An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Three-dimensional turbopump flowfield analysis

A program was conducted to develop a flow prediction method applicable to rocket turbopumps. The complex nature of a flowfield in turbopumps is described and examples of flowfields are discussed to illustrate that physics based models and analytical calculation procedures based on computational fluid dynamics (CFD) are needed to develop reliable design procedures for turbopumps. A CFD code developed at NASA ARC was used as the base code. The turbulence model and boundary conditions in the base code were modified, respectively, to: (1) compute transitional flows and account for extra rates of strain, e.g., rotation; and (2) compute surface heat transfer coefficients and allow computation through multistage turbomachines. Benchmark quality data from two and three-dimensional cascades were used to verify the code. The predictive capabilities of the present CFD code were demonstrated by computing the flow through a radial impeller and a multistage axial flow turbine. Results of the program indicate that the present code operated in a two-dimensional mode is a cost effective alternative to full three-dimensional calculations, and that it permits realistic predictions of unsteady loadings and losses for multistage machines

Doping - dependent superconducting gap anisotropy in the two-dimensional 10-3-8 pnictide Ca10_{10}(Pt3_3As8_8)[(Fe1−x_{1-x}Ptx_{x})2_2As2_2]5_5

The characteristic features of Ca$_{10}$(Pt$_3$As$_8$)[(Fe$_{1-x}$Pt$_x$)$_2$As$_2$]$_5$ ("10-3-8") superconductor are relatively high anisotropy and a clear separation of superconductivity and structural/magnetic transitions, which allows studying the superconducting gap without complications due to the coexisting order parameters. The London penetration depth, measured in underdoped single crystals of 10-3-8 ($x =$ 0.028, 0.041, 0.042, and 0.097), shows behavior remarkably similar to other Fe-based superconductors, exhibiting robust power-law, $\Delta \lambda(T) = A T^n$. The exponent $n$ decreases from 2.36 ($x =$ 0.097, close to optimal doping) to 1.7 ($x =$ 0.028, a heavily underdoped composition), suggesting that the superconducting gap becomes more anisotropic at the dome edge. A similar trend is found in low-anisotropy superconductors based on BaFe$_2$As$_2$ ("122"), implying that it is an intrinsic property of superconductivity in iron pnictides, unrelated to the coexistence of magnetic order and superconductivity or the anisotropy of the normal state. Overall this doping dependence is consistent with $s_{\pm}$ pairing competing with intra-band repulsion

Ellipsometry noise spectrum, suspension transfer function measurement and closed-loop control of the suspension system in the Q & A experiment

The Q & A experiment, aiming at the detection of vacuum birefringence predicted by quantum electrodynamics, consists mainly of a suspended 3.5 m Fabry-Perot cavity, a rotating permanent dipole magnet and an ellipsometer. The 2.3 T magnet can rotate up to 10 rev/s, introducing an ellipticity signal at twice the rotation frequency. The X-pendulum gives a good isolation ratio for seismic noise above its main resonant frequency 0.3 Hz. At present, the ellipsometry noise decreases with frequency, from 1*10^{-5} rad Hz^{-1/2} at 5 Hz, 2*10^{-6} rad Hz^{-1/2} at 20 Hz to 5*10^{-7} rad Hz^{-1/2} at 40 Hz. The shape of the noise spectrum indicates possible improvement can be made by further reducing the movement between the cavity mirrors. From the preliminary result of yaw motion alignment control, it can be seen that some peaks due to yaw motion of the cavity mirror was suppressed. In this paper, we first give a schematic view of the Q & A experiment, and then present the measurement of transfer function of the compound X-pendulum-double pendulum suspension. A closed-loop control was carried out to verify the validity of the measured transfer functions. The ellipsometry noise spectra with and without yaw alignment control and the newest improvement is presented.Comment: 7 pages, 5 figures, presented in 6th Edoardo Amaldi Conference on Gravitational Waves, June 2005, Okinawa Japan and submitted to Journal of Physics: Conference Series. Some modifications are made according to the referee's comments: mainly to explain the relation between the displacement of cavity mirror and the ellipticity noise spectru

Single Crystal Growth and Characterization of the Iron-Based Superconductor KFe2As2 Synthesized by KAs Flux Method

