Stability of the surface area preserving mean curvature flow in Euclidean space

We show that the surface area preserving mean curvature flow in Euclidean space exists for all time and converges exponentially to a round sphere, if initially the L^2-norm of the traceless second fundamental form is small (but the initial hypersurface is not necessarily convex).Comment: 17 page

Spin-polarized currents generated by magnetic Fe atomic chains

Fe-based devices are widely used in spintronics because of high spin-polarization and magnetism. In this work, free-standing Fe atomic chains were proposed to be used as the thinnest wires to generate spin-polarized currents due to the spin-polarized energy bands. By ab initio calculations, the zigzag structure was found more stable than the wide-angle zigzag structure and has higher ratio of spin-up and spin-down currents. By our theoretical prediction, Fe atomic chains have sufficiently long thermal lifetime only at T<=150 K, while C atomic chains are very stable even at T=1000 K. This result means that the spintronic devices based on Fe chains could only work at low temperature. A system constructed by a short Fe chain sandwiched between two graphene electrodes was proposed as a spin-polarized current generator, while a C chain does not have such property. The present work may be instructive and meaningful to further practical applications based on recent technical development on the preparation of metal atomic chains [Proc. Natl. Acad. Sci. U.S.A. 107, 9055 (2010)].Comment: Nanotechnology (2014

The wavefunction reconstruction effects in calculation of DM-induced electronic transition in semiconductor targets

The physics of the electronic excitation in semiconductors induced by sub-GeV dark matter (DM) have been extensively discussed in literature, under the framework of the standard plane wave (PW) and pseudopotential calculation scheme. In this paper, we investigate the implication of the all-electron (AE) reconstruction on estimation of the DM-induced electronic transition event rates. As a benchmark study, we first calculate the wavefunctions in silicon and germanium bulk crystals based on both the AE and pseudo (PS) schemes within the projector augmented wave (PAW) framework, and then make comparisons between the calculated excitation event rates obtained from these two approaches. It turns out that in process where large momentum transfer is kinetically allowed, the two calculated event rates can differ by a factor of a few. Such discrepancies are found to stem from the high-momentum components neglected in the PS scheme. It is thus implied that the correction from the AE wavefunction in the core region is necessary for an accurate estimate of the DM-induced transition event rate in semiconductors.Comment: A missing factor $64^{-3/2}=1/512$ associated with the Fourier transformation is added to both the AE and PS event rates in this version. The ratio between the AE and PS event rates is not affecte