分形和混沌理论在太阳物理学中的应用

本文对非线性科学的两修发支－分形和混沌－在太阳物理学中的应用情况作了综述，主要内容包括；太阳活动混沌性的揭示；对太阳活动混沌的可能解释－太阳非线性发电机；一些太阳现象的分形描述；耀斑的自组织临界行为研究。最后给出了作者对这一领域工作前景的展望。     

分形和混沌理论在太阳物理学中的应用

本文对非线性科学的两个重要分支－分形和混沌－在太阳物理学中的应用情况作了综述，主要内容包括：太阳活动混沌性的揭示；对太阳活动混沌性的可能解释－太阳非线性发电机理论；一些太阳现象的分形描述；耀斑的自组织临界行为研究。最后给出了作者对这一领域工作前景的展望。     

控制太阳活动的混沌吸引子

随着非线性科学研究的进展,可利用表征太阳活动的太阳活动指数组成的时间序列来寻找或许存在的太阳混沌吸引子,并计算其关联维数、最大Ｌｙａｐｕｎｏｖ指数及其它特征量。文中综述了用非线性科学的某些概念来研究太阳活动的进展及其在太阳活动预报方面的一些应用。     

控制太阳活动的混沌吸引子(英)

随着非线性科学研究的进展,可利用表征太阳活动的太阳活动指数组成的时间序列来寻找或许存在的太阳混沌吸引子,并计算其关联维数、最大Lyapunov指数以及其它特征量．文中综述了用非线性科学的某些概念来研究太阳活动的进展及其在太阳活动预报方面的一些应用．     

分形和混沌理论在天体物理中的应用

本文对当前应用日益广泛的非线性科学的两个重要分支──分形和混沌动力系统理论──作概述性的介绍，并简介了这两种非线性方法在天体物理中应用的重要结果，特别强调一些天体物理中典型的分形和混沌现象，诸如星系大尺度结构（分形）和星系动力学（混沌）。     

分形和混沌理论在天体物理中的应用

本文对当前应用日益广泛的非线性科学的两个重要分支－分形和混沌动力系统理论－作概述性的介绍，并简介弛这两种非线性方法在天体物理应用的重要结果，特别强调一些于体物理中典型的分形和混沌现象，诸如星系大尺度结构和星系动力学。     

基于日球物理学事件知识库的太阳活动识别

太阳图像中包含明显的太阳活动区域,以及无现象的太阳宁静区。从太阳图像中识别有效的太阳活动区域,是图像处理技术在天文研究中的典型应用。得益于美国太阳动力学天文台的日球物理学事件知识库提供的实时太阳观测数据,提出了一种基于日球物理学事件知识库的太阳活动识别方法。此方法获取6种太阳活动的信息(发生时间、位置、区域面积),建立对应时间的全日面图像的尺度变换模型。结合位置与区域面积信息,对不同太阳活动进行梯度阈值分割,边界识别方法被用来定位和识别太阳活动的区域。然后,对太阳图像特征参数相关性的研究,得到每种太阳活动的最佳特征参数组合。方法实现了对太阳活动的精确定位和有效识别,为后续工作的开展提供了便利。此外,对不同太阳活动区域提取特定组合的特征,可以为基于内容的图像检索系统建立精简的图像特征集提供一种可行办法。     

类星体3C 446射电光变非线性特性分析

类星体有剧烈、大幅度的光变现象, 光变研究有助于建立与观测相符的理论模型. 这篇文章从密歇根大学射电天文台数据库收集了类星体3C 446射电4.8、8.0和14.5GHz波段的长期观测数据. 传统的线性方法难以分析复杂的光变现象, 文章采用了集合经验模态分解(Ensemble Empirical Mode Decomposition, EEMD)方法和非线性分析方法相结合, 从混沌动力学特性、分形特性和周期性多角度对类星体光变随时间演化的规律进行了较全面的分析, 并重点对比分析了除去周期成分或混沌成分前后, 光变的周期性和非线性特性是否存在明显区别. 分析结果表明, 类星体3C 446射电波段光变资料由周期成分、趋势成分和混沌成分组成, 光变具有周期性、混沌性和分形特性. 除去混沌成分和趋势成分后的光变周期与原始光变资料的周期完全相同, 而两者的混沌和分形特性有明显不同. 从饱和关联维数来看, 重构动力学系统时, 除去周期成分和趋势成分后的光变资料比原始光变资料需要更多的独立参量, Kolmogorov熵值表明前者信息的损失率比后者大, 系统的混沌程度更高, 系统也更复杂, Hurst值表明后者自相似性和长程相关性比前者略强.     

