Fractal Model for Snow

Abstract:

We analyze the distribution of grains in solid cubes of ice in terms of deterministic and stochastic 3d fractal models. We argue that the fractal dimension D or the Hurst exponent H optimally describe the void distribution in the snow sample and can be used as a parameter to describe the mechanical properties of snow at different scales.

• Periodical: Materials Science Forum (Volumes 638-642)
• Pages: 2555-2560
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.638-642.2555
• Online since: January 2010
• Authors: Anna Carbone, Bernardino Chiaia, Barbara Frigo, Christian Türk
• Keywords: Fractal, Hurst Exponent, Snow Density

References

[1] H. Narita, H.O.K. Kirchner, G. Michot and T. Suzuki Snow as a foam of ice: plasticity, fracture and the brittle-to-ductile transition. Philosophical Magazine A, 81(9): 2161-2181, (2001).

DOI: 10.1080/01418610108217141

[2] J. J. Petrovic Review mechanical properties of ice and snow. Journal of Materials Science, 38: 1-6, (2003).

[3] www. cnrm. meteo. fr/passion/neige1. htm.

[4] J. Faillettaz Le déclenchement des avalanches de plaque de neige: de l'approche mécanique à l'approche statistique. PhD thesis, Université Joseph Fourier (Grenoble I), (2003).

[5] J.G.M. Van Mier, B. Chiaia and A. Vervuurt Numerical simulation of chaotic and selforganizing damage in brittle disordered materials, Computer Methods In Applied Mechanics and Engineering, 42 (1-2) (1997) 189- 201.

DOI: 10.1016/s0045-7825(96)01128-0

[6] B.M. Chiaia, P. Cornetti and B. Frigo Triggering of dry snow slab avalanches: stress versus fracture mechanical approach, Cold Regions Science and Technology 53, pp.170-178 (2008).

DOI: 10.1016/j.coldregions.2007.08.003

[7] B. Chiaia and B. Frigo A scale-invariant model for snow avalanches. Journal of Statistical Mechanics: Theory and Experiment, P02056, (2009).

DOI: 10.1088/1742-5468/2009/02/p02056

[8] V. N. Golubev and A. D. Frolov Modelling the change in structure and mechanical properties in dry-snow densification to ice. Annals of Glaciology, 26: 45-50, (1998).

DOI: 10.1017/s0260305500014531

[9] J. Feder Fractals. New York: Plenum, (1998).

[10] R. H. Voss Fundamental Algorithms for Computer Graphics. Berlin/Heidelberg: Springer Verlag, (1985).

[11] A. Carbone Algorithm to estimate the Hurst exponent of high-dimensional fractals. Phys. Rev. E, 76: 056703, (2007).

DOI: 10.1103/physreve.76.056703

[12] S. Arianos and A. Carbone Detrending Moving Average (DMA) Algorithm: a closed form approximation of the scaling law. Physica A 382, 9 (2007).

DOI: 10.1016/j.physa.2007.02.074

[13] A. Carbone and Stanley H.E. Scaling properties and entropy of long range correlated series. Physica A 384, 21 (2007).

DOI: 10.1016/j.physa.2007.04.105

[14] T. Nakamura et al. Spectral reflectance of snow with a known grain-size distribution in successive metamorphism. Cold Regions Science and Technology 32, pp.13-26, (2001).

DOI: 10.1016/s0165-232x(01)00019-2

[15] M. Gay et al. Snow grain-size measurements in Antarctica. Journal of Glