Applied and Computational Mathematics

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Meandering Fractals in Water Resources Management

Received: 29 April 2019    Accepted: 21 May 2019    Published: 19 May 2020
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Abstract

Fractal dimension is a measure for the degree of complexity or that of fractals. An alternative to fractal dimension is ht-index, which quantifies complexity in a unique way. Back to your question, the physical meaning of fractal dimension is that many natural and social phenomena are nonlinear rather than linear, and are fractal rather than Euclidean. We need a new paradigm for studying our surrounding phenomena, Not Newtonian physics for simple systems, but complexity theory for complex systems, Not linear mathematics such as calculus, Gaussian statistics, and Euclidean geometry, but online mathematics including fractal geometry, chaos theory, and complexity science in general. A channel is characterized by its width, depth, and slope. The regime theory relates these characteristics to the water and sediment discharge transported bye the channel empirically. Empirical measurements are taken on channels and attempts are made to fit empirical equations to the observed data. The channel characteristics are related primarily to the discharge but allowance is also made for variations in other variables, such as sediment size.

DOI 10.11648/j.acm.20200902.12
Published in Applied and Computational Mathematics (Volume 9, Issue 2, April 2020)
Page(s) 26-29
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Natural Dimensions, Nonlinearity, Fractals, Meanders

References
[1] Jiang B. and Yin J. (2014), Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104 (3), 530–541.
[2] Jiang B. (2015), Geospatial analysis requires a different way of thinking: The problem of spatial heterogeneity, GeoJournal, 80 (1), 1-13.
[3] F. Moisy (2008) https://www.math.dartmouth.edu//archive/m53f09/public_html/proj/Alexis_writeup.pdf.
[4] Fractal Dimension and Self-Similarity https://www.math.dartmouth.edu//archive/m53f09/public_html/proj/Alexis_writeup.pdf.
[5] Longley, P. A. and Batty, M. (1996), Spatial Analysis: Modelling in a GIS Environment, https://books.google.com.tr/books?isbn=0470236159.
[6] Normant, F. and Tricot, G., (1995) Fractals in Engineering https://www.google.com/search?q=Normant+and+Triart&tbm=isch&source=univ&sa=X&ved=2ahUKEwjgurqA5O_hAhVSyqQKHeK7ChAQsAR6BAgJEAE&biw=1366&bih=6.
[7] Yilmaz, L., “Maximum Entropy Theory by Using the Meandering Morphological Investigation-II”, Journal of RMZ-Materials and Geoenvironment, 2007, CSA / ASCE, Printed also in CSA Illumina, CSA: Guide to Discovery, enews@csa.com.
[8] Sierpinski, S. (2002) https://www.mathsisfun.com/sierpinski-triangle.html https://wwwmathworld.wolfram.com/SierpinskiSieve.html.
[9] Kennedy, J. F., et al., Proc. Am. Soc. civ. Engrs, 97, 101–141 (1971).
[10] Hey, R. D., UK geol. Soc. Misc. Pap. 3, 42–56 (1974).
[11] Yalin, M. S., Mechanics of Sediment Transport (Pergamon, Oxford, 1972).
[12] Leopold, L. B., and Wolman, M. G., Bull. geol. Soc. Am., 71, 769–793 (1960).
[13] Leopold, L. B., Wolman, M. G., and Miller, J. P., Fluvial Processes in Geomorphology (Freeman, London, 1964).
[14] Shen, H. W., and Komura, S., Proc. Am. Soc. civ. Engrs, 94, 997–1015 (1968).
[15] Hey, R. D., and Thorne, C. R., Area, 7, 191–195 (1975).
Author Information
  • Nisantasi University Neocampus, Maslak, Istanbul, Turkey

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    Levent Yilmaz. (2020). Meandering Fractals in Water Resources Management. Applied and Computational Mathematics, 9(2), 26-29. https://doi.org/10.11648/j.acm.20200902.12

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    Levent Yilmaz. Meandering Fractals in Water Resources Management. Appl. Comput. Math. 2020, 9(2), 26-29. doi: 10.11648/j.acm.20200902.12

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    Levent Yilmaz. Meandering Fractals in Water Resources Management. Appl Comput Math. 2020;9(2):26-29. doi: 10.11648/j.acm.20200902.12

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  • @article{10.11648/j.acm.20200902.12,
      author = {Levent Yilmaz},
      title = {Meandering Fractals in Water Resources Management},
      journal = {Applied and Computational Mathematics},
      volume = {9},
      number = {2},
      pages = {26-29},
      doi = {10.11648/j.acm.20200902.12},
      url = {https://doi.org/10.11648/j.acm.20200902.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20200902.12},
      abstract = {Fractal dimension is a measure for the degree of complexity or that of fractals. An alternative to fractal dimension is ht-index, which quantifies complexity in a unique way. Back to your question, the physical meaning of fractal dimension is that many natural and social phenomena are nonlinear rather than linear, and are fractal rather than Euclidean. We need a new paradigm for studying our surrounding phenomena, Not Newtonian physics for simple systems, but complexity theory for complex systems, Not linear mathematics such as calculus, Gaussian statistics, and Euclidean geometry, but online mathematics including fractal geometry, chaos theory, and complexity science in general. A channel is characterized by its width, depth, and slope. The regime theory relates these characteristics to the water and sediment discharge transported bye the channel empirically. Empirical measurements are taken on channels and attempts are made to fit empirical equations to the observed data. The channel characteristics are related primarily to the discharge but allowance is also made for variations in other variables, such as sediment size.},
     year = {2020}
    }
    

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