Solution of the Roth-Marques-Durian Rotational Abrasion Model

Details Solution of the Roth-Marques-Durian Rotational Abrasion Model Solution of the Roth-Marques-Durian Rotational Abrasion Model

2010-12-10

arxiv.org/abs/1012.2356v1

Phys. Rev. E 83, 031304 (2011)

Physics

Condensed Matter

Soft Condensed Matter

5 pages, 4 figures

Scientific paper

10.1103/PhysRevE.83.031304

We solve the rotational abrasion model of Roth, Marques and Durian (arXiv:1009.3492), a one-dimensional quasilinear partial differential equation resembling the inviscid Burgers equation with the unusual feature of a step function factor as a coefficient. The complexity of the solution is primarily in keeping track of the cases in the piecewise function that results from certain amputation and interpolation processes, so we also extract from it a model of an evolving planar tree graph that tracks the evolution of the coarse features of the contour.

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