22周上升相日面各经度带的活动规律

本文回顾了１９８３年以来的一些对太阳活动的谱分析结果，大致可分为两种规律；在太阳活动１１年周期的上升相一般呈现８０天左右的周期。下降相呈现１５０天左右的周期。这些规律均是由太阳全日面总体活动指数得到的谱分析结果。     

地球自转变化中的太阳物理效应

对太阳活动和太阳风影响地球自转的研究现状作了评述。首先了地球自转变化的表示和测定方法，引起地球自转变化的各种扰动源以及自转长期变化中的潮汐效应和非潮汐效应。然后对地球自转变化中的太阳活动周期调制，太阳耀斑可能引起地球自转突然减速以及太阳风能否影响地球自转等问题的国内外研究现状和结果、分析作了谰论性阐述，最后作了简要总结。     

Diffusion of magnetic flux elements on a fractal geometry

Recent observations have indicated that magnetic field elements are distributed on the Sun in fractal patterns with dimension D < 2. We suggest that the transport of magnetic field elements across the solar surface should be treated as diffusion on a fractal geometry. We review a semi-analytical, theoretical treatment of fractal diffusion. Comparison with observations of small-scale motions of solar magnetic flux concentrations indicates that fractal diffusion may be taking place with dimension in the range 1.3 to 1.8. It is shown that, compared to the predictions that would be made for two-dimensional diffusion, fractal diffusion in this range would lead to an increased level of in situ flux cancellation in decaying active regions by 7% to 35%. Other work in specialities outside of solar physics may be useful in explaining solar magnetic phenomena.     

Fractal dimensions of solar activity

Solar activity changes in amplitude and long-term behavior irregularly. Fractal theory is used to examine the variation of solar activity, using daily solar indices (i.e., sunspot number, 10.7 cm radio flux, the SME L, Fexiv coronal emission, and the total solar irradiance measured by the ERB (Earth Radiation Budget) on the NIMBUS-7. It can handle irregular variations quantitatively. The fractal dimension of 10.7 cm radio fluxes in cycle 21 for periods of 7 days or less was 1.28, 1.3 for periods longer than 272 days, and 1.86 for periods between them, for example. Fractal dimensions for other solar indices show similar tendencies. These results suggest that solar activity varies more irregularly for time scales that are longer than several days and shorter than several months. Yearly values of fractal dimensions and bending points do not change in concert with the solar cycle.     

A Fractal Structure of the Time Series of Global Indices of Solar Activity

The structure of time series of daily global indices of solar activity is investigated: the sunspot numbers for the time interval between the years 1854 and 1996, the Greenwich total sunspot area for 1874–1983, the radio-flux at 10.7 cm (F10.7) for 1964–1996, and the Stanford mean solar magnetic field for 1975–1996. The fractal dimensions are determined by two fractal and spectral methods. The identified three time-scale ranges, 2 days–2 months, 2 months–2 years, 2 years–8 and more years, with the fractal dimensions 1.4–1.6, 2, 1.2–1.6, respectively, show perhaps some fractal structure of time series of global indices. The first time-scale range may correspond to ordinary brownian noise and the second to flicker noise. The solar rotation influence of the value of the fractal dimensions at the time range close to the rotational period is studied.     

