The autocorrelation function for island areas on self-affine surfaces

Srinivasa B. Ramisetti, Carlos Campana, Guillaume Anciaux, Jean-Francois Molinari, Martin H. Mueser, Mark O. Robbins

Research output: Contribution to journalArticlepeer-review

Abstract

The spatial distribution of regions that lie above contours of constant height through a self-affine surface is studied as a function of the Hurst exponent H. If the surface represents a landscape, these regions correspond to islands. When the surface represents the height difference for contacting surfaces, the regions correspond to mechanical contacts in the common bearing area model. The autocorrelation function C(Delta r) is defined as the probability that points separated by Delta r are both within islands. The scaling of C has important implications for the stiffness and conductance of mechanical contacts. We find that its Fourier transform (C) over tilde (q) scales as a power of the wavevector magnitude q: (C) over tilde (q) alpha q(-mu) with mu = 2 + H rather than the value mu = 2 + 2H reported previously. An analytic argument for mu = 2 + H is presented using the distribution of areas contained in disconnected islands.

Original languageEnglish
Article number215004
Number of pages5
JournalJournal of Physics: Condensed Matter
Volume23
Issue number21
DOIs
Publication statusPublished - 1 Jun 2011

Keywords

  • 3D MULTISCALE APPROACH
  • ROUGH SURFACES
  • CONTACT MECHANICS
  • ELASTIC CONTACT

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