We derive rigorously, for both R and [−L,L], the cubic nonlinear Schrödinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cub...

We derive rigorously, for both R and [−L,L], the cubic nonlinear Schrödinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cub...

We derive rigorously, for both R2 and [−L, L]×2, the cubic nonlinear Schrödinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the...

As an attractive high-entropy alloy, AlCrCoNiCu alloy has excellent corrosion resistance, wear and anti-bacterial capabilities, is considered to be a potential substitute material for marine nuclear industry materials with great potential. One key further optimizing the performance of high entropy was prepare powder uniform composition, good flow-ability, stable performance. In this work, prepa...

In volume visualization, the Cartesian grid is by far the most popular type of grid because it is convenient to handle. But it requires 29.3% more samples than the BodyCentered Cubic grid. In order to convince people used to Cartesian grids for years of the advantages of BodyCentered Cubic grids, we must prove their usability in many different volume rendering algorithms. Therefore we introduce...

Results of numerical modeling of dilute 2D and 3D crystalline lattices are presented. The percolation thresholds for face-centered cubic (fcc), body-centered cubic (bcc) and the simple cubic (sc) lattices for the first, second and third coordination spheres are obtained by means of Monte Carlo (MC) method. It is shown, that the mean value of the percolation cluster density has a minimum value a...