Parametric resonant states of charged fermions in the magnetar’s crust

We have presently derived the positive-energy solutions to the Dirac equation minimally coupled to a depth-dependent spatially harmonic tangential magnetostatic field to the magnetar crust, similar to the one proposed by Wareing and Hollerbach. It turns out that, for ultra-relativistic fermions and time-intervals much less the characteristic time (comparable to the average Ohmic timescale in the crust), the corresponding linearly independent modes get their depth-dependent amplitudes expressed in terms of Mathieu’s functions and therefore, non-trivial resonances arise, leading to instabilities in the system, for computable ranges of the model parameters. In order to detail these features, we have also discussed the current density components, pointing out the regions for which the particle density has a double bounded modulation. Finally as the magnetic field induction is increasing, the instability range gets larger triggering the exponential growth of the amplitudes, once the imaginary part of the Mathieu Characteristic Exponent becomes more and more dominant.     

Initial stress formulae of high-order NMM and DDA for large deformation analysis

With high-order numerical manifold method (NMM) or high-order discontinuous deformation analysis method (DDA), computational accuracy of structure deformation can be improved greatly. However, poor accuracy is obtained and even computation is not convergent while treating large deformation problems, due to inaccurate or incorrect high-order initial stress formulae. Based on 2D triangular mathematical meshes and polynomial cover functions in high-order NMM, exact formulae for high-order initial stresses are deduced to depict configuration change of structures under large deformations. The formulae are expressed in polynomial forms so as to be used in simplex integrations. The approach is also extended to high-order DDA. Comparing with analytical solutions, accurate results for large deformation of a cantilever beam prove the validity of the proposed formulae.     

单位圆内亚纯函数及其导数的公共Borel方向

证明了单位圆内的有究正级亚纯函数及其导数的Borel半径分布安全一致。     

Effects of Wave-Particle Interactions on Double-Hump Distributions of the H + Polar Wind

A Monte Carlo simulation is used in order to study the effects of wave-particle interactions (WPI) on H⁺ distributions in the polar wind outflow. The simulation also considers effects of the gravity, the polarization electric field, the divergence of geomagnetic field lines and H⁺−O⁺ Coulomb collisions. The proton velocity distribution function (VDF) and the profiles of its moments (density, bulk velocity, parallel and perpendicular temperatures, heat flux…) are found for different levels of WPI, i.e., for different values of the normalized diffusion rate in the velocity space (D _⊥). We find that the wave-particle interactions accelerate the polar wind and can have important effects on the double-hump H⁺ distribution obtained in the transition region between the collision-dominated low altitudes and the collisionless high altitude regions.     

基于等价方差-协方差的粗差探测敏感度分析及实现

选权迭代法在面对独立观测量中的粗差时能够表现出良好的探测效果,但由于其只是一种基于独立观测值的稳健估计法,没有考虑到观测值之间的相关性[1]。而现有的等价权函数虽然都满足稳健估计的要求,但由于所构造的等价权阵不对称,使得最后平差结果严重偏离实际情况。本文介绍在传统稳健估计的基础上,在定权时充分考虑相关观测值之间相关性的不变性,构造对称的方差—协方差阵不断扩大,并通过VB进行编程及实例分析,发现该方法对粗差的敏感度非常强,探测精度很高。     

Analytical model of magnetic reconnection in the presence of shock waves attached to a current sheet

We consider a stationary two-dimensional model of magnetic reconnection in plasma. The model includes a current sheet and four MHD shock waves attached to its endpoints. The solution to the problem has been found in an analytical form that admits of efficient numerical implementation. We analyze in detail the structure of the magnetic field in the reconnection region and its variation with model parameters.