How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth
We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to 108 particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive...
| Main Authors: | , |
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| Format: | Journal article |
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American Physical Society
2017
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| _version_ | 1797096139016634368 |
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| author | Grebenkov, D Belyaev, D |
| author_facet | Grebenkov, D Belyaev, D |
| author_sort | Grebenkov, D |
| collection | OXFORD |
| description | We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to 108 particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and onedimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has non-trivial box-counting fractal dimension which corresponds to the overall growth rate which, in turn, is smaller than the growth rate along the axes. This suggests that the fractal nature of the lattice DLA should be understood in terms of fluctuations around one-dimensional backbone of the cluster. |
| first_indexed | 2024-03-07T04:37:47Z |
| format | Journal article |
| id | oxford-uuid:d08ea221-8818-48c8-81fc-c01e60c1f1ae |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:37:47Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:d08ea221-8818-48c8-81fc-c01e60c1f1ae2022-03-27T07:50:48ZHow anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growthJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d08ea221-8818-48c8-81fc-c01e60c1f1aeSymplectic Elements at OxfordAmerican Physical Society2017Grebenkov, DBelyaev, DWe study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to 108 particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and onedimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has non-trivial box-counting fractal dimension which corresponds to the overall growth rate which, in turn, is smaller than the growth rate along the axes. This suggests that the fractal nature of the lattice DLA should be understood in terms of fluctuations around one-dimensional backbone of the cluster. |
| spellingShingle | Grebenkov, D Belyaev, D How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth |
| title | How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth |
| title_full | How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth |
| title_fullStr | How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth |
| title_full_unstemmed | How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth |
| title_short | How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth |
| title_sort | how anisotropy beats fractality in two dimensional on lattice diffusion limited aggregation growth |
| work_keys_str_mv | AT grebenkovd howanisotropybeatsfractalityintwodimensionalonlatticediffusionlimitedaggregationgrowth AT belyaevd howanisotropybeatsfractalityintwodimensionalonlatticediffusionlimitedaggregationgrowth |