Statistical analysis on abrasion processes of pebble populations – running

The shape of pebbles is an important problem in sedimentology because shape carries information on the abrasion and transport processes. In our research we study a new classification system for pebble shapes[2] which is based on the number and type of static equilibrium points, and the relationship between equilibria carried by the so called Morse-Smale complex. Grant TÁMOP-4.2.2.B-10/1-2010-0009 enabled us to scan a few hundred pebbles by a 3D laser scanner. Scanning results in a dense triangulated polyhedron, often with 100.000 faces or more, thus identifying equilibrium points needs high computational capacity. Our first goal in this project is to identify equilibrium points and Morse-Smale complexes of the scanned pebbles.

Our other goal is to model the abrasion processes of pebble populations, based on the PDE called box equations by Domokos and Gibbons [1]. The simulation of the equations treats 100-1000 pebbles simultaneously, following the shape evolution of the pebble population in time. We are interested whether there are self-similar solutions or not, and also in the role of segregation which can be often observed on shingle beaches.

[1] G. Domokos, G. W. Gibbons: The evolution of pebble size and shape
in space and time. Proc R Soc A, published online May 9, 2012, doi:
[2] G. Domokos, A.Á. Sipos, T. Szabó, P. Várkonyi: Pebbles, shapes and
equilibria. Math Geosciences (2010) Vol 42 (1) 29-47.

Project owner:
Szabó Tímea (Szilárdságtani és Tartószerkezeti Tanszék)
Szilárdságtani és Tartószerkezeti Tanszék (ÉPK-SZT)