in the metallic phase and to the transformation of the square-root singularity of the compressibility (cha...

To solve the low-frequency breakdown inherent from the electric field integral equation (EFIE), an alternative new form of the EFIE is proposed by using the Coulomb-gauge Green’s function of quasi-static approximation. Different from the commonly adopted Lorentz-gauge EFIE, the Coulomb-gauge EFIE separates the solenoidal and irrotational surface currents explicitly, which captures inductive and...

Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model the target distribution. We introduce Coulomb GANs, which pose the GAN learnin...

We present a preliminary version of a software package, CHEM1D, that performs molecular orbital calculations on onedimensional atoms and molecules using the unadorned Coulomb operator 1/|x1 − x2|. We describe methods for computing the necessary oneand two-electron integrals and outline the overall structure of the package. We use CHEM1D to perform calculations on a set of small molecules and sh...

We derive diffusive currents in strongly coupled Coulomb ion mixtures in dense stellar matter. Coulomb coupling in the presence of gravity and electric fields, induced by gravity owing to plasma polarization, creates a specific diffusion current which separates ions with the same A/Z (mass to charge number ratios) but different Z. This Coulomb separation can be important in white dwarfs and neu...

Breakup reactions are generally quite complicated, they involve nuclear and electromagnetic forces including interference effects. Coulomb dissociation is an especially simple and important mechanism since the perturbation due to the electric field of the nucleus is exactly known. Therefore firm conclusions can be drawn from such measurements. Electromagnetic matrixelements, radiative capture c...