Modeling Multifractality of the Solar Wind

The question of multifractality is of great importance because it allows us to investigate interplanetary hydromagnetic turbulence. The multifractal spectrum has been investigated with Voyager (magnetic field) data in the outer heliosphere and with Helios (plasma) data in the inner heliosphere. We use the Grassberger and Procaccia method that allows calculation of the generalized dimensions of the solar wind attractor in the phase space directly from the cleaned experimental signal. We analyze time series of plasma parameters of the low-speed streams of the solar wind measured in situ by Helios in the inner heliosphere. The resulting spectrum of dimensions shows a multifractal structure of the solar wind attractor. In order to quantify that multifractality, we use a simple analytical model of the dynamical system. Namely, we consider the generalized self-similar baker’s map with two parameters describing uniform compression and natural invariant measure on the attractor of the system. The action of this map exhibits stretching and folding properties leading to sensitive dependence on initial conditions. The obtained solar wind singularity spectrum is consistent with that for the multifractal measure on the weighted baker’s map.     

基于自仿射分形建模的干涉仿真

对合成孔径雷达干涉仿真进行了深入研究,阐述了干涉仿真的基本原理,分析了影响干涉合成孔径雷达图像质量的各种噪声干扰因素,重点讨论了干涉合成孔径雷达仿真模型以及建立准确模型的重要性.比较了目前常用的干涉仿真模型,分析了这些模型在仿真过程中存在的缺陷,并基于自仿射分形理论建模仿真了实际的干涉过程,获得了满足合成孔径雷达空间采样率的数字高程模型.仿真结果表明,利用自仿射分形理论仿真不仅可以真实逼真地反映自然目标场景的随机起伏特性和雷达图像特有的几何畸变现象,而且可以对去相干因素进行定量分析,同时有助于验证干涉处理算法和优化系统设计.      

Self-acceleration of nuclear flames in supernovae

The speed of the laminar flame in a degenerate carbon-oxygen white dwarf is too slow to produce a Type I supernova. We draw attention to the role of the Landau instability in wrinkling the flame front. This roughening of the front surface can cause an appreciable enhancement in the flame velocity. For typical presupernova conditions the density jump across the front is small. This implies the applicability of the potential approximation for describing the flow pattern and allows derivation of the Frankel equation for flame propagation. We report the results of our numerical experiments with this equation in a highly nonlinear regime. These calculations, coupled with analytic approximations allow us to determine the dependence of the fractal dimension of the front surface on the density jump across the front. Astrophysical implications of our results are discussed.     

基于DFT的水射流红外热像频域时空分析

基于二维离散傅里叶变换及空间频谱分析,对水射流湍流脉动的空间尺度进行了研究,得到了由红外辐射温度表征的被动标量湍流场在对流区、耗散区、惯性子区的特征空间尺度及其时间演化规律.对射流不同区域的关心点重新采样,得到湍流场中关心点的时间序列,利用一维离散傅里叶变换,分析了对流区大尺度涡中心、惯性子区小尺度涡中心、耗散区及射流轴心线上各关心点的湍流波动特征.计算了时间序列频谱的分形维数,研究了自由湍流不同尺度区间上述各关心点湍流脉动的分形特征.