New paths for random walkers

@article{Shlesinger1992NewPF,
  title={New paths for random walkers},
  author={M. Shlesinger},
  journal={Nature},
  year={1992},
  volume={355},
  pages={396-397}
}
Number of common sites visited by N random walkers.
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Absence of PS integrins or laminin A affects extracellular adhesion, but not intracellular assembly, of hemiadherens and neuromuscular junctions in Drosophila embryos.
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It is suggested that neuromuscular contact in part requires basement membrane adhesion to the general muscle surface, and this form of adhesion is completely abolished in the absence of laminin A. Expand
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References

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Territory covered by N diffusing particles
THE number of distinct sites visited by a random walker after t steps is of great interest1–21, as it provides a direct measure of the territory covered by a diffusing particle. Thus, this quantityExpand
On reptation in polymer melts
A rederivation of the basic scaling laws for polymer reptation in a condensed phase yield directly for the coefficient of self‐diffusion. Dr∼M−2, where M is proportional to the polymer molecularExpand
On the Williams-Watts function of dielectric relaxation.
  • M. Shlesinger, E. Montroll
  • Chemistry, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1984
TLDR
This work derives this form of varphi(alpha)(t) from the following random-walk model: if the diffusion of defects toward dipoles is executed as a continuous-time random walk composed of an alternation of steps and pauses and the pausing-time distribution function has a long tail of the form psi(t) infinity t(-1-alpha), then the relaxation function has the above fractional exponential form. Expand
Walks, walls, wetting, and melting
New results concerning the statistics of, in particular,p random walkers on a line whose paths do not cross are reported, extended, and interpreted. A general mechanism yielding phase transitions inExpand
Reptation of a Polymer Chain in the Presence of Fixed Obstacles
We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannotExpand