分形空间中的消失：热熔融与流体动力学坍缩
Vanishing in Fractal Space: Thermal Melting and Hydrodynamic Collapse
AI总结：
本研究探讨分形空间中热熔融与流体动力学坍缩的消失动力学，提出估计消失时间的解析表达式，并揭示粘度与分形维数耦合产生最小坍缩时间。
摘要：
分形在自然界中无处不在，通过跨越多个尺度的自组织模式展现出复杂的几何结构。在此，我们研究超越稳态的几何与消失动力学之间的相互作用，涉及分数阶连续模型中的相变热熔融和流体动力学空穴坍缩。我们提出了用于估计消失时间的一般解析表达式，其适用性取决于空间的分形性。我们将我们的发现应用于对植物生长至关重要的分形环境：自然土壤。我们聚焦于不可压缩流体中空腔收缩的输运现象，进行了超越无粘极限的数值研究。我们揭示了如何通过流体粘度与表面分形维数之间的非平凡耦合产生最小坍缩时间。
英文摘要：
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the vanishing dynamics, through phase-transitional thermal melting and hydrodynamic void collapse, within fractional continuous models. We present general analytical expressions for estimating vanishing times with their applicability contingent on the fractality of space. We apply our findings on the fractal environments crucial for plant growth: natural soils. We focus on the transport phenomenon of cavity shrinkage in incompressible fluid, conducting a numerical study beyond the inviscid limit. We reveal how a minimal collapsing time can emerge through a non-trivial coupling between the fluid viscosity and the surface fractal dimension.
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