Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.Comment: 18 pages, 6 figure

Surface phase separation in nanosized charge-ordered manganites

Recent experiments showed that the robust charge-ordering in manganites can be weakened by reducing the grain size down to nanoscale. Weak ferromagnetism was evidenced in both nanoparticles and nanowires of charge-ordered manganites. To explain these observations, a phenomenological model based on surface phase separation is proposed. The relaxation of superexchange interaction on the surface layer allows formation of a ferromagnetic shell, whose thickness increases with decreasing grain size. Possible exchange bias and softening of the ferromagnetic transition in nanosized charge-ordered manganites are predicted.Comment: 4 pages, 3 figure

China's grave demographic challenges in coming decades

This paper systematically analyzes the uncertainties of major demographic indicators from China's 2000 census, such as fertility, gender ratio at birth, and age structure, and through a probability demographic forecast gives an assessment of the situation facing the country. Research outcomes suggest that great differences exist in the estimate of China's fertility, gender ratio at birth and low-age child population. These differences directly affect China's current and future demographic uncertainties, and have implications for policy and future research. The demographic uncertainties caused by current conditions are of great value to decision-makers and the public alike

Sintering-Induced Phase Transformation of Nanoparticles: A Molecular Dynamics Study

Sintering-induced phase transformation of TiO2 nanoparticles is investigated systematically via molecular dynamics simulation. Upon defining a coordination number and bond angle distribution criteria, local phase information is identified for each individual Ti atom originating from amorphous or crystal structure as well as three TiO2 polymorphs, anatase, brookite, and rutile. Size-dependent structures of nanoparticles lead to different dynamics of the sintering-induced phase transformation. Grain boundaries that form between nanoparticles during sintering trigger the nucleation and growth of new phases. During the sintering of two equal-sized core–shell anatase nanoparticles, crystal core regions melt with the temperature increase and the surface energy decrease in the microcanonical (NVE) ensemble. The new phase that develops from the grain boundary spreads into the destroyed core regions in stages, forming a new larger spherical nanoparticle with an ordered atomic arrangement. During the sintering of two unequal-sized nanoparticles (amorphous and core–shell anatase), atoms from the amorphous nanoparticle first nucleate to form crystal anatase in the contact region, and a grain boundary is then developed between the original core region and the newly formed anatase crystal. After that, phase transformation follows much the same route as the equal-sized case from anatase to brookite

Real Scalar Field Scattering with Polynomial Approximation around Schwarzschild-de Sitter Black-hole

As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter black-hole. The complex relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schr$\ddot{o}$dinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm-Liouville type problem. Then this boundary value problem can be solved numerically according to two limiting cases: the first one is the Nariai black-hole whose horizons are close to each other, the second one is when the horizons are widely separated. Compared with previous results (Brevik and Tian), the field near the event horizon and cosmological horizon can have a better description.Comment: revtex4 source file, 11 pages, 8 figure