Interpretazione multifrattale dei tratti vallivi dei corsid'acqua Calabresi
DOI:
https://doi.org/10.4995/ia.2006.3534Palabras clave:
Cauces trenzados, Multifractales, Algoritmos multifractalesResumen
Se realiza una investigación sobre el comportamiento multifractal en la parte final de algunos cursos fluviales de Calabria (sur de Italia).
Esta investigación se ha llevado a cabo mediante la utilización del Método de la Integral de Correlación Generalizada. Los datos derivan de los sistemas de los cauces trenzados extraídos de cartografía a escala 1:10000. Particularmente, se han estimado los espectros de las dimensiones fractales generalizadas, Dq, la secuencia de los exponentes de masa, Tq, los espectros de las singularidades,, y los espectros multlfractales, f().
Los análisis multifractales hechos sobre las configuraciones estáticas de sistemas de cauces trenzados que han sido objeto de este estudio tienen comportamientos de auto-similitud. Los resultados muestran que los sistemas de cauces trenzados objeto de estudio tienen un comportamiento auto-similar y multifractal.
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Aharony, A., ( 1989). Measuring multifractals. Physica D, 38: 1-4. https://doi.org/10.1016/0167-2789(89)90165-6
Avnir, D., Biham, O., Lidar, D. A. e Malcai, O., (1998). Is the geometry of nature fractal? Science, 279: 39-40. https://doi.org/10.1126/science.279.5347.39
Badii, R. e Politi, A., (1984). Hausdorff Dimension and uniformity factor of strange attractors, Physical Review Letters, 52, 1661-1664, 1984. https://doi.org/10.1103/PhysRevLett.52.1661
Badii, R. e Politi, A., (1985). Statistical Description of Chaotic Attractors : the Dimension Function, Journal of Statistical Physics, 40: 725-750. https://doi.org/10.1007/BF01009897
Bassler, K.E., Paczuski, M., e Reiter, G. F. (1999). Braided rivers and superconducting vortex avalanches, Physical Review Letters, 83: 3957-3959. https://doi.org/10.1103/PhysRevLett.83.3956
Block, A., Bloh, W. von e Schellnhuber, H.J. (1990). Efficient box-counting determination of generalized fractal dimensions. Physical Review A, 42(4): 1869-1874. https://doi.org/10.1103/PhysRevA.42.1869
Chhabra, A., e Jensen, R. V. (1989). Direct determination of the f() singularity spectrum. Physical Review Lctters. 62: 1327-1330. https://doi.org/10.1103/PhysRevLett.62.1327
De Bartolo, S.G., Maiolo, M., Veltri, M. e Veltri, P. (1995). Sulla caratterizzazione multifrattale delle reti fluviali. Idrotecnica, 6:329-340.
De Bartolo, S.G., Gabriele, S. e Gaudio, R. (1998). Analisi sperimentale sulla natura multifrattale delle reti fluviali, XXVI Convegno di Idraulica e Costruzioni Idrauliche, IV, 53-64, Catania 1998.
De Bartolo, S.G., Gabriele, S. e Gaudio, R. (2000). Multifractal behaviour of river networks, Hydrology and Earth System Sciences, 4(1): 105-112. https://doi.org/10.5194/hess-4-105-2000
De Bartolo, S.G., Veltri, M. e Primavera, S. (2003). Indagine con tecniche a taglia fissa sulla struttura multifrattale delle reti fluviali, L'Acqua, 6: 9-15.
De Bartolo, S.G., Gaudio, R. e Gabriele, S. (2004). Multifractal analysis of river networks: a sand-box approach. Water Resources Research, 40, W02201. doi: 10.1029/2003WR002760. https://doi.org/10.1029/2003WR002760
De Bartolo, S.G., Veltri, M. e Primavera, S. (2005). Estimated generalized dimensions of river networks, Journal of Hydrology, doi: 10.1016/j.jbyclrol.2005.02.033.
Evertsz, G.J .G. e Mandelbrot, B.B. (1992). Multifractal measures, in H-O. Peitgen. H. Jürgens and D. Saupe (eds.), Chaos and fractals, new frontiers of science, Springer Verlag, New York, 921-953.
