Chord length distributions in binary stochastic media in two and three dimensions Academic Article uri icon


  • Simple models for transport through stochastic media usually assume that the chord lengths of materials are distributed exponentially. Theory predicts that, in a medium consisting of disks/spheres that can interpenetrate, chord lengths in the background material (between the disks/spheres) should exactly follow an exponential. In a medium with impenetrable (non-overlapping) disks/spheres, the distribution is only approximately exponential. This paper demonstrates, through direct numerical simulations, that for randomly distributed disks in 2D and spheres in 3D, with distributions of radii, chord lengths in the background material (between the disks/spheres) are accurately described by exponentials over five orders of magnitude when the material is dilute. The chord lengths inside the disks and spheres are not exponentially distributed, but those distributions can be calculated. A scaling relationship between the mean chord lengths in the two materials is presented for an infinite medium. By knowing the mean properties of the disks/spheres in a medium, this relationship allows one to accurately describe the statistical properties of the background material. The stochastic simulations are validated by this infinite medium relationship. When the fraction of space occupied by the disks or spheres becomes large, the distributions are no longer accurately described by an exponential. 2005 Elsevier Ltd. All rights reserved.

published proceedings


altmetric score

  • 6

author list (cited authors)

  • Olson, G. L., Miller, D. S., Larsen, E. W., & Morel, J. E.

citation count

  • 25

complete list of authors

  • Olson, Gordon L||Miller, David S||Larsen, Edward W||Morel, Jim E

publication date

  • September 2006