The Dynamics of Vanishing in Fractal Spaces

What is it about?

Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. 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.

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Photo by Deleece Cook on Unsplash

Photo by Deleece Cook on Unsplash

Why is it important?

Fractals, while appearing complex, are created simply by repeating the same patterns. Mother nature has employed fractal designs for eons, and it is only in recent times that humans have started emulating these natural structures for innovative device design and development. The investigation of transport phenomena such as heat transfer and fluid flow within fractal spaces not only deepens our scientific understanding but also translates into tangible advancements in various industries. By capitalizing on the unique attributes of fractal geometries, engineers and scientists are poised to revolutionize processes and technologies across sectors ranging from energy to environmental management and nanomedicine. Here, 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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