Low-Density Series Expansion for the Domany-Kinzel Model
Domany-Kinzel (DK) model is a family of the 1+1 dimensional stochastic cellular automata with two parameters p(1) and p(2), which simulate time evolution of interacting active elements in a random medium. By identifying a set of active sites on the spatio-temporal plane with a percolation cluster, w...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
2001
|
| Subjects: | |
| Online Access: | http://shdl.mmu.edu.my/2698/ |
| _version_ | 1848790126612709376 |
|---|---|
| author | Inui, Norio Katori, Makoto Bhatti, Faqir M |
| author_facet | Inui, Norio Katori, Makoto Bhatti, Faqir M |
| author_sort | Inui, Norio |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | Domany-Kinzel (DK) model is a family of the 1+1 dimensional stochastic cellular automata with two parameters p(1) and p(2), which simulate time evolution of interacting active elements in a random medium. By identifying a set of active sites on the spatio-temporal plane with a percolation cluster, we discuss the directed percolation (DP) transitions in the DK model. We parameterize p(1) = p and p(2) = alphap with p is an element of [0, 1] and alpha is an element of [0, 2] and calculate the mean cluster size and other quantities characterizing the DP cluster as the series of p up to order 51 for several values of alpha by using a graphical expansion formula recently given by Konno and Katori. We analyze the series by the first- and second-order differential approximations and the Zinn-Justin method and study the dependence on alpha of the convergence of estimations of critical values and critical exponents. In the mixed site-bond DP region; 1 less than or equal to alpha less than or equal to 1.3553, the convergence is excellent. As alpha -> 2 slowing down of convergence and as alpha -> 0 peculiar oscillation of estimations are observed. This paper is the first report of the systematic study of DK model by series expansion method. |
| first_indexed | 2025-11-14T18:07:40Z |
| format | Article |
| id | mmu-2698 |
| institution | Multimedia University |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:07:40Z |
| publishDate | 2001 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | mmu-26982011-09-09T03:03:45Z http://shdl.mmu.edu.my/2698/ Low-Density Series Expansion for the Domany-Kinzel Model Inui, Norio Katori, Makoto Bhatti, Faqir M QC Physics Domany-Kinzel (DK) model is a family of the 1+1 dimensional stochastic cellular automata with two parameters p(1) and p(2), which simulate time evolution of interacting active elements in a random medium. By identifying a set of active sites on the spatio-temporal plane with a percolation cluster, we discuss the directed percolation (DP) transitions in the DK model. We parameterize p(1) = p and p(2) = alphap with p is an element of [0, 1] and alpha is an element of [0, 2] and calculate the mean cluster size and other quantities characterizing the DP cluster as the series of p up to order 51 for several values of alpha by using a graphical expansion formula recently given by Konno and Katori. We analyze the series by the first- and second-order differential approximations and the Zinn-Justin method and study the dependence on alpha of the convergence of estimations of critical values and critical exponents. In the mixed site-bond DP region; 1 less than or equal to alpha less than or equal to 1.3553, the convergence is excellent. As alpha -> 2 slowing down of convergence and as alpha -> 0 peculiar oscillation of estimations are observed. This paper is the first report of the systematic study of DK model by series expansion method. 2001-02 Article NonPeerReviewed Inui, Norio and Katori, Makoto and Bhatti, Faqir M (2001) Low-Density Series Expansion for the Domany-Kinzel Model. Journal of the Physics Society Japan, 70 (2). pp. 359-366. ISSN 0031-9015 http://dx.doi.org/10.1143/JPSJ.70.359 doi:10.1143/JPSJ.70.359 doi:10.1143/JPSJ.70.359 |
| spellingShingle | QC Physics Inui, Norio Katori, Makoto Bhatti, Faqir M Low-Density Series Expansion for the Domany-Kinzel Model |
| title | Low-Density Series Expansion for the Domany-Kinzel Model |
| title_full | Low-Density Series Expansion for the Domany-Kinzel Model |
| title_fullStr | Low-Density Series Expansion for the Domany-Kinzel Model |
| title_full_unstemmed | Low-Density Series Expansion for the Domany-Kinzel Model |
| title_short | Low-Density Series Expansion for the Domany-Kinzel Model |
| title_sort | low-density series expansion for the domany-kinzel model |
| topic | QC Physics |
| url | http://shdl.mmu.edu.my/2698/ http://shdl.mmu.edu.my/2698/ http://shdl.mmu.edu.my/2698/ |