Unified Formalism for calculating Polarization, Magnetization, and more in a Periodic Insulator

In this paper, we propose a unified formalism, using Green's functions, to integrate out the electrons in an insulator under uniform electromagnetic fields. We derive a perturbative formula for the Green's function in the presence of uniform magnetic or electric fields. Applying the formula, we derive the formula for the polarization, the orbital magnetization, and the orbital magneto-polarizability, without assuming time reversal symmetry. Specifically, we realize that the terms linear in the electric field can only be expressed in terms of the Green's functions in one extra dimension. This observation directly leads to the result that the coefficient of the $\theta$ term in any dimensions is given by a Wess-Zumino-Witten-type term, integrated in the extended space, interpolating between the original physical Brillouin zone and a trivial system, with the group element replaced by the Green's function. This generalizes an earlier result for the case of time reversal invariance [see Z. Wang, X.-L. Qi, and S.-C. Zhang, Phys. Rev. Lett. {\bf 105}, 256803 (2010)].Comment: 16 pages, 1 figure. The version accepted by PR

Search for serendipitous TNO occultation in X-rays

To study the population properties of small, remote objects beyond Neptune's orbit in the outer solar system, of kilometer size or smaller, serendipitous occultation search is so far the only way. For hectometer-sized Trans-Neptunian Objects (TNOs), optical shadows actually disappear because of diffraction. Observations at shorter wave lengths are needed. Here we report the effort of TNO occultation search in X-rays using RXTE/PCA data of Sco X-1 taken from June 2007 to October 2011. No definite TNO occultation events were found in the 334 ks data. We investigate the detection efficiency dependence on the TNO size to better define the sensible size range of our approach and suggest upper limits to the TNO size distribution in the size range from 30 m to 300 m. A list of X-ray sources suitable for future larger facilities to observe is proposed.Comment: Accepted to publish in MNRA

Numerical Studies of Quantum Oscillations in the Superconducting vortex mixed state

We studied the quantum oscillations in superconducting vortex mixed states with d-wave pairing. We showed that the Onsager relation does not always apply. Furthermore, at mean field level the quantum oscillations from electron pockets are suppressed by the pairing. We conclude that an interpretation of the experimental results asccoming from the four hole pockets created by a $(\pi,\pi)$ folding cannot be ruled out.Comment: 5 pages, 6 figure

Color-complexity enabled exhaustive color-dots identification and spatial patterns testing in images

Targeted color-dots with varying shapes and sizes in images are first exhaustively identified, and then their multiscale 2D geometric patterns are extracted for testing spatial uniformness in a progressive fashion. Based on color theory in physics, we develop a new color-identification algorithm relying on highly associative relations among the three color-coordinates: RGB or HSV. Such high associations critically imply low color-complexity of a color image, and renders potentials of exhaustive identification of targeted color-dots of all shapes and sizes. Via heterogeneous shaded regions and lighting conditions, our algorithm is shown being robust, practical and efficient comparing with the popular Contour and OpenCV approaches. Upon all identified color-pixels, we form color-dots as individually connected networks with shapes and sizes. We construct minimum spanning trees (MST) as spatial geometries of dot-collectives of various size-scales. Given a size-scale, the distribution of distances between immediate neighbors in the observed MST is extracted, so do many simulated MSTs under the spatial uniformness assumption. We devise a new algorithm for testing 2D spatial uniformness based on a Hierarchical clustering tree upon all involving MSTs. Our developments are illustrated on images obtained by mimicking chemical spraying via drone in Precision Agriculture.Comment: 21 pages, 21 figure

Economic lot sizing with imperfect rework derived without derivatives

This paper presents an algebraic method for solving economic production quantity (EPQ) model with imperfect rework. Conventional method for deriving optimal lot size is by using differential calculus on the cost function with the need to prove optimality first. Recent articles proposed algebraic approach to the solution of classic economic order quantity (EOQ) and EPQ model without reference to the use of derivatives. This note extends them to an EPQ model taking into consideration an imperfect rework of defective items. We demonstrate that the optimal lot size and the expected production-inventory cost for such a realistic EPQ model can be derived without derivatives

Examining the online reading behavior and performance of fifth-graders: evidence from eye-movement data

Online reading is developing at an increasingly rapid rate, but the debate concerning whether learning is more effective when using hypertexts than when using traditional linear texts is still persistent. In addition, several researchers stated that online reading comprehension always starts with a question, but little empirical evidence has been gathered to investigate this claim. This study used eye-tracking technology and retrospective think aloud technique to examine online reading behaviors of fifth-graders (N = 50). The participants were asked to read four texts on the website. The present study employed a three-way mixed design: 2 (reading ability: high vs. low) 2 (reading goals: with vs. without) 2 (text types: hypertext vs. linear text). The dependent variables were eye-movement indices and the frequencies of using online reading strategy. The results show that fifth-graders, irrespective of their reading ability, found it difficult to navigate the nonlinear structure of hypertexts when searching for and integrating information. When they read with goals, they adjusted their reading speed and the focus of their attention. Their offline reading ability also influenced their online reading performance. These results suggest that online reading skills and strategies have to be taught in order to enhance the online reading abilities of elementary-school students