Fractal Properties of the Magnetic Polarity Scale in the Stochastic Hereditary αω-Dynamo Model
Fractal Properties of the Magnetic Polarity Scale in the Stochastic Hereditary αω-Dynamo Model
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DOI：
10.3390/fractalfract6060328
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发表时间：
2022-06
影响因子：
5.4
通讯作者：
Gleb Vodinchar -Gleb-Vodinchar -2170461579;L. Feshchenko
中科院分区：
文献类型：
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作者：
Gleb Vodinchar -Gleb-Vodinchar -2170461579;L. Feshchenko
在双模近似下研究了遗传αω-发电机模型的分形性质.该模型的相位变量描述了磁场的环向和极向分量的时间动态。利用Riemann-Liouville分数阶微分算子确定了数值模拟中场螺旋度对α效应猝灭的遗传算子。该模型还包括一个随机项。这一项的结构对应于小尺度磁场和速度模的相干结构的影响。编制了数值模拟的差分格式和程序，并进行了验证.利用该模型进行了一系列的计算实验。计算了模型中极性尺度的Hausdorff维数和极性间隔的分布。结果表明，极性尺度的Hausdorff维数小于1，即，这个比例是分形的某些控制参数值的维数值为0.87，与真实的地磁极性标度的维数值一致。模型中极性区间的分布直方图具有明显的幂律尾，这也符合真实的极性尺度的性质。
We study some fractal properties of the hereditary αω-dynamo model in the two-mode approximation. The phase variables of the model describe the temporal dynamics of the toroidal and poloidal components of the magnetic field. The hereditary operator of the quenching the α-effect by field helicity in numerical simulation is determined using the Riemann–Liouville fractional differentiation operator. The model also includes a stochastic term. The structure of this term corresponds to the effect of coherent structures from small-scale magnetic field and velocity modes. A difference scheme and a program code for numerical simulation have been developed and verified. A series of computational experiments with the model has been carried out. The Hausdorff dimension of the polarity scale in the model and the distribution of polarity intervals are calculated. It is shown that the Hausdorff dimension of the polarity scale is less than 1, i.e., this scale is a fractal. The numerical value of the dimension for some values of the control parameters is 0.87, which is consistent with the dimension of the real geomagnetic polarity scale. The distribution histogram of polarity intervals in the model has a pronounced power-law tail, which also agrees with the properties of real polarity scales.