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摘要翻译：
考虑了具有空间离散尺度不变性(DSI)的分形过程的动力学和动力学行为。空间DSI意味着存在一个基本标度比(b_1)。我们讨论了与时间相关的物理过程，由于时间的演化，这些过程形成了一个形式为$\xi\propto t^{1/z}$的特征长度，其中z是动力学指数。因此，我们推测，物理过程和分形对称性之间的相互作用导致了时间DSI的出现，其基本时间标度比为$\tau=b_1^z$。在不可逆和平衡临界现象领域中，对随机游动和具有广泛普适类的代表性系统进行了数值检验。
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英文标题：
《On the occurrence of oscillatory modulations in the power-law behavior
of dynamic and kinetic processes in fractals》
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作者：
M. A. Bab, G. Fabricius and Ezequiel V. Albano. (INIFTA, UNLP. La
Plata. Argentina)
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b_1). We address time-dependent physical processes, which as a consequence of the time evolution develop a characteristic length of the form $\xi \propto t^{1/z}$, where z is the dynamic exponent. So, we conjecture that the interplay between the physical process and the symmetry properties of the fractal leads to the occurrence of time DSI evidenced by soft log-periodic modulations of physical observables, with a fundamental time scaling ratio given by $\tau = b_1 ^z$. The conjecture is tested numerically for random walks, and representative systems of broad universality classes in the fields of irreversible and equilibrium critical phenomena.
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PDF链接：
https://arxiv.org/pdf/708.2222
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