Falconer, K .J. (1990). Fractal Geometry: Mathematical Foundations and Applications, J. Wiley, Chichester, England. https://doi.org/10.2307/2532125
Feder, J (1988). Fractals, Plenum, New York. https://doi.org/10.1007/978-1-4899-2124-6
Feeny, B. F. (2000). Fast multifractal analysis by recursive box covering. lnternational Journal of Bifurcation and Chaos. 10(9): 2277-2287. https://doi.org/10.1142/S0218127400001420
Foufoula-Georgiou, E. e Sapozhnikov, V. (1996). Self-affinity in braided rivers. Water Resources Research, 32(5): 1429-1439. https://doi.org/10.1029/96WR00490
Foufoula-Georgiou, E. e Sapozhnikov, V. (1997). Experimental evidence of dynamic scaling and indications of self-organized criticality in braided rivers. Water Resources Research, 33(8): 1983-1991. https://doi.org/10.1029/97WR01233
Foufoula-Georgiou, E. e Sapozhnikov, V. (2001). Scale invariances in the morphology and evolution of braided rivers, Mathematical Geology, 33(3): 273-291. https://doi.org/10.1023/A:1007682005786
Grassberger, P. e Procaccia, I. (1983). Characterization of strange attractors, Physical Review Letters, 50(3): 346-349. https://doi.org/10.1103/PhysRevLett.50.346
Grassberger, P. (1983). Generalized dimensions of strange attractors, Physics Letters, 97 A(6): 227-230. https://doi.org/10.1016/0375-9601(83)90753-3
Hakansson, J. e Russberg, G. (1990). Finite-size effects on the characterization of fractal sets: f() construction via box counting on a finite two-scaled Cantor set, Physical Review A, 41(4): 1855-1861. https://doi.org/10.1103/PhysRevA.41.1855
Halsey, T.C., Jensen, M.H., Kadanoff, L.P., Procaccia, I. e Shraiman, B.I. (1986). Fractal measures and their singularities: The characterization of strange sets. Physical Review A, 33(2): 1141-1151. https://doi.org/10.1103/PhysRevA.33.1141
Hentschel, H. G. E. e Procaccia, l. (1983). The infinite number of generalized dimensions of fractals and strange attractors. Physica D, 8: 435-444. https://doi.org/10.1016/0167-2789(83)90235-X
Hjelmfelt, A. T. (1988). Fractals and the river-length catchment-area ratio. Water Resources Bulletin, 24(2): 455-459. https://doi.org/10.1111/j.1752-1688.1988.tb03005.x
Horton, R.E. (1932). Drainage basin characteristics. Transactions of the American Geophysical Union (AGU), 13: 350-370. https://doi.org/10.1029/TR013i001p00350
Horton, R.E. (1945). Erosional development of streams and their drainage basins: hydrophysical approach to quantitative geomorphology, Geological Society American Bulletin, 56: 275-370. https://doi.org/10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2
Hou, X.-J. Gilmore, R., Mindlin, G. e Solari, H. (1990). An efficient algorithm for fast O(N*ln(N)) box-counting. Physics Letters A, 151 (12): 43-46. https://doi.org/10.1016/0375-9601(90)90844-E
La Barbera, P. e Rosso, R. (1987). Fractal geometry of river networks (abstract), Eos Trans. AGU, 68(44): 1276.
La Barbera, P. e Rosso, R. (1989). On the fractal dimension of stream networks, Water Resources Research, 25(4): 735-741. https://doi.org/10.1029/WR025i004p00735
Liebovitch, L. S. e Toth, T. (1989). A fast algorithm to determine fractal dimensions by box-counting. Physics Letters A, 141(8.9), 386-390. https://doi.org/10.1016/0375-9601(89)90854-2
Mach, J., F. Mas, e Sagués, F. (1995). Two representations in multifractal analysis, J. Phys. A Math Gen. 28: 5607- 5622. https://doi.org/10.1088/0305-4470/28/19/015
Malcai, O., Lidar, D. A., Biham, O. e Avnir, D. (1997). Scaling range and cutoffs in empirical fractals, Physical Review E. 56(3): 2817-2828. https://doi.org/10.1103/PhysRevE.56.2817
Mandelbrot, B. B. (1972). Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. ln: Statistical Models and Turbulence (ed. By M. Rosenblatt & C. Van Atta), Lecture Notes in Physics 12, Springer, New York, 333-351. https://doi.org/10.1007/3-540-05716-1_20
Mandelbrot, B. B. (1974). Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier, Journal of Fluid Mechanics, 62: 331-358. https://doi.org/10.1017/S0022112074000711
Mandelbrot, B. R. (1977). Fractals: form, chance and dimension, W. H. Freeman and Co, San Francisco, California.
