Pebbles,Shapes, and Equilibria |
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Authors: | Gábor Domokos András Sipos Tímea Szabó Péter Várkonyi |
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Institution: | 1.Department of Mechanics, Materials and Structures,Budapest University of Technology and Economics,Budapest,Hungary |
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Abstract: | The shape of sedimentary particles may carry important information on their history. Current approaches to shape classification
(e.g. the Zingg or the Sneed and Folk system) rely on shape indices derived from the measurement of the three principal axes
of the approximating tri-axial ellipsoid. While these systems have undoubtedly proved to be useful tools, their application
inevitably requires tedious and ambiguous measurements, also classification involves the introduction of arbitrarily chosen
constants. Here we propose an alternative classification system based on the (integer) number of static equilibria. The latter
are points of the surface where the pebble is at rest on a horizontal, frictionless support. As opposed to the Zingg system,
our method relies on counting rather than measuring. We show that equilibria typically exist on two well-separated (micro
and macro) scales. Equilibria can be readily counted by simple hand experiments, i.e. the new classification scheme is practically
applicable. Based on statistical results from two different locations we demonstrate that pebbles are well mixed with respect
to the new classes, i.e. the new classification is reliable and stable in that sense. We also show that the Zingg statistics
can be extracted from the new statistics; however, substantial additional information is also available. From the practical
point of view, E-classification is substantially faster than the Zingg method. |
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