Centimeter sized platelet single crystals of KFe2As2 were grown using a self-flux method. An encapsulation technique using commercial stainless steel container allowed the stable crystal growth lasting for more than 2 weeks. Ternary K-Fe-As systems with various starting compositions were examined to determine the optimal growth conditions. Employment of KAs flux led to the growth of large single crystals with the typical size of as large as 15 mm x 10 mm x 0.4 mm. The grown crystals exhibit sharp superconducting transition at 3.4 K with the transition width 0.2 K, as well as the very large residual resistivity ratio exceeding 450, evidencing the good sample quality.Comment: 4 pages, 6 Postscript figure

Non-exponential London penetration depth in Ba1−_{1-}Kx_{x}Fe2_{2}As2_{2} single crystals

We have studied the in- and out-of-plane magnetic penetration depths in the hole- doped iron based superconductor Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ ($T_{c}\approx$ 30K). The study was performed on single crystals grown from different fluxes and we find that the results are nearly the same. The in-plane London penetration depth $\lambda_{ab}$ does not show exponential saturation at low temperature, as would be expected from a fully gapped superconductor. Instead, $\lambda_{ab}(T)$ shows a power-law behavior, $\lambda\propto T^{n}$ ($n\approx 2$), down to $T\approx 0.02 T_{c}$, similar to the electron doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$. The penetration depth anisotropy $\gamma_{\lambda}=\lambda_{c}(T)/\lambda_{ab}(T)$ increases upon cooling, opposite to the trend observed in the anisotropy of the upper critical field, $\gamma_{\xi}=H_{c2}^{\perp c}(0)/H_{c2}^{\parallel c}(0)$. These are universal characteristics of both the electron and hole doped 122 systems, suggesting unconventional superconductivity. The behavior of the in-plane superfluid density $\rho_{ab}(T)$ is discussed in light of existing theoretical models proposed for the iron pnictides superconductors

Acceleration disturbances due to local gravity gradients in ASTROD I

The Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) mission consists of three spacecraft in separate solar orbits and carries out laser interferometric ranging. ASTROD aims at testing relativistic gravity, measuring the solar system and detecting gravitational waves. Because of the larger arm length, the sensitivity of ASTROD to gravitational waves is estimated to be about 30 times better than Laser Interferometer Space Antenna (LISA) in the frequency range lower than about 0.1 mHz. ASTROD I is a simple version of ASTROD, employing one spacecraft in a solar orbit. It is the first step for ASTROD and serves as a technology demonstration mission for ASTROD. In addition, several scientific results are expected in the ASTROD I experiment. The required acceleration noise level of ASTROD I is 10^-13 m s^-2 Hz^{-1/2} at the frequency of 0.1 mHz. In this paper, we focus on local gravity gradient noise that could be one of the largest acceleration disturbances in the ASTROD I experiment. We have carried out gravitational modelling for the current test-mass design and simplified configurations of ASTROD I by using an analytical method and the Monte Carlo method. Our analyses can be applied to figure out the optimal designs of the test mass and the constructing materials of the spacecraft, and the configuration of compensation mass to reduce local gravity gradients.Comment: 6 pages, presented at the 6th Edoardo Amaldi Conference (Okinawa Japan, June 2005); to be published in Journal of Physics: Conference Serie

Magnetic properties of Gd_xY_{1-x}Fe_2Zn_{20}: dilute, large, S\textbf {S} moments in a nearly ferromagnetic Fermi liquid

Single crystals of the dilute, rare earth bearing, pseudo-ternary series, Gd_xY_{1-x}Fe_2Zn_{20} were grown out of Zn-rich solution. Measurements of magnetization, resistivity and heat capacity on Gd_xY_{1-x}Fe_2Zn_{20} samples reveal ferromagnetic order of Gd^{3+} local moments across virtually the whole series ($x \geq 0.02$). The magnetic properties of this series, including the ferromagnetic ordering, the reduced saturated moments at base temperature, the deviation of the susceptibilities from Curie-Weiss law and the anomalies in the resistivity, are understood within the frame work of dilute, $\textbf {S}$ moments (Gd^{3+}) embedded in a nearly ferromagnetic Fermi liquid (YFe_2Zn_{20}). The s-d model is employed to further explain the variation of $T_{\mathrm{C}}$ with x as well as the temperature dependences of of the susceptibilities