Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

An Empirical Study of Using Imitation-Based Error Correction to Reduce Repeated Errors in English Writing of Rural Junior High School Students

Junior high school students in rural areas constitute a particular group of English learners, for whom English writing is not only important, but also difficult. In order to find out an effective means to help them enhance English writing proficiency. To this end, after carefully analyzing the writing characteristics of this group of English learners, one intact class in Grade 8 of No. 14 junior middle school in Wuwei was given an experimental treatment which required them to imitate the correct examples of expressions provided by their teacher where they used to make errors. Results revealed that students in experimental class outperform their peers in control class significantly.

Payload topography camera of Chang'e-3

Chang＇e-3 was China＇s first soft-landing lunar probe that achieved a successful roving exploration on the Moon. A topography camera functioning as the lander＇s “eye” was one of the main scientific payloads installed on the lander. It was composed of a camera probe, an electronic component that performed image compression, and a cable assembly. Its exploration mission was to obtain optical images of the lunar topography in the landing zone for investigation and research. It also observed rover movement on the lunar surface and finished taking pictures of the lander and rover. After starting up successfully, the topography camera obtained static images and video of rover movement from different directions, 360？panoramic pictures of the lunar surface around the lander from multiple angles, and numerous pictures of the Earth. All images of the rover, lunar surface, and the Earth were clear, and those of the Chinese national flag were recorded in true color. This paper describes the exploration mission, system design, working principle, quality assessment of image compression, and color correction of the topography camera. Finally, test results from the lunar surface are provided to serve as a reference for scientific data processing and application.

Autonomous vicarious calibration based on automated test-site radiometer

We employ the in-site automated observation radiometric calibration（AORC） approach to perform vicarious calibration, which does not require the manual efforts of a field team to measure the surface conditions. By using an automated test-site radiometer（ATR）, the surface radiance at any moment in time can be obtained. This Letter describes the AORC approach and makes use of data to compute top-of-atmosphere radiance and compare it to measurements from the Moderate Resolution Imaging Spectroradiometer. The result shows that the relative deviation is less than 5% and the uncertainty is less than 6.2%, which indicates that the in-site AORC maintains an accuracy level on par with traditional calibration.

Application of real-time digitization techniques in beam measurement for accelerators

Beam measurement is very important for accelerators. In this paper, modern digital beam measurement techniques based on I Q（In-phase ＆ Quadrature-phase） analysis are discussed. Based on this method and highspeed high-resolution analog-to-digital conversion, we have completed three beam measurement electronics systems designed for the China Spallation Neutron Source（CSNS）, Shanghai Synchrotron Radiation Facility（SSRF）, and Accelerator Driven Sub-critical system（ADS）. Core techniques of hardware design and real-time system calibration are discussed, and performance test results of these three instruments are also presented.