Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.

Study on the Polarization Effect by Ce Doping in MnSb Alloy

Using discrete variational X. method within the local-density-functional theory and cluster models, the electronic structure and magnetic property or MnSh(Ce) are investigated.It is round that Sb5p state is much polarized by Ce doping.The spin moment of Sb changes from -0.06 V,in MnSh to -0.32μb, in MnSh(Ce).The interaction between Mn and doped Ce is small compared with that between Sb and Ce in MnSh(Ce).The influence to the magneto-optical Property of MnSh by the doped Ce is discussed. It is expected that the Sb-5p polarization caused by Ce will make MnSh(Ce)a promising magneto-optical material.

Study of electronic structures and absorption bands of BaMgF_4 crystal with F colour centre

The electronic structures of BaMgF4 crystals containing an F colour centre are studied within the framework of the fully relativistic self-consistent Direc-Slater theory, using a numerically discrete variational （DV-Xa） method. It is concluded from the calculated results that the energy levels of the F colour centre are located in the forbidden band. The optical transition energy from the ground state to the excited state for the F colour centre is about 5.12 eV, which corresponds to the 242-nm absorption band. These calculated results can explain the origin of the absorption bands.

The Theoretical Study of O_2 Adsorption on NiTi (100) and (110) Surfaces

The discrete variational Xα method (DV-Xα) within the framework of density-functional theory was applied to study O 2 molecule adsorption on NiTi (100) and (110) surfaces.The bond order and charge distribution between Ti and O atoms for two possible O 2 molecule adsorption ways on NiTi(100) and (110) surfaces were calculated.It is found that the adsorption way for O-O bond perpendicular to NiTi surface is preferred to that for O-O bond parallel to NiTi surface,and O 2 molecule only interacted with one nearest surface titanium atom during the adsorption process.Mulliken population and the partial density of state analysis show that the interaction between Ti and O atoms is mainly donated by O 2p and Ti 4s electrons on NiTi(110) surface,O 2p and Ti 4s,4p electrons on NiTi(100) surface,respectively.The total density of state analysis shows that NiTi(100) surface is more favorable for O 2 molecule adsorption.

A Structure-Preserving Numerical Method for the Fourth-Order Geometric Evolution Equations for Planar Curves

For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a structure-preserving method based on a discrete variational derivative method.Furthermore,to prevent the vertex concentration that may lead to numerical instability,we discretely introduce Deckelnick’s tangential velocity.Here,a modification term is introduced in the process of adding tangential velocity.This modified term enables the method to reproduce the equations’properties while preventing vertex concentration.Numerical experiments demonstrate that the proposed approach captures the equations’properties with high accuracy and avoids the concentration of vertices.