How to grow a sphere: the puzzle of giant stone balls

Speaker(s)

Piotr Szymczak

Affiliation

FUW

Language of the talk

English

Date

Oct. 27, 2026, 4:15 p.m.

Room

room 5070

Seminar

Seminar "Mathematics and Physics of Complex Systems"

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How can a stone grow to several metres across and remain nearly spherical? Such objects, known as concretions, form by mineral precipitation in the pores of sediment. Their roundness is often attributed to diffusion, which supplies dissolved material from all directions. Yet diffusion preferentially feeds protrusions and can destabilize a growing sphere. The existence of giant, smooth stone balls therefore poses a problem of morphological stability.

In this talk, I will approach concretion growth as a moving-boundary problem coupling diffusion to finite-rate precipitation. A stability analysis reveals how slow reactions allow radial expansion to outpace the amplification of surface irregularities: a body can become rounder even while its bumps grow, without surface tension smoothing its boundary. With fixed reaction coefficients, however, increasing size eventually favours instability. I will show how nonlinear precipitation kinetics and competition between neighbouring concretions for a limited supply can prevent this transition, allowing spheres to grow to metre scales. Maintaining roundness comes at a cost in growth time, providing a link between geometry, chemistry and geological history. I will discuss how the sizes, shapes and ages of natural concretions can be used to test this picture.
 

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