We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Tree Growth Parameter in the Eden Model on Face-Centered Hypercubic Lattices.
- Authors
Zobov, V. E.; Popov, M. A.
- Abstract
In the Eden model, we investigate how the tree growth parameter depends on the space dimension d for face-centered hypercubic lattices. We find the first three terms of the 1/d-expansion for this parameter directly from the generating function without calculating the number of trees because the growth parameter is the reciprocal coordinate of the singular point of the tree generating function. The same growth parameter was calculated by computer experiment where the ratios between the numbers of trees without intersections and trees without restrictions in the dimensions 3, 4, 6, 8, and 10 were estimated by the Monte Carlo method on face-centered cubic lattices. The results of the two methods agree well. Comparing with the previously performed computer experiment for simple hypercubic lattices, we observe that the values of the singular exponents for the tree generating functions are close for two different types of lattices.
- Subjects
COMBINATORICS; MONTE Carlo method; MATHEMATICAL models; STATISTICAL sampling; PROBABILITY theory; VALUES (Ethics)
- Publication
Theoretical & Mathematical Physics, 2005, Vol 144, Issue 3, p1361
- ISSN
0040-5779
- Publication type
Academic Journal
- DOI
10.1007/s11232-005-0165-z