自组织临界性系统分形能量耗散域的普适标度律
A Universal Scaling Law for the Fractal Energy Dissipation Domain in Self-Organized Criticality Systems
摘要：
自组织临界性状态下的非线性耗散系统在各种规模的雪崩中零星地释放能量，例如地震，极光亚暴，太阳和恒星耀斑，软伽马射线中继器和脉冲星故障。事件能量$E$的统计发生频率分布通常呈现幂律状函数$N(E)\propto E^{-α_E}$，其具有幂律斜率$α_E \approx 1.5$。能量的幂律斜率$α_E$可以通过$D=3/α_E$与空间能量耗散域的分维$D$相关联，该分维预测了具有$D=2$的区域破裂或区域扩展过程的幂律斜率$α_E=1.5$。对于太阳耀斑和恒星耀斑，在磁场重联区域的电流片或分界线表面自然地提供了2-D面积扩展耗散域。因此，这个普遍的标度律提供了一个有用的新的诊断拓扑结构的空间能量耗散域的地球物理和天体物理观测。
英文摘要：
Nonlinear dissipative systems in the state of self-organized criticality release energy sporadically in avalanches of all sizes, such as in earthquakes, auroral substorms, solar and stellar flares, soft gamma-ray repeaters, and pulsar glitches. The statistical occurrence frequency distributions of event energies $E$ generally exhibit a powerlaw-like function $N(E)\propto E^{-α_E}$ with a powerlaw slope of $α_E \approx 1.5$. The powerlaw slope $α_E$ of energies can be related to the fractal dimension $D$ of the spatial energy dissipation domain by $D=3/α_E$, which predicts a powerlaw slope $α_E=1.5$ for area-rupturing or area-spreading processes with $D=2$. For solar and stellar flares, 2-D area-spreading dissipation domains are naturally provided in current sheets or separatrix surfaces in a magnetic reconnection region. Thus, this universal scaling law provides a useful new diagnostic on the topology of the spatial energy dissipation domain in geophysical and astrophysical observations.
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