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Ridge network in crumpled paper.

Christian André Andresen1, Alex Hansen, Jean Schmittbuhl

  • 1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Christian.Andresen@ntnu.no

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
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Researchers analyzed crumpled paper networks, revealing power-law and log-normal distributions in ridge lengths. Network analysis showed disassortative correlations and an exponential degree distribution tail.

Area of Science:

  • Materials Science
  • Network Science
  • Statistical Physics

Background:

  • Crumpled paper exhibits complex network structures.
  • Understanding these networks provides insights into material properties and topological organization.

Purpose of the Study:

  • To characterize the network formed by ridges in crumpled and unfolded paper.
  • To investigate the statistical and spatial properties of this paper network.

Main Methods:

  • Square paper sheets were crumpled, unfolded, and their height profiles measured using laser profilometry.
  • Ridges were extracted from height profiles to form network nodes (intersections) and links (ridges).
  • Network properties, including ridge length distribution, degree distribution, and degree correlation, were analyzed.

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Main Results:

  • Ridge length distribution followed a log-normal pattern for shorter ridges and a power law for longer ridges.
  • The network's degree distribution exhibited an exponentially decaying tail.
  • Degree correlation analysis indicated a disassortative network structure.
  • Facets and Voronoi diagrams formed by nodes were also investigated.

Conclusions:

  • The study quantifies the complex network topology of crumpled paper ridges.
  • Findings contribute to understanding the statistical mechanics of disordered materials and network formation.