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arXiv · 1602.06394

Ooid growth: Uniqueness of time-invariant, smooth shapes in 2D

Andras A. Sipos
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Abstract

Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping we demonstrate that the steady parameters associated with the physical environment determine a unique, time-invariant, compact shape among smooth, convex curves embedded in $R^2$. It is also revealed that any time-invariant solution possesses $D_2$ symmetry. The model predictions remarkably agree with ooid shapes observed in nature.

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Andras A. Sipos. 2016-02-20. Ooid growth: Uniqueness of time-invariant, smooth shapes in 2D. https://doi.org/10.1017/s0956792519000019

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