Random walk modeling has been extensively used for oil dispersion studies. However, there is some misusing about the expression. The aim of this study is to clarify the essence of the method. Expressions used in published papers are reviewed firstly, and different methods are discussed. The results show that the random method can successfully predict the dye patch dimensions and the dilution of the dye with time in contrast with the other method. Also, some critical factor in applying the random walk method is emphasized in the paper. Two types of formula used to simulate the turbulent diffusion are discussed. Results have shown a need for care in determining the concentrations from the random walk model.

Rouse equation, which was derived from the diffusion theory, is well known in the study of steady state suspended sediment transport over erodible beds. Although this equation being regarded as Rouse law could be applied effectively, it is unrealistic that the concentration at the free surface is always zero. In addition, for deriving the depth-averaged concentration, the numerical integration or the table lookup has to be performed. Bose and Dey[1] improved the Rouse equation using a modified sediment diffusivity in order to overcome the zero value concentration, but this equation can not be integrated analytically yet. In this paper, according to two equilibrium profiles respect to constant and linear diffusion coefficients, an approximate solution of the improved Rouse equation is given using a general weight-averaged method in order to be integrated analytically. Through verification with experimental data, the results show that the approximation of the improved Rouse equation behave generally better than itself, as well as the Rouse equation and van Rijn equation over the whole water depth. It is revealed that, nevertheless some empirical, this approximation is reasonable, and has higher accuracy. Moreover it can be integrated analytically.

Effect of Si on the forming ability of quasicrystalline phase in Al65Cu20Fe15 alloys fabricated under conventional casting conditions has been studied using X-ray diffraction (XRD), optical microscopy (OM), and scanning electron microscopy (SEM). The results show that under the conventional casting conditions, it is found that the addition of certain amount of Si into the Al-Cu-Fe melts can change the formation of Al62.5Cu25Fe12.5 quasicrystals during the solidification process. Compared with Al65Cu20Fe15 alloy, Al64.5Cu20Fe15Si0.5 alloy has smaller volume fraction of β phase solidifying initially, larger volume fraction of the quasicrystal phase generating in the subsequent peritectic reaction, and larger volume fraction of ω phase solidifying finally. Both experimental results and the theory of Hume-Rothery show that addition of Si can promote the formation ability of the icosahedral quasicrystalline Al62.5Cu25Fe12.5 phase in Al-Cu-Fe alloy.

No abstract

The Explicit Finite Difference (EFD) method is used for calculating the energy conservation equation during solidification. In order to improve the computational efficiency, the equivalent specific heat method is adopted to calculate the latent heat and the high order Alternating Direction Implicit (ADI) method is also applied, which is fourth order in space and second order in time. The degree of similarity between the simulation results and experimental results is analyzed quantitatively by the Hamming Distance (HD) for the first time, and results show that this high order mathematical model based on the equivalent specific heat method and the high order ADI method is faster and more accurate than the EFD method.