Phase transition in an elementary probabilistic cellular automaton

We investigate the inactive–active phase transition in an array of additive (exclusive-or) cellular automata (CA) under noise. The model is closely related with the Domany-Kinzel (DK) probabilistic cellular automaton (PCA), for which there are rigorous as well as numerical estimates on the transition probabilities. Here, we characterize the critical behavior of the noisy additive cellular automaton by mean field analysis and finite-size scaling and show that its phase transition belongs to the directed percolation universality class of critical behavior. As a by-product of our analysis, we argue that the critical behavior of the noisy elementary CA 90 and 102 (in Wolfram’s enumeration scheme) must be the same. We also perform an empirical investigation of the mean field equations to assess their quality and find that away from the critical point (but not necessarily very far away) the mean field approximations provide a reasonably good description of the dynamics of the PCA.

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A Probabilistic Cellular Automaton for Evolution

Journal de Physique I ◽

10.1051/jp1:1995186 ◽

1995 ◽

Vol 5 (9) ◽

pp. 1129-1134 ◽

Cited By ~ 2

Author(s):

Nikolaus Rajewsky ◽

Michael Schreckenberg

Keyword(s):

Cellular Automaton ◽

Probabilistic Cellular Automaton

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Effect of acceleration threshold on the phase transition in a cellular automaton traffic flow model

Chinese Physics B ◽

10.1088/1674-1056/20/6/064501 ◽

2011 ◽

Vol 20 (6) ◽

pp. 064501 ◽

Cited By ~ 8

Author(s):

Cheng-Jie Jin ◽

Wei Wang ◽

Kun Gao ◽

Rui Jiang

Keyword(s):

Phase Transition ◽

Cellular Automaton ◽

Traffic Flow ◽

Flow Model ◽

Traffic Flow Model ◽

Acceleration Threshold

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On the first-order phase transition in a cellular automaton traffic flow model without a slow-to-start effect

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2010/03/p03018 ◽

2010 ◽

Vol 2010 (03) ◽

pp. P03018 ◽

Cited By ~ 15

Author(s):

Cheng-Jie Jin ◽

Wei Wang ◽

Rui Jiang ◽

Kun Gao

Keyword(s):

Phase Transition ◽

Cellular Automaton ◽

Traffic Flow ◽

Order Phase Transition ◽

Flow Model ◽

Traffic Flow Model ◽

First Order ◽

First Order Phase Transition ◽

First Order Phase

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INTERACTIONS OF PEDESTRIANS INTERLACED IN T-SHAPED STRUCTURE USING A MODIFIED MULTI-FIELD CELLULAR AUTOMATON

International Journal of Modern Physics C ◽

10.1142/s0129183113500241 ◽

2013 ◽

Vol 24 (04) ◽

pp. 1350024 ◽

Cited By ~ 9

Author(s):

ZHIJIAN FU ◽

LIZHONG YANG ◽

PING RAO ◽

TAOLIN ZHANG

Keyword(s):

Phase Transition ◽

Cellular Automaton ◽

Free Flow ◽

Dominant Factor ◽

Pedestrian Flow ◽

Transition Diagram ◽

Open Boundaries ◽

The Right

Little work has been done before in the study of separating pedestrian flow interlaced. Under open boundaries, the interaction of separating pedestrian flow interlaced in a T-shaped structure was simulated, using a modified multi-field cellular automaton updating synchronously. The free-jammed phase transition diagram of pedestrian flow and principles of the pedestrian interference were obtained. The movement of pedestrians is free flow in the low entrance density. While it is a complete jammed flow with the entrance density increasing to a certain level and little difference existing between the left moving probability and the right moving probability. Thus, the dominant factor influencing pedestrian flow is the interference of opposite pedestrian flows due to changing movement directions. And it is changing to an incomplete jammed flow with this difference increasing. Thus, the dominant factor is changing to the interference of the coincident pedestrian flow and the limitation of the bottleneck.

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THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

International Journal of Modern Physics C ◽

10.1142/s0129183103005443 ◽

2003 ◽

Vol 14 (10) ◽

pp. 1305-1320 ◽

Cited By ~ 14

Author(s):

BÜLENT KUTLU

Keyword(s):

Phase Transition ◽

Ising Model ◽

Cellular Automaton ◽

Intermediate Phase ◽

Finite Size ◽

Square Lattice ◽

Two Dimensional ◽

Finite Size Scaling ◽

Creutz Cellular Automaton ◽

Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

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