Investigating the mechanisms of diamond polishing using Raman spectroscopy

Recent research has shown that a phase transformation of diamond to a different form of carbon is involved when diamonds are polished in the traditional fashion. The question as to how this phase transformation is activated and maintained to produce high wear rates is of great technological interest since it may radically change the way we view the processing of diamond. This paper describes the use of Raman spectroscopy to examine debris produced on the diamond polishing wheel, both during its preparation and during polishing. In addition, polished diamond surfaces were examined for the possible existence of non-diamond surface layers in an attempt to identify material removal mechanisms. Raman spectroscopy proves ideal for these analyses because its relatively high spatial resolution is well suited to the analysis of small wear features and debris particles, and because of the wealth of information it reveals about chemical structure. This level of structural information has been lacking in previous analyses of diamond polishing debris. In addition to the non-diamond carbon found in the wear debris, significant quantities of two iron oxides, magnetite (Fe₃O₄) and haematite (α-Fe₂O₃), were also found. An interesting observation was that a transformation from magnetite to haematite could be induced either by using high power laser excitation or by frictional heating during polishing. It is suggested that some of the Raman peaks previously attributed to lonsdaleite might better be explained by the presence of these oxides.     

Testing coefficients of AR and bilinear time series models by a graphical approach

AR and bilinear time series models are expressed as time series chain graphical models, based on which, it is shown that the coefficients of AR and bilinear models are the conditional correlation coefficients conditioned on the other components of the time series. Then a graphically based procedure is proposed to test the significance of the coefficients of AR and bilinear time series. Simulations show that our procedure performs well both in sizes and powers. This work was supported by the Hong Kong Polytechnic University Research Council, the National Natural Science Foundation of China (Grant No. 10671044) and the Science and Technology Bureau of Guangzhou Municipal Government of China (Grant No. LSBH-017)     

Testing heteroscedasticity by wavelets in a nonparametric regression model

In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.     

Testing coeffcients of AR and bilinear time series models by a graphical approach

AR and bilinear time series models are expressed as time series chain graphical models, based on which, it is shown that the coefficients of AR and bilinear models are the conditional correlation coefficients conditioned on the other components of the time series. Then a graphically based procedure is proposed to test the significance of the coeffcients of AR and bilinear time series. Simulations show that our procedure performs well both in sizes and powers.