HISTORY of BOOTSTRAP PERCOLATION
Name ''Bootstrap Percolation'' first
mentioned (to my knowledge) in the literature in 1981
(J Chalupa, P L Leath and G R Reich 1981 J. Phys. C.
12 L31; P M Kogut and P L Leath 1981 J. Phys. C 14 3187)
independently proposed earlier by
M Pollak and I Riess 1975 Phys. Status Solidi b
69 K15 and
R Kopelman, private communication.
- Different motivations for the creation of BP models.
Above references (condensed matter physics)
had atoms, which were present with
p, assumed to participate in a certain ordered state,
such as ferromagnetism,
only if a
requisite number of neighbouring atoms were also present. For some of
these early realizations the related high density percolation models
(only a single step in the culling process is realized) may be a
more suitable description of the materials involved.
Adler, Palmer and Meyer, PRL 1987 58 882.
that environmental effects of a bootstrap type
play a crucial role
in the orientational ordering process of quadrupoles in solid molecular
(ortho-H2)x (para-H2)1-x or (para-D2)x (ortho-D2)1-x
- The models have connections to rigidity percolation,
(E W Marshall E W and A B Harris 1988, Phys. Rev. B 38,
4929, and references therein; M Sahimi and S Arbibi 1989 Phy. Rev. B.
Time developments according to
the local rules of Bootstrap Percolation can be viewed as cellular automata
(D Griffeath 1988 Notices of the AMS 35 1472 and
G Vichniac 1984 Physica 10 D, 96 and 1986
''Disordered Systems and Biological Organization'',
Ed. E Bienenstock, F Fogelman-Soulie and G Weisbuch
Nato Asi. series Vol 20 Springer, Heidelberg).
- There are also metastable bootstrap models, not considered
Models closely related to canonical BP have been proposed as
descriptions of fluid flow in porous media. In these cases crack
development (J Adler and A Aharony 1988 J. Phys. A 21 1387)
of the fluid front (R Lenormand and C Zarcone 1984,
Kinetics of Aggregation and
Gelation ed F Family and D P Landau (Amsterdam: Elsevier), p.177,
M Cieplak and M O Robbins 1988 Phys. Rev. Lett. 60,
2042; 1990 Phys. Rev. B 41, 11508)
assumed to be strongly dependent on the local microstructure.