Accurate gradient computations at interfaces using finite element methods

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface

An Ultra Low Mass and Small Radius Compact Object in 4U 1746-37?

Photospheric radius expansion (PRE) bursts have already been used to constrain the masses and radii of neutron stars. RXTE observed three PRE bursts in 4U 1746-37, all with low touchdown fluxes. We discuss here the possibility of low mass neutron star in 4U 1746-37 because the Eddington luminosity depends on stellar mass. With typical values of hydrogen mass fraction and color correction factor, a Monte-Carlo simulation was applied to constrain the mass and radius of neutron star in 4U 1746-37. 4U 1746-37 has a high inclination angle. Two geometric effects, the reflection of the far side accretion disc and the obscuration of the near side accretion disc have also been included in the mass and radius constraints of 4U 1746-37. If the reflection of the far side accretion disc is accounted, a low mass compact object (mass of $0.41\pm0.14~M_{\odot}$ and radius of $8.73\pm1.54~\rm km$ at 68% confidence) exists in 4U 1746-37. If another effect operated, 4U 1746-37 may contain an ultra low mass and small radius object ($M=0.21\pm0.06~M_{\odot},~R=6.26\pm0.99~\rm km$ at 68% confidence). Combined all possibilities, the mass of 4U 1746-37 is $0.41^{+0.70}_{-0.30}~M_\odot$ at 99.7% confidence. For such low mass NS, it could be reproduced by a self-bound compact star, i.e., quark star or quark-cluster star.Comment: accepted by Ap

Composites of Piezoelectric Materials and Silicon as Anode for Lithium Ion Batteries

Group IVA elements (Si, Ge and Sn) are promising candidates for the anode materials of lithium ion batteries (LIBs) due to their large theoretical specific capacities. However, serious problems of pulverization and capacity degradation resulted from the huge volume changes during charge/discharge operations hindered their successful applications as the anode materials in the LIBs. In this work, diffusion behaviors of Li ions in Si(100) and Si(111) slabs with a piezoelectric field applied perpendicularly to the surfaces were investigated using density functional theory. Results showed that the diffusivity of the Li in Si can be significantly enhanced by applying the electric field generated from the piezoelectric material. This finding can explain well the recent experimental observations in which improved electrochemical performance was obtained using Si/carbon nanotube/BaTiO3 as the anode for the LIBs. New generation of anode composite materials can be designed based on this idea and the piezoelectric material is used not only to accommodate the volume variation of active materials of Si, but also to enhance the charging rate of the LIBs

Hydrothermally synthesized CeO2 nanowires for H2S sensing at room temperature

CeO2 nanowires were synthesized using a facile hydrothermal process without any surfactant, and their morphological, structural and gas sensing properties were systematically investigated. The CeO2 nanowires with an average diameter of 12.5 nm had a face-centered cubic fluorite structure and grew along [111] of CeO2. At the room temperature of 25 °C, hydrogen sulfide (H2S) gas sensor based on the CeO2 nanowires showed excellent sensitivity, low detection limit (50 ppb), and short response and recovery time (24 s and 15 s for 50 ppb H2S, respectively)