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

Part of: Equations of mathematical physics and other areas of application Geophysics (general) General theory in ordinary differential equations Geophysics

Published online by Cambridge University Press:  08 February 2019

ANDRÁS A. SIPOS Open the ORCID record for ANDRÁS A. SIPOS [Opens in a new window]
ANDRÁS A. SIPOS*
Affiliation:
MTA-BME Morphodynamics Research Group, Budapest, Hungary Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Budapest, Hungary email: [email protected]
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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 ℝ2. It is also revealed that any time-invariant solution possesses D2 symmetry. The model predictions remarkably agree with ooid shapes observed in nature.

Keywords

Shape evolutionooid growthtime-invariant solutionnonlocal equation

MSC classification

Primary: 35Q86: PDEs in connection with geophysics
Secondary: 34A05: Explicit solutions and reductions 34A26: Geometric methods in differential equations 86A60: Geological problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 1 , February 2020 , pp. 172 - 182
Copyright
© Cambridge University Press 2019 

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Footnotes

†

The author acknowledges the support of the NKFIH grant K-119245 and grant BME FIKP-VÍZ by EMMI.

References

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