The ideal micro-cracks are treated with the number-density function; the characteristics of their evolution are investigated; a deterministic model is applied to the discussion of their extension. It is discowred that...The ideal micro-cracks are treated with the number-density function; the characteristics of their evolution are investigated; a deterministic model is applied to the discussion of their extension. It is discowred that under certain conditions saturation may occur in the number-density. The main features of the statistical formulationare illustrated by several examples and compared with those observed in experiments.展开更多
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 descri...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.展开更多
The electromagnetic wave growth or damping depends basically on the number density and anisotropy of energetic particles as the resonant interaction takes place between the particles and waves in the magnetosphere. Th...The electromagnetic wave growth or damping depends basically on the number density and anisotropy of energetic particles as the resonant interaction takes place between the particles and waves in the magnetosphere. The variance of both the number density and anisotropy along the magnetic field line is evaluated systematically by modeling four typically prescribed distribution functions. It is shown that in the case of ＂the positive anisotropy＂ （namely, the perpendicular temperature T⊥ exceeds the parallel temperature T｜｜）, the number density of energetic electrons always decreases with the magnetic latitude for a regular increasing magnetic field and the maximum wave growth is therefore generally confined to the equator where the resonant energy is minimum, and the number density is the largest. However, the ＂loss-cone＂ anisotropy of the electrons with a ＂pancake＂ distribution or kappa distribution keeps invariant or nearly invariant, whereas the ＂temperature＂ anisotropy with a pure bi-Maxwellian distribution or Ashour-Abdalla and Kennel＇s distributions decreases with the magnetic latitude. The results may provide a useful approach to evaluating the number density and anisotropy of the energetic electrons at latitudes where the observation information is not available.展开更多
基金Project partly supported by the National Natural Science Foundation of China.
文摘The ideal micro-cracks are treated with the number-density function; the characteristics of their evolution are investigated; a deterministic model is applied to the discussion of their extension. It is discowred that under certain conditions saturation may occur in the number-density. The main features of the statistical formulationare illustrated by several examples and compared with those observed in experiments.
基金The project partially supported by National Natural Science Foundation of China.
文摘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.
基金supported by National Natural Science Foundation of China (Nos. 40474064, 40404012)the Scientific Research Foundation for ROCS, SEMthe Outstanding Youth Foundation of the Education Bureau of Hunan Province (No. 04B003)
文摘The electromagnetic wave growth or damping depends basically on the number density and anisotropy of energetic particles as the resonant interaction takes place between the particles and waves in the magnetosphere. The variance of both the number density and anisotropy along the magnetic field line is evaluated systematically by modeling four typically prescribed distribution functions. It is shown that in the case of ＂the positive anisotropy＂ （namely, the perpendicular temperature T⊥ exceeds the parallel temperature T｜｜）, the number density of energetic electrons always decreases with the magnetic latitude for a regular increasing magnetic field and the maximum wave growth is therefore generally confined to the equator where the resonant energy is minimum, and the number density is the largest. However, the ＂loss-cone＂ anisotropy of the electrons with a ＂pancake＂ distribution or kappa distribution keeps invariant or nearly invariant, whereas the ＂temperature＂ anisotropy with a pure bi-Maxwellian distribution or Ashour-Abdalla and Kennel＇s distributions decreases with the magnetic latitude. The results may provide a useful approach to evaluating the number density and anisotropy of the energetic electrons at latitudes where the observation information is not available.
