Low-Density Series Expansion for the Domany-Kinzel Model : General Physics
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概要
- 論文の詳細を見る
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 = αp with p ∈ [0, 1] and α ∈ [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 α 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 α of the convergence of estimations of critical values and critical exponents. In the mixed site-bond DP region, 1 ≤ α ≤ 1.3553, the convergence is excellent. As a ⇾ 2 slowing down of convergence and as a ⇾ 0 peculiar oscillation of estimations are observed. This paper is the first report of the systematic study of DK model by series expansion method.
- 社団法人日本物理学会の論文
- 2001-02-15
著者
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Katori Makoto
Department Of Pharmacology Kitasato University School Of Medicine
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INUI Norio
Department of Mechanical and Inteligent Engineering,Himeji Institute of Technology
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Inui Norio
Department Of Mechanical And Intelligent Engineering Himeji Institute Of Technology
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M BHATTI
Faculty of Information Science and Technology, Multimedia University
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M Bhatti
Faculty Of Information Science And Technology Multimedia University
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Bhatti Faqir
Faculty Of Information Science And Technology Multimedia University
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KATORI Makoto
Department of Physics, Faculty of Science and Engineering, Chuo University
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Inui Norio
Department of Mechanical and Inteligent Engineering, Himiji Institute of Technology
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