Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

CALCULATIONS OF THE EIGENVALUES OF PURE QUADRUPOLE INTERACTION IN MOSSBAUER-EFFECT STUDIES

Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in Mossbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spin I = 3/2 divided-by 9/2 and the electric-field gradient with different asymmetry parameter (eta = 0 divided-by 1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spin I = 5/2.

有限元结构动力分析的广义特征值的神经计算

广义特征值问题是结构动力分析计算的关键之一.应用Reyle igh极小值原理,将神经网络的能量函数的极小点对应于广义特征值问题的最小特征值所对应的特征向量,在神经网络朝着能量函数极小点运动的同时得到了最小特征值所对应的特征向量的精确解答.从特征值的变分特性出发,给出了基于罚函数法的其他特征值的神经网络求解方案,从而在理论上给出了广义特征值问题的所有特征值的神经网络求解方法.仿真计算表明,该方法正确、有效可行.

中低纬度变化磁场的暴时特征研究

Magnetic storm is a kind of severe disturbances in the whole solar-earth electromagnetic space. It has significant effects on communication, electric power, oil transport pipe and human activities in space. Therefore, magnetic storms are worth for applications systems, not only being a favorable issue for scientists. In this paper, the spatial and temporal distributions of the magnetic fields produced by the magnetosphere-ionosphere current systems during storms are studied. Four parts are included in this paper decomposion of different disturbances with different origins, topological structure of the ring current, the asymmetric characteristics of the ring current, and the statistic peculiarities of the day-to-day variability (DTD) of Sq. 1 The decomposition of magnetic disturbances at mid-low latitudes and its evolutions during storms Transient variations in the geomagnetic field recorded at mid-low latitudes mainly include the storm-time variation (Dst), solar quiet daily variation (Sq) and disturbance daily variation (SD). With the data of the geomagnetic meridian chain observatories in China, 25 storms during the period of 1997 to 1999 have been analyzed. According to the features of different variations, a method of “three-steps decomposition” is developed by using the method of Natural Orthogonal Components (NOC), Correlation Analysis and Fourier Analysis to separate those three components in turn. The results show that, the first eigenmode by the MNOC clearly describing the special distribution and temporal evolution of storm-time variation, in addition, Correlation Analysis and Fourier Analysis offer a useful method to extract the Sq and SD variations. The latitudinal shift of the Sq current focus seems to be the principal reason of the day-to-day variaitons in the daily range of Sq. The magnitude of SD reaches a maximum during the main phase, and then gradually decreases. 2 The topology structure of the ring current during storms Both the mechanism of the ring current and the geomagnetic data suggest that the central plane of the ring current is declining to the geomagnetic equator plane with a tilt angle δ. Using the H and Z component data at two stations in a meridian chain, we deduce a new parameter describing the invariable peculiarity of different storms. Then the δ angle is calculated by using the data from a meridian chain and tested with the ERC model. Finally the deduced tilt angles are used to modify Dst index. 3 The asymmetric characteristics of the ring current during storms The variations of the geomagnetic field at mid-low latitudes show a significant dawn-dusk asymmetry, resulting from the superposition of the fields from the symmetric ring current and the partial ring current. On the basis of the data from the 20°E, 30°E meridian chains and 30°N latitudinal chain, the dawn-dusk asymmetry is investigated by using three methods, namely, statistic analysis, ring current model calculation and typical event analysis. This characteristic implies the asymmetry of the spatial distribution of the ring current. In addition, during the main phase after the sudden commencement (SC), H field increases and reaches maximum around noontime, implying the effect of the Chapman-Ferraro current. 4 The statistic characteristics of the day-to-day variability and its mechanism The day-to-day variability of the geomagnetic Sq field is studied by using the magnetic data from a meridian chain of magnetometers along 120° E longitude. The method of NOC is applied to separate the Sq variation from complicated disturbances. The first eigenmode with the largest eigenvalue represents fairly well the Sq variation with a conspicuous day-to-day variability in the daily range. For the stations on the same north- or south-side of the Sq current system focus, the day-to-day variations show a positive correlation. In contrast, for the stations on the different sides of the Sq focus, they show a negative correlation, suggesting an important role of latitudinal shift of the Sq current system focus to the day-to-day variability of the Sq daily range. The Sq daily range is correlated with the magnetic indices Ap and Dst in a peculiar way: on some severe disturbed days, noticeably enhancements of the Sq are observed, implying increases of the ionospheric conductivities and/or tidal wind velocities; on other severe disturbed days, however, dramatically reduced Sq variations occur, suggesting dominant effects of the ‘disturbance dynamo’ process.