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

Autor:	Sipos, Andras A.
Rok vydání:	2016
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs
Zdroj:	SIPOS, A. (2020). Ooid growth: Uniqueness of time-invariant, smooth shapes in 2D. European Journal of Applied Mathematics, 31(1), 172-182
Druh dokumentu:	Working Paper
DOI:	10.1017/S0956792519000019
Popis:	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. Comment: 10 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.06394 Zobrazit plný text záznamu View this record from Arxiv