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
The empirically reported values of the critical current density (<i>j<sub>c</sub></i>) of Bi-2212 as 2.4 × 10<sup>5</sup> (<i>j<sub>c</sub></i><sub&g...The empirically reported values of the critical current density (<i>j<sub>c</sub></i>) of Bi-2212 as 2.4 × 10<sup>5</sup> (<i>j<sub>c</sub></i><sub>1</sub>;Sample 1) and 1.0 × 10<sup>6</sup> A/cm<sup>2</sup> (<i>j<sub>c</sub></i><sub>2</sub>;Sample 2) are intriguing because both of them correspond to the <i>same</i> values of the temperature <i>T</i> = 4.2 K and the applied magnetic field <i>H</i> = 12 × 10<sup>4</sup> G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential <i>μ</i> subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of <i>μ</i> of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (<i>e-e</i>) and the hole-hole (<i>h-h</i>) pairs to <i>j<sub>c</sub></i>—a feature to which no heed was paid earlier. The essence of our findings is that the <i>j<sub>c</sub></i>s of the two samples differ because they are characterized by different values of the <i>primary</i> variables <i>μ<sub>i</sub></i><sub> </sub>and <img src="Edit_e1b831e9-dc51-4c3b-bd84-fa905e3e62b5.png" alt="" />, where <img src="Edit_1f775a80-30ab-447d-861f-afb4ba8fba6a.png" alt="" /> is the effective mass of a charge-carrier and <i>m<sub>e</sub></i><sub> </sub>is the free-electron mass and <i>i</i> = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being <i>predominantly h-h</i> pairs, the values of these parameters are estimated to be: <i>μ</i><sub>1</sub> ≈ 12.3 meV, <i>η</i><su展开更多
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.
文摘The empirically reported values of the critical current density (<i>j<sub>c</sub></i>) of Bi-2212 as 2.4 × 10<sup>5</sup> (<i>j<sub>c</sub></i><sub>1</sub>;Sample 1) and 1.0 × 10<sup>6</sup> A/cm<sup>2</sup> (<i>j<sub>c</sub></i><sub>2</sub>;Sample 2) are intriguing because both of them correspond to the <i>same</i> values of the temperature <i>T</i> = 4.2 K and the applied magnetic field <i>H</i> = 12 × 10<sup>4</sup> G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential <i>μ</i> subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of <i>μ</i> of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (<i>e-e</i>) and the hole-hole (<i>h-h</i>) pairs to <i>j<sub>c</sub></i>—a feature to which no heed was paid earlier. The essence of our findings is that the <i>j<sub>c</sub></i>s of the two samples differ because they are characterized by different values of the <i>primary</i> variables <i>μ<sub>i</sub></i><sub> </sub>and <img src="Edit_e1b831e9-dc51-4c3b-bd84-fa905e3e62b5.png" alt="" />, where <img src="Edit_1f775a80-30ab-447d-861f-afb4ba8fba6a.png" alt="" /> is the effective mass of a charge-carrier and <i>m<sub>e</sub></i><sub> </sub>is the free-electron mass and <i>i</i> = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being <i>predominantly h-h</i> pairs, the values of these parameters are estimated to be: <i>μ</i><sub>1</sub> ≈ 12.3 meV, <i>η</i><su