Low-dimensional chaos and fractal properties of long-term sunspot activity

Two primary solar-activity indicators sunspot numbers(SNs)and sunspot areas(SAs)in the time interval from November 1874 to December 2012 are used to determine the chaotic and fractal properties of solar activity.The results show that(1)the long-term solar activity is governed by a low-dimensional chaotic strange attractor,and its fractal motion shows a long-term persistence on large scales;(2)both the fractal dimension and maximal Lyapunov exponent of SAs are larger than those of SNs,implying that the dynamical system of SAs is more chaotic and complex than SNs;(3)the predictions of solar activity should only be done for short-to mid-term behaviors due to its intrinsic complexity;moreover,the predictability time of SAs is obviously smaller than that of SNs and previous results.     

Fractal dimensions of the time variation of solar radio emission

The fractal dimensions of solar radio fluxes at 245, 410, 610, 1415, 2695, 2800, 4995, 8800, and 15400 MHz are calculated for the data period 1976–1990. The fractal dimension used here is an index to quantify the time variability of radio emission. The fractal dimensions were found to have values in the range of 1.2–2.0 for time scales of 10 days, 1–10 months, and 10 months. The lowest values were found around 3 GHz. The annual variations of fractal dimensions are small and are not in concert with the solar cycle for most of the fractal dimension at the analyzed frequencies except those for 4995 and 8800 MHz. The annual variations of the fractal dimensions are similar for the sunspot number and radio emission around 3 GHz; this implies a close relation between them. According to a simulation, larger fractal dimensions correspond to shorter e-folding time constants in the distribution of radio-source lifetimes.     

Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent Than Others?

Multiple recent investigations of solar magnetic-field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17?733 magnetograms in total) observed by SOHO’s Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i)?a?widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii)?a?lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately, for major solar-flare prediction.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.     

EVALUATION OF TWO FRACTAL METHODS FOR MAGNETOGRAM IMAGE ANALYSIS

Fractal and multifractal techniques have been applied to various types of solar data to study the fractal properties of sunspots as well as the distribution of photospheric magnetic fields and the role of random motions on the solar surface in this distribution. Other research includes the investigation of changes in the fractal dimension as an indicator for solar flares. Here we evaluate the efficacy of two methods for determining the fractal dimension of an image data set: the Differential Box Counting scheme and a new method, the Jaenisch scheme. To determine the sensitivity of the techniques to changes in image complexity, various types of constructed images are analyzed. In addition, we apply this method to solar magnetogram data from Marshall Space Flight Center's vector magnetograph.     

A New Algorithm for Pattern Recognition and its Application to Granulation and Limb Faculae

We have developed a new pattern-recognition algorithm based on multiple intensity clips which assures an optimal adaptation to the solar structure under study. The shapes found at higher clip levels are repeatedly extended to lower levels, thus filling more and more of the observed intensity contours. Additionally, at each intensity threshold new shapes, exceeding the level, are integrated. The number and height of the levels can be optimized making this `multiple level tracking' algorithm (MLT) superior to commonly used Fourier-based recognition techniques (FBR). The capability of MLT is demonstrated by application to the intensity structure of solar granulation near the disk center, both speckle reconstructed and not. Comparisons with Doppler maps prove its reliability. The granular pattern recognized by MLT differs essentially from that obtained with FBR. Elongated `snake-like' granules do not occur with MLT and, consequently, the perimeter-area distribution exhibits only a marginal `second branch' of higher fractal dimension, which dramatically diminishes the better the MLT pattern matches the granular structure. The final distribution obtained with optimized parameters has a single fractal dimension near 1.1, making the question of a `critical size', a `second branch', and the often discussed dimension of 4/3; highly questionable. This result is equally obtained from application of MLT to the corresponding Doppler velocity map of granular up-flows. In contrast, the pattern of down-flows contains some elongated `snake-like' structures with higher fractal dimension. We also use the new algorithm to recognize speckle-reconstructed limb faculae, which MLT separates from their granular surroundings, and compare both, granules and faculae, using large statistical samples. The facular grains near cos=57° exhibit a slightly different ellipticity than the (geometrically foreshortened) adjacent granules. However, small facular grains are more round than small granules and larger grains are more similar to granules.