A study by the University of Pennsylvania’s Douglas Jerolmack and mathematicians at Budapest University of Technology and Economics indicates that the abrasion of river rocks occurs in two stages.
The Budapest mathematicians considered what is typically regarded as a geological problem from a purely geometric perspective. They developed a mathematical model formalizing the idea that the more a part of a rock protrudes the faster it will be worn down. It relates the erosion rate of a pebble to the pebble's curvature.
The model predicts two stages of abrasion: First any protruding parts are worn down without the diameter of the pebble decreasing; then, once the pebble is spherical, it begins to shrink in size.
The new model will help geologists answer questions like how far a pebble found in a riverbed has traveled and how long it took to make that journey.
Read the University of Pennsylvania's coverage.