Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table

First-principles Calculations of Engineered Surface Spin Structures

The engineered spin structures recently built and measured in scanning tunneling microscope experiments are calculated using density functional theory. By determining the precise local structure around the surface impurities, we find the Mn atoms can form molecular structures with the binding surface, behaving like surface molecular magnets. The spin structures are confirmed to be antiferromagnetic, and the exchange couplings are calculated within 8% of the experimental values simply by collinear-spin GGA+U calculations. We can also explain why the exchange couplings significantly change with different impurity binding sites from the determined local structure. The bond polarity is studied by calculating the atomic charges with and without the Mn adatoms

Coexistence and competition of multiple charge-density-wave orders in rare-earth tri-telluride RTe3

The occurrences of collective quantum states, such as superconductivity (SC) and charge- or spin-densitywaves (CDWs or SDWs), are among the most fascinating phenomena in solids. To date much effort has been made to explore the interplay between different orders, yet little is known about the relationship of multiple orders of the same type. Here we report optical spectroscopy study on CDWs in the rare-earth tri-telluride compounds RTe3 (R = rare earth elements). Besides the prior reported two CDW orders, the study reveals unexpectedly the presence of a third CDW order in the series which evolves systematically with the size of R element. With increased chemical pressure, the first and third CDW orders are both substantially suppressed and compete with the second one by depleting the low energy spectral weight. A complete phase diagram for the multiple CDW orders in this series is established.Comment: 7 pages, 4 figures, 1 tabl