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

Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory

We study the ground-state octet baryon masses and sigma terms using the covariant baryon chiral perturbation theory (ChPT) with the extended-on-mass-shell (EOMS) renormalization scheme up to next-to-next-to-next-to-leading order (N$^3$LO). By adjusting the available 19 low-energy constants (LECs), a reasonable fit of the $n_f=2+1$ lattice quantum chromodynamics (LQCD) results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved. Finite-volume corrections to the lattice data are calculated self-consistently. Our study shows that N$^3$LO BChPT describes better the light quark mass evolution of the lattice data than the NNLO BChPT does and the various lattice simulations seem to be consistent with each other. We also predict the pion and strangeness sigma terms of the octet baryons using the LECs determined in the fit of their masses. The predicted pion- and strangeness-nucleon sigma terms are $\sigma_{\pi N}=43(1)(6)$ MeV and $\sigma_{s N}=126(24)(54)$ MeV, respectively.Comment: 28 pages, 6 figures, minor revisions, typos corrected, version to appear in JHE

Morphological study of the hoof in yak

The fore- and hindlimb of yak have been studied by the gross anatomical methods and standard histological techniques. The artery of ungula was also determined by X-ray and acrylonitrile-butadiene-styrene casting. Anatomical features of the forelimb of yak resemble those of hindlimb, including hoof periphery, hoof coronal, hoof wall, hoof sole, and hoof sphere. The forelimb and hindlimb are almost the same in histological structure. The epidermis comprised all 5 strata: stratum corneum, stratum lucidum, stratum granulosum, stratum spinosum and stratum basale. The papillary layers and dermal lamellae contained a variable amount of capillary as well as collagen and elastic fibres. Many venules and arteriovenous anastomosis were distributed among the reticular layer. Subcutaneous tissue was composed of rich adipose and connective tissue in hoof periphery, hoof coronal, and, especially, hoof sphere. Major arteria in forelimb of yak include arteria digitalis palmaris communis III and arteriae digitales palmares propriae III and IV axialis. Those in hindlimb include arteria digitalis plantaris communis III and arteria digitalis plantaris propria III and IV axialis. Our findings highlight the main morphological features of yak and provide a morphological basis useful to researchers using yak hoof

High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic response for statistical moment and reliability analyses; a novel integration of the adaptive-sparse PDD approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and standard gradient-based optimization algorithms. New analytical formulae are presented for the design sensitivities that are simultaneously determined along with the moments or the failure probability. Numerical results stemming from mathematical functions indicate that the new method provides more computationally efficient design solutions than the existing methods. Finally, stochastic shape optimization of a jet engine bracket with 79 variables was performed, demonstrating the power of the new method to tackle practical engineering problems.Comment: 18 pages, 2 figures, to appear in Sparse Grids and Applications--Stuttgart 2014, Lecture Notes in Computational Science and Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer International Publishing, 201

Refinement and growth enhancement of Al2Cu phase during magnetic field assisting directional solidification of hypereutectic Al-Cu alloy.

International audienceUnderstanding how the magnetic fields affect the formation of reinforced phase during solidification is crucial to tailor the structure and therefor the performance of metal matrix in situ composites. In this study, a hypereutectic Al-40 wt.% Cu alloy has been directionally solidified under various axial magnetic fields and the morphology of Al2Cu phase was quantified in 3D by means of high resolution synchrotron X-ray tomography. With rising magnetic fields, both increase of Al2Cu phase's total volume and decrease of each column's transverse section area were found. These results respectively indicate the growth enhancement and refinement of the primary Al2Cu phase in the magnetic field assisting directional solidification. The thermoelectric magnetic forces (TEMF) causing torque and dislocation multiplication in the faceted primary phases were thought dedicate to respectively the refinement and growth enhancement. To verify this, a real structure based 3D simulation of TEMF in Al2Cu column was carried out, and the dislocations in the Al2Cu phase obtained without and with a 10T high magnetic field were analysed by the transmission electron microscope

Performance of Photosensors in the PandaX-I Experiment

We report the long term performance of the photosensors, 143 one-inch R8520-406 and 37 three-inch R11410-MOD photomultipliers from Hamamatsu, in the first phase of the PandaX dual-phase xenon dark matter experiment. This is the first time that a significant number of R11410 photomultiplier tubes were operated in liquid xenon for an extended period, providing important guidance to the future large xenon-based dark matter experiments.Comment: v3 as accepted by JINST with modifications based on reviewers' comment

The long-term effects of alfalfa on soil water content in the Loess Plateau of northwest China

Soil desiccation is the most serious problem in forest vegetations and grassland, which lead to widespread land degradation in the Loess Plateau of China. The soil water variations at 0 to 1000 cm depth of different vegetations were studied to explore the hydrological effects of vegetations and determine the optimal length of alfalfa (Medicago sativa L.) phase at the Zhenyuan Agri-ecological Station of the Loess Plateau in China. Eight treatments were designed in this study: waste land, wheat land and six continuous growing alfalfa treatments, including 4-year-old (4 year), 6-year-old (6 year), 8- year-old (8 year), 12-year-old (12 year), 18-year-old (18 year) and 26-year-old (26 year) alfalfa grasslands.  Results showed that the wheat field had the best soil water content and no dry soil layer, while slightly dry soil layer occurred in wasteland and 4, 6 and 8 year alfalfa grasslands. After alfalfa grew for > 8 years, moderately dry soil layer appeared in the grassland and expanded beyond 500 cm soil depth. The result also showed that wheat field, wasteland and the alfalfa grasslands growing for 4, 6 and 8 years had no unfavorable impacts on the ecological environments of the soil moisture but the grasslands for 12, 18 and 26 years did exert relatively stronger unfavorable influences on the hydrological effects. Considering all the factors, this study recommends that the optimal length of alfalfa phase should be 8 years.Key words: Different vegetation, alfalfa grasslands, soil water content, ecological effect, soil desiccation, Loess Plateau of China

Applications of digital technology for the morphological study of C3–C7 vertebral arch pedicle in children

Background: This study aims to investigate the morphological characteristics and developmental patterns of the vertebral arch pedicle (VAP) in the lower cervical vertebrae of children, and to subsequently help guide the implantation of the pedicle screw. Materials and methods: The cervical vertebral multi-slice computed tomography (MSCT) data of 60 paediatric patients aged 4–12 years were collected and grouped. A reconstructed 3-dimensional model measured the following: pedicle width (PW), pedicle height (PH), pedicle osseous channel (POCL), pedicle transverse angle (PTA, namely the E angle), and pedicle sagittal angle (PTA, namely the F angle). Results: We calculated the ratio of PW/PH (I value) to assess the statistical difference between age groups and segments. The PW, PH, POCL, and E angles exhibited an overall increasing trend with increasing age. The PW, PH, and POCL of each vertebra in group C showed statically significant differences compared to groups A and B (p < 0.05). The PW of different vertebral sequences in each group showed a gradually increasing trend. The intervertebral F angle among different groups showed the biggest difference, a change from positive values to negative values gradually, among which the negative value of C7’s F angle was the largest. The I value exhibited an overall decreasing trend with increasing age. Conclusions: The morphological characteristics and development of the different pedicle segments exhibited obvious patterns. In the lower cervical vertebrae of children over 7 years of age, the vertebrae had the feasibility for the implantation of pedicle screws