### Abstract

If an isotropic rough surface is intersected with a plane near the highest points of the surface, the resulting intersection will comprise a set of approximately circular islands whose size distribution gives some information about the nature of the contact process for the rough surface. Statistical arguments are used to predict the distribution of line segment lengths obtained when a random straight line intersects a random distribution of circular islands. The resulting expression leads to an Abel equation, which can be inverted explicitly to predict the distribution of island radii from the distribution of length segments above the given height in a two-dimensional profilometer output.The resulting expression is tested by comparing its predictions with the bearing area island distribution for an isotropic fractal rough surface defined by the random mid-point displacement (RMD) algorithm. Also, by adding extra scales in the RMD algorithm, the effect of measurement resolution on the mean island radius and the predicted distribution is explored.

Original language | English |
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Pages (from-to) | 131-137 |

Number of pages | 7 |

Journal | Wear |

Volume | 257 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2004 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Materials Chemistry

### Cite this

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*Wear*, vol. 257, no. 1-2, pp. 131-137. https://doi.org/10.1016/j.wear.2003.10.020

**Distribution of three-dimensional islands from two-dimensional line segment length distribution.** / Jang, Yong Hoon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Distribution of three-dimensional islands from two-dimensional line segment length distribution

AU - Jang, Yong Hoon

PY - 2004/7/1

Y1 - 2004/7/1

N2 - If an isotropic rough surface is intersected with a plane near the highest points of the surface, the resulting intersection will comprise a set of approximately circular islands whose size distribution gives some information about the nature of the contact process for the rough surface. Statistical arguments are used to predict the distribution of line segment lengths obtained when a random straight line intersects a random distribution of circular islands. The resulting expression leads to an Abel equation, which can be inverted explicitly to predict the distribution of island radii from the distribution of length segments above the given height in a two-dimensional profilometer output.The resulting expression is tested by comparing its predictions with the bearing area island distribution for an isotropic fractal rough surface defined by the random mid-point displacement (RMD) algorithm. Also, by adding extra scales in the RMD algorithm, the effect of measurement resolution on the mean island radius and the predicted distribution is explored.

AB - If an isotropic rough surface is intersected with a plane near the highest points of the surface, the resulting intersection will comprise a set of approximately circular islands whose size distribution gives some information about the nature of the contact process for the rough surface. Statistical arguments are used to predict the distribution of line segment lengths obtained when a random straight line intersects a random distribution of circular islands. The resulting expression leads to an Abel equation, which can be inverted explicitly to predict the distribution of island radii from the distribution of length segments above the given height in a two-dimensional profilometer output.The resulting expression is tested by comparing its predictions with the bearing area island distribution for an isotropic fractal rough surface defined by the random mid-point displacement (RMD) algorithm. Also, by adding extra scales in the RMD algorithm, the effect of measurement resolution on the mean island radius and the predicted distribution is explored.

UR - http://www.scopus.com/inward/record.url?scp=2642544727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2642544727&partnerID=8YFLogxK

U2 - 10.1016/j.wear.2003.10.020

DO - 10.1016/j.wear.2003.10.020

M3 - Article

AN - SCOPUS:2642544727

VL - 257

SP - 131

EP - 137

JO - Wear

JF - Wear

SN - 0043-1648

IS - 1-2

ER -