First Passage Percolation on \(\mathbb {Z}^2\): A Simulation Study

First Passage Percolation on \(\mathbb {Z}^2\) : A Simulation Study

Deijfen, Maria (author): Stockholms universitet,Matematiska institutionen,Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.

(creator_code:org_t)

2015-08-30
2015
English.
In: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 161:3, s. 657-678

Related links:: https://urn.kb.se/re...; show more...; https://doi.org/10.1...; https://urn.kb.se/re...; show less...

Abstract Subject headings

First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Probability Theo ...

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.