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Dissimilar bouncy walkers

Lomholt, Michael A; Lizana, Ludvig and Ambjörnsson, Tobias LU (2011) In Journal of Chemical Physics 134(4).
Abstract
We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0<α<1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows... (More)
We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0<α<1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows as t(δ) with time t, where δ = α∕(1 + α). If instead ϱ is light-tailed such that the mean friction constant exist, S(Q, t) decays exponentially and the MSD scales as t(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Chemical Physics
volume
134
issue
4
publisher
American Institute of Physics
external identifiers
  • wos:000286897600127
  • pmid:21280802
  • scopus:79551609552
ISSN
0021-9606
DOI
10.1063/1.3526941
language
English
LU publication?
yes
id
1773bf5b-9c69-4d50-8b1f-f4f4250e98ba (old id 1832507)
date added to LUP
2011-03-30 14:13:58
date last changed
2017-01-01 03:11:57
@article{1773bf5b-9c69-4d50-8b1f-f4f4250e98ba,
  abstract     = {We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0&lt;α&lt;1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows as t(δ) with time t, where δ = α∕(1 + α). If instead ϱ is light-tailed such that the mean friction constant exist, S(Q, t) decays exponentially and the MSD scales as t(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.},
  articleno    = {045101},
  author       = {Lomholt, Michael A and Lizana, Ludvig and Ambjörnsson, Tobias},
  issn         = {0021-9606},
  language     = {eng},
  number       = {4},
  publisher    = {American Institute of Physics},
  series       = {Journal of Chemical Physics},
  title        = {Dissimilar bouncy walkers},
  url          = {http://dx.doi.org/10.1063/1.3526941},
  volume       = {134},
  year         = {2011},
}