Abelian Manna model in three dimensions and below
The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration, and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional...
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sg-ntu-dr.10356-951752023-02-28T19:39:22Z Abelian Manna model in three dimensions and below Huynh, Hoai Nguyen. Pruessner, Gunnar. School of Physical and Mathematical Sciences The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration, and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the coefficients of an ε expansion. By rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices. Published version 2013-02-19T04:50:43Z 2019-12-06T19:09:38Z 2013-02-19T04:50:43Z 2019-12-06T19:09:38Z 2012 2012 Journal Article Huynh, H. N., & Pruessner, G. (2012). Abelian Manna model in three dimensions and below. Physical Review E, 85(6), 061133-. https://hdl.handle.net/10356/95175 http://hdl.handle.net/10220/9156 10.1103/PhysRevE.85.061133 en Physical Review E © 2012 American Physical Society. This paper was published in Physical Review E and is made available as an electronic reprint (preprint) with permission of American Physical Society. The paper can be found at the following official DOI: [http://dx.doi.org/10.1103/PhysRevE.85.061133]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
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The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration, and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the coefficients of an ε expansion. By rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Huynh, Hoai Nguyen. Pruessner, Gunnar. |
| format |
Article |
| author |
Huynh, Hoai Nguyen. Pruessner, Gunnar. |
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Huynh, Hoai Nguyen. Pruessner, Gunnar. Abelian Manna model in three dimensions and below |
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Huynh, Hoai Nguyen. |
| title |
Abelian Manna model in three dimensions and below |
| title_short |
Abelian Manna model in three dimensions and below |
| title_full |
Abelian Manna model in three dimensions and below |
| title_fullStr |
Abelian Manna model in three dimensions and below |
| title_full_unstemmed |
Abelian Manna model in three dimensions and below |
| title_sort |
abelian manna model in three dimensions and below |
| publishDate |
2013 |
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https://hdl.handle.net/10356/95175 http://hdl.handle.net/10220/9156 |
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