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.

Double plate system with a discontinuity in the elastic bonding layer

The double plate system with a discontinuity in the elastic bonding layer of Winker type is studied in this paper. When the discontinuity is small, it can be taken as an interface crack between the bi-materials or two bodies （plates or beams）. By comparison between the number of multifrequencies of analytical solutions of the double plate system free transversal vibrations for the case when the system is with and without disconti- nuity in elastic layer we obtain a theory for experimental vibration method for identification of the presence of an interface crack in the double plate system. The analytical analysis of free transversal vibrations of an elastically connected double plate systems with discontinuity in the elastic layer of Winkler type is presented. The analytical solutions of the coupled partial differential equations for dynamical free and forced vibration processes are obtained by using method of Bernoulli＇s particular integral and Lagrange＇s method of variation constants. It is shown that one mode vibration corresponds an infinite or finite multi-frequency regime for free and forced vibrations induced by initial conditions and one- frequency or corresponding number of multi-frequency regime depending on external excitations. It is shown for every shape of vibrations. The analytical solutions show that the discontinuity affects the appearance of multi-frequency regime of time function corresponding to one eigen amplitude function of one mode, and also that time functions of different vibration basic modes are coupled. From final expression we can separate the newgeneralized eigen amplitude functions with correspon- ding time eigen functions of one frequency and multifrequency regime of vibrations.

Latest advances in discontinuous deformation analysis method

Discontinuous deformation analysis （DDA） method, proposed firstly by Shi [1] in 1988, is a novel numerical approach to simulate the discontinuous deformation behaviors of blocky rock structures. In DDA, the domain of interest is represented as an assemblage of discrete blocks and the joints are treated as interfaces between blocks. The governing equations of DDA are derived from Newton’s Second Law of Motion and the Principle of Minimum Potential Energy.

Recent developments of miniature ion trap mass spectrometers

With outstanding analytical performance and portability, miniature mass spectrometer is one of the most powerful tools for in-situ analysis. The miniaturization of mass spectrometers has lasted for more than ten years, during which a number of miniature mass spectrometers employing different techniques have been developed. Small-in-size, working at relatively high pressure region and capable of performing tandem mass spectrometry, ion trap is the most widely used mass analyzer in miniature mass spectrometer systems. The recent development of miniature ion trap mass spectrometer systems in the last ten years was reviewed in this paper. These instruments adopt different atmospheric pressure interfaces （APIs）, which are membrane inlets （MIs）, discontinuous atmospheric pressure interface （DAPI） and continuous atmospheric pressure interface （CAPI）. This review emphasizes on the mini mass spectrometry （MS） system that can be handheld by one person, but not the field-able ones that are too large to be hand-portable.