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Network formation by contact arrested propagation

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Abstract
We propose here a network growth model which we term Contact Arrested Propagation (CAP). One representation of the CAP model comprises a set of two-dimensional line segments on a lattice, propagating independently at constant speed in both directions until they collide. The generic form of the model extends to arbitrary networks, and, in particular, to three-dimensional lattices, where it may be realised as a set of expanding planes, halted upon intersection. The model is implemented as a simple and completely background independent substitution system. We restrict attention to one-, two- and three-dimensional background lattices and investigate how CAP networks are influenced by lattice connectivity, spatial dimension, system size and initial conditions. Certain scaling properties exhibit little sensitivity to the particular lattice connectivity but change significantly with lattice dimension, indicating universality. Suggested applications of the model include various fracturing and fragmentation processes, and we expect that CAP may find many other uses, due to its simplicity, generality and ease of implementation.
Keywords
DIFFUSION-LIMITED AGGREGATION, Substitution systems, Cellular automata, Percolation, Fragmentation, Fracturing, Networks, CRACKS, FORM, GROWTH, EVOLUTION, FRACTURE NETWORKS, MODEL, FRAGMENTATION, INVASION PERCOLATION, RIVER NETWORKS

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Citation

Please use this url to cite or link to this publication:

Chicago
Hafver, Andreas, Espen Jettestuen, Jan Baetens, and Anders Malthe-Sorenssen. 2014. “Network Formation by Contact Arrested Propagation.” Physica A-statistical Mechanics and Its Applications 413: 240–255.
APA
Hafver, A., Jettestuen, E., Baetens, J., & Malthe-Sorenssen, A. (2014). Network formation by contact arrested propagation. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 413, 240–255.
Vancouver
1.
Hafver A, Jettestuen E, Baetens J, Malthe-Sorenssen A. Network formation by contact arrested propagation. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS. 2014;413:240–55.
MLA
Hafver, Andreas, Espen Jettestuen, Jan Baetens, et al. “Network Formation by Contact Arrested Propagation.” PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 413 (2014): 240–255. Print.
@article{6846790,
  abstract     = {We propose here a network growth model which we term Contact Arrested Propagation (CAP). One representation of the CAP model comprises a set of two-dimensional line segments on a lattice, propagating independently at constant speed in both directions until they collide. The generic form of the model extends to arbitrary networks, and, in particular, to three-dimensional lattices, where it may be realised as a set of expanding planes, halted upon intersection. The model is implemented as a simple and completely background independent substitution system. 
We restrict attention to one-, two- and three-dimensional background lattices and investigate how CAP networks are influenced by lattice connectivity, spatial dimension, system size and initial conditions. Certain scaling properties exhibit little sensitivity to the particular lattice connectivity but change significantly with lattice dimension, indicating universality. Suggested applications of the model include various fracturing and fragmentation processes, and we expect that CAP may find many other uses, due to its simplicity, generality and ease of implementation.},
  author       = {Hafver, Andreas and Jettestuen, Espen and Baetens, Jan and Malthe-Sorenssen, Anders},
  issn         = {0378-4371},
  journal      = {PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS},
  keyword      = {DIFFUSION-LIMITED AGGREGATION,Substitution systems,Cellular automata,Percolation,Fragmentation,Fracturing,Networks,CRACKS,FORM,GROWTH,EVOLUTION,FRACTURE NETWORKS,MODEL,FRAGMENTATION,INVASION PERCOLATION,RIVER NETWORKS},
  language     = {eng},
  pages        = {240--255},
  title        = {Network formation by contact arrested propagation},
  url          = {http://dx.doi.org/10.1016/j.physa.2014.07.006},
  volume       = {413},
  year         = {2014},
}

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