Sobre la suave y salvaje rugosidad mecánica de la litósfera
DOI:
https://doi.org/10.4067/S0718-28132012000100005Palabras clave:
fractalidad, lithosphere, roughnessResumen
La fractalidad mecánica espacio-temporal de la litósfera puede ser representada por medio de la estadística de Lévy y cαlculo fraccional. Este nuevo concepto es planteado con argumentos geométricos y energéticos. La fractalidad se origina del sistema poroso y aparece en desplazamientos, tensiones y sismicidad. Se muestra que la rugosidad podría no ser considerada en el rango estable, pero esto no es posible en fenómenos críticos al borde de convexidad energética. Este planteamiento cubre bordes costeros rugosos, muestras de arena y reacciones tectónicas en cadena. Ecuaciones y teoremas son interpretados físicamente sin la necesidad de αlgebra ni pruebas.
Referencias
Bak, P., Tang, C. and Wiesenfeld, K. (1987). Self-organized criticality: an explanation of 1/f noise. Physical Review Letters 59 (4): 381-384. https://doi.org/10.1103/PhysRevLett.59.381
Binney, J. (1992). The Theory of Critical Phenomena. Clarendon Press.
Budiansky, B. and Rice, J.R. (1973). Conservation laws and energy release rates. Journal of Applied Mechanics 40, 201-203. https://doi.org/10.1115/1.3422926
Cartwright, J.H.E., Hernαndez-García, E. and Oreste Piro, O. (1997). Burridge-Knopoff Models as Elastic Excitable Media. Physical Review Letters 79, 527-30. https://doi.org/10.1103/PhysRevLett.79.527
Gorenflo, R. and Mainardi, F. (2000). Essentials of Fractional Calculus. Printed from MaPhySto Center, free online.
Gorenflo, A., Gudehus, G. and Touplikiotis, A. (2012). On the stability of a fractal fault system. Zeitschrift für Angewandte Mathematik und Mechanik ZAMM (under preparation).
Griffith, A.A. (1921). The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London A 221, 163-198. https://doi.org/10.1098/rsta.1921.0006
Gudehus, G. (2009). Mechanics of natural solids - a symposium in Horton, Greece. Obras y Proyectos 6, 4-7.
Gudehus, G. (2010). Psammodynamics - Attractors and Energetics. 9th HSTAMInt. Congr. Mechan., Limassol, online.
Gudehus, G. (2011) Physical Soil Mechanics. Springer, Berlin.
Gudehus, G., Jiang, Y. and Liu, M. (2010). Seismo- and thermodynamics of granular solids. Granular Matter 13 (4), 319-340. https://doi.org/10.1007/s10035-010-0229-0
Gudehus, G. and Touplikiotis, A. (2012). Clasmatic seismodynamics - Oxymoron or pleonasm?. Soil Dynamics and Earthquake Engineering 38, 1-14. https://doi.org/10.1016/j.soildyn.2011.11.002
Guyon, E. et Troadec, J.-P. (1994). Du sac de billes au tas de sable. Odile Jacob, Paris.
Hatzo, Y., Sulem, J. and Vardoulakis, I. (2009). Meso-scale Shear Physics in Earthquake and Landslide Mechanics. Taylor and Francis. https://doi.org/10.1201/b10826
Heidbach, O.,Tingay, M. and Wenzel, F. (2010). Frontiers in Stress Research: Preface. Tectonophysics 482, 1-4. https://doi.org/10.1016/j.tecto.2009.11.009
Hyndman, D. and Hyndman, D. (2009). Natural Hazards and Disasters. Chapter 3: Earthquakes and their causes. Brooks/ Cole: Cengage Learning, 2nd ed.
Laskin, N. (2000). Fractional quantum mechanics. Physical Review E 62/3, 3135-3145. https://doi.org/10.1103/PhysRevE.62.3135
Luong, M.P. (1982). Mechanical aspects and thermal effects of cohesionless soils under cyclic and transient loading. IUTAAM Conf. Deform. Fail. Gran. Mat. Delft, 239-246.
Mainardi, F. and Tomoirotti M. (1997). Seismic pulse propagation with constant Q and stable probability distributions. Annali di Geofisica XL 5, 1311-1328. https://doi.org/10.4401/ag-3863
Mandelbrot, B. (1982). The Fractal Geometry of Nature. W.H. Freeman, New York.
Mandelbrot, B. (1999). Multifractals and 1/f Noise - Wild Self-Affinity in Physics. Springer, New York.
Mantegna, R. and Stanley, H.E. (1994). Stochastic process with ultraslow convergence to Gaussian: The truncated Levy Flight. Physical Review Letters 73, 2946-2994. https://doi.org/10.1103/PhysRevLett.73.2946
Mayer, M. and Liu, M. (2010). Propagation of elastic waves in granular solid hydrodynamics. Physical Review E 82, art. 042301. https://doi.org/10.1103/PhysRevE.82.042301
Ren, F.-Y., Liang, J.-R., Wang, X.-T. and Qiu, W.-Y. (2003). Integrals and derivatives on net fractals. Chaos, Solitons and Fractals 16, 107-117. https://doi.org/10.1016/S0960-0779(02)00211-4
Rice, J.R. (1978). Thermodynamics of the quasi-static growth of Griffith cracks. Journal of the Mechanics and Physics of Solids 26, Issue 3, 61-78. https://doi.org/10.1016/0022-5096(78)90014-5
Sato, K.-I. (1999). Levy Processes and Infinitely Divisible Distributions. Cambridge University Press.
Silva Bustos, N.A. (2008). Caracterización y determinación del peligro sísmico en la región metropolitana. Civil Eng. thesis, Universidad de Chile, online.
Turcotte, D.L. (1997). Fractals and Chaos in Geology and Geophysics. 2nd ed., Cambridge University Press. https://doi.org/10.1017/CBO9781139174695
Vardoulakis, I. (2002). Steady shear and thermal run-away in clayey gauges. International Journal of Solids and Structures 39, Issues 13-14, 3831-3844. https://doi.org/10.1016/S0020-7683(02)00179-8
Xie, H. (1993). Fractals in Rock Mechanics. Balkema, Rotterdam. https://doi.org/10.1201/9781003077626
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