A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases

By comparing the discontinuous Galerkin (DG) methods, the k-exact finite volume (FV) methods and the lift collocation penalty (LCP) methods, a concept of ‘static reconstruction’ and ‘dynamic reconstruction’ was introduced for higher-order numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods was presented for one-dimensional conservation law using a ‘hybrid reconstruction’ approach. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called as ‘dynamic reconstruction’), while the higher-order derivatives are re-constructed by the ‘static reconstruction’ of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent face neighboring cells. In this follow-up paper, the hybrid DG/FV schemes are extended onto two-dimensional unstructured and hybrid grids. The two-dimensional linear and non-linear scalar conservation law and Euler equations are considered. Some typical cases are tested to demonstrate the performance of the hybrid DG/FV method, and the numerical results show that they can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy in the same mesh.     

A Two-Level Preconditioned Conjugate-Gradient Method in Distorted and Structured Grids

In this paper, we propose a new two-level preconditioned C-G method which uses the quadratic smoothing and the linear correction in distorted but topologically structured grid. The CPU time of this method is less than that of the multigrid preconditioned C-G method (MGCG) using the quadratic element, but their accuracy is almost the same. Numerical experiments and eigenvalue analysis are given and the results show that the proposed two-level preconditioned method is efficient.     

Entanglement between nuclear spin and field mode in GaAs semiconductors

In this paper we investigate entanglement between the nuclear spin and field mode in a GaAs semiconductor. The eigenfuctions of nuclear spin in the quantized external field are obtained and thus the von Neumann entropy is evaluated explicitly. It is shown that the von Neumann entropy monotonously increases with the spin-field coupling constant but monotonously decreases with the anisotropy energy.     

Comparison of performance between rescaled range analysis and rescaled variance analysis in detecting abrupt dynamic change

In the present paper, a comparison of the performance between moving cutting data-rescaled range analysis(MCR/S) and moving cutting data-rescaled variance analysis(MC-V/S) is made. The results clearly indicate that the operating efficiency of the MC-R/S algorithm is higher than that of the MC-V/S algorithm. In our numerical test, the computer time consumed by MC-V/S is approximately 25 times that by MC-R/S for an identical window size in artificial data. Except for the difference in operating efficiency, there are no significant differences in performance between MC-R/S and MC-V/S for the abrupt dynamic change detection. MC-R/S and MC-V/S both display some degree of anti-noise ability. However, it is important to consider the influences of strong noise on the detection results of MC-R/S and MC-V/S in practical application processes.     

Measurement of acoustic dispersion using both transmitted and reflected pulses

Traditional broadband transmission method for measuring acoustic dispersion requires the measurements of the sound speed in water, the thickness of the specimen, and the phase spectra of two transmitted ultrasound pulses. When the sound speed in the specimen is significantly different from that in water, the overall uncertainty of the dispersion measurement is generally dominated by the uncertainty of the thickness measurement. In this paper, a new water immersion method for measuring dispersion is proposed which eliminates the need for thickness measurement and the associated uncertainty. In addition to recording the two transmitted pulses, the new method requires recording two reflected pulses, one from the front surface and one from the back surface of the specimen. The phase velocity as well as the thickness of the specimen can be determined from the phase spectra of the four pulses. Theoretical analysis and experimental results from three specimens demonstrate the advantages of this new method.     

An Optimized Passive Shimming Method for Bi-planar Permanent MRI Magnets

An optimized passive shimming method with iron shims is presented in this paper. First, the influence value of a single iron or magnetized shim is fast calculated and determined by analytic solution with a single practical measurement. Then, the correlation between the influence value and parameters of a single shim is analyzed, and the proper parameters, including the position, polarity, and size (radius and thickness), of the shimming pieces are well selected. Finally, the numbers and locations of the passive shims are optimized by mixed-integer linear programming method based on a modified central magnetic field. The optimized method is applied to a 0.5 T Bi-planar permanent magnet magnetic resonance imaging system, and the presented results prove the efficacy of this optimized passive shimming methodology.     

Solute transport and composition profile during direct metal deposition with coaxial powder injection

Direct metal deposition (DMD) with coaxial powder injection allows fabrication of three-dimensional geometry with rapidly solidified microstructure. During DMD, addition of powder leads to the interaction between laser and powder, and also the redistribution of solute. The concentration distribution of the alloying element is very important for mechanical properties of the deposited clad material. The evolution of concentration distribution of carbon and chromium in the molten pool is simulated using a self-consistent three-dimensional model, based on the solution of the equations of mass, momentum, energy conservation and solute transport in the molten pool. The experimental and calculated molten pool geometry is compared for model validation purposes.     

Analysis of electrical tree propagation in XLPE power cable insulation

Electrical treeing is one of the major breakdown mechanisms for solid dielectrics subjected to high electrical stress. In this paper, the characteristics of electrical tree growth in XLPE samples have been investigated. XLPE samples are obtained from a commercial XLPE power cable, in which electrical trees have been grown from pin to plane in the frequency range of 4000-10,000 Hz, voltage range of 4-10 kV, and the distances between electrodes of 1 and 2 mm. Images of trees and their growing processes were taken by a CCD camera. The fractal dimensions of electric trees were obtained by using a simple box-counting technique. The results show that the tree growth rate and fractal dimension was bigger when the frequency or voltage was higher, or the distance between electrodes was smaller. Contrary to our expectation, it has been found that when the distance between electrodes changed from 1 to 2 mm, the required voltage of the similar electrical trees decreased only 1or 2 kV. In order to evaluate the difficulties of electrical tree propagation in different conditions, a simple energy threshold analysis method has been proposed. The threshold energy, which presents the minimum energy that a charge carrier in the well at the top of the tree should have to make the tree grow, has been computed considering the length of electrical tree, the fractal dimension, and the growth time. The computed results indicate that when one of the three parameters of voltage, frequency, and local electric field increase, the trends of energy threshold can be split into 3 regions.