Mandelbrot, B. B. e Evertsz, C. J. G. (1991). Exactly selfsimilar left-sided multifractals, in A. Bunde e S. Havlin (Eds.), Fractals and disordered systems, Springer-Verlag, Berlin Heidelberg. https://doi.org/10.1007/978-3-642-51435-7_10
Meisel, L.V. Johnson, M. e Cote, P. J. (1992). Box-counting multifractal analysis, Physical Review A, 45(10): 6989-6996. https://doi.org/10.1103/PhysRevA.45.6989
Meisel, L. V. e Johnson, M. (1994). Multifractal analysis of imprecise data: Badii-Politi and correlation integral approach, Physical Review E, 50(5): 4214-4219. https://doi.org/10.1103/PhysRevE.50.4214
Meisel, L. V., e Johnson, M. (1997). Convergence of numerical box-counting and correlation integral multifractal analysis techniques, Pattern Recognition, 30(9): 1565-1570. https://doi.org/10.1016/S0031-3203(96)00162-8
Molteno, T. C. A. (1993). Fast O(N) box-counting algorithm for estimating dimensions, Physical Review E, 48(5): R3263-R3266. https://doi.org/10.1103/PhysRevE.48.R3263
Nikora, V. l., Hicks, D.M, Smart, G. M. e Noever, D. A. (1995). Some fractal properties of braided rivers, paper presented at the 2nd lnternational Symposium on Fractals and Dynamic System in Geoscience, John Wolfgang Goethe Univ., Frankfurt, Germany, 4-7 April 1995.
Nykanen, D. K., Foufoula-Georgiou, E. e Sapozhnikv, V. B. (1998). Study of spatial scaling in braided river patterns using synthetic aperture radar imagery, Water Resources Research, 34(7): 1795-1807. https://doi.org/10.1029/98WR00940
Oiwa, N. N. e Fiedler-Ferrara, N. (1998). A moving-box algorithm to estimate generalized dimensions and f() spectrum, Physica D, 124: 210-224. https://doi.org/10.1016/S0167-2789(98)00195-X
Pastor-Satorras, R. e Riedi, R. H. (1996). Numerical estimates of the generalized dimensions oh the Hénon attractor for negative q, Journal of Physics A: Mathematical and General, 29: L391 -L398. https://doi.org/10.1088/0305-4470/29/15/005
Pawelzik, K. e Schuster, H. G. (1987). Generalized dimensions and entropies from a measured time series, Physical Review A, 35(1): 481-484. https://doi.org/10.1103/PhysRevA.35.481
Petrucci, O., Chiodo, G. e Caloiero D. (1996). Eventi alluvionali in Calabria nel decennio 1971-1980. CNR IRPI (CS), GNDCI, Linea di ricerca N. 1, U.O. 14, Pubbl. n. 1374.
Renyi, A. (1955). On a new axiomatic theory of probability, Acta Mathematica Hungarica, 6: 285-335. https://doi.org/10.1007/BF02024393
Renyi, A. (1970). Probability Theory, North-Holland Publishing Company, Budapest.
Rigon, R. (1994). Principi di auto-organizzazione nella dinamica evolutiva delle reti idrografiche, Tesi del dottorato di ricerca in Idrodinamica, Trento, Febbraio.
Robert, A. e Roy, A. (1990). On the fractal Interpretation of the mainstream length-drainage area relationship, Water Resources Research, 26: 839-842. https://doi.org/10.1029/WR026i005p00839
Rodriguez-lturbe, l. e Rinaldo, A. (1997). Fractal River Basins: Chance and Self-Organization, Cambridge University Press, Cambridge.
Rosatti, G. (2002). Validation of the physical modeling approach for braided rivers, Water Resources Research, 38(12): 1295, doi: 10.1029/2001WR000433. https://doi.org/10.1029/2001WR000433
Strahler, A.N. (1952). Hypsometric (area-altitude) analysis of erosional topography, Geological Society American Bulletin, 63: 1117-1142. https://doi.org/10.1130/0016-7606(1952)63[1117:HAAOET]2.0.CO;2
Strahler, A.N. (1964). Quantitative geomorphology of drainage basins and channel networks, Handbook of applied hydrology, ed. V.T. Chow, section 4, McGraw-Hill, New York.
Tarboton, D.G., Bras, R.L. e Rodriguez-Iturbe, l. (1988). The fractal nature of river networks, Water Resources Research, 24: 1317-1322. https://doi.org/10.1029/WR024i008p01317
Veneziano, D., Moglen, G. E. y Bras, R. L. (1995). Multi fractal analysis: pitfalls of standard procedures and altematives. Physical Review E, 52(2): 1387-1398. https://doi.org/10.1103/PhysRevE.52.1387
Viparelli, M. (1972). La sistemazione delle aste terminali delle fiumare calabre, Liguore Editore.
Walsh, J. e Hicks, M. D. (2002). Braided channels: self-similar or self-affine?, Water Resources Research, 38(6): 1082, doi: 10.1029/2001WR000749. https://doi.org/10.1029/2001WR000749
Yamaguti, M. e Prado, C. (1995). A direct calculation of the spectrum of singularities f() of multifractals, Physics Letters A, 206: 318-322. https://doi.org/10.1016/0375-9601(95)00656-N
Yamaguti, M e Prado, C. (1997). Smart covering for a box-counting algorithm. Physical Review E, 55(6): 7726-7732. https://doi.org/10.1103/PhysRevE.55.7726
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