FORMULATION OF STATISTICAL EVOLUTION OF MICROCRACKS IN SOLIDS

The paper presents a principal formulation of statistical evolution of microcracks, occurring in solids, subjected to external loading. In particular, the concept of ideal microcracks is elaborated, in order to describe the fundamental features of damage resulting from nucleation and extension of microcracks. Relevant average damage functions are also discussed.

The redshift number density evolution of Mg Ⅱ absorption systems

We make use of the recent large sample of 17 042 Mg Ⅱ absorption systems from Quider et al. to analyze the evolution of the redshift number density. Regardless of the strength of the absorption line, we find that the evolution of the redshift number density can be clearly distinguished into three different phases. In the intermediate redshift epoch （0.6 ≤ z ≤ 1.6）, the evolution of the redshift number density is consis- tent with the non-evolution curve, however, the non-evolution curve over-predicts the values of the redshift number density in the early （z ≤ 0.6） and late （z ≥ 1.6） epochs. Based on the invariant cross-section of the absorber, the lack of evolution in the red- shift number density compared to the non-evolution curve implies the galaxy number density does not evolve during the middle epoch. The fiat evolution of the redshift number density tends to correspond to a shallow evolution in the galaxy merger rate during the late epoch, and the steep decrease of the redshift number density might be ascribed to the small mass of halos during the early epoch.

A Statistical Model for Predicting the Average Abundance Patterns of Heavier Elements in Metal-Poor Stars

We have collected nearly all the available observed data of the elements from Ba to Dy in halo and disk stars in the metallicity range -4.0 <[Fe/H]< 0.5. Based on the observed data of Ba and Eu, we evaluated the least-squares regressions of [Ba/Fe] on [Fe/H], and [Eu/H] on [Ba/H]. Assuming that the heavy elements (heavier than Ba) are produced by a combination of the main components of s- and r-processes in metal-poor stars, and choosing Ba and Eu as respective representative elements of the main s- and the main r-processes, a statistical model for predicting the Galactic chemical evolution of the heavy elements is presented. With this model, we calculate the mean abundance trends of the heavy elements La, Ce, Pr, Nd, Sm, and Dy with the metallicity. We compare our results with the observed data at various metallicities, showing that the predicted trends are in good agreement with the observed trends, at least for the metallicity range [Fe/H]≥ -2.5. Finally, we discuss our results and deduce some important information about the Galactic chemical evolution.

Spectral Synthesis via Mean Field approach to Independent Component Analysis

We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis（MF-ICA） in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components（ICs）, and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used：（1） parameter recovery for simulated galaxies,（2） comparison with parameters estimated by other methods, and（3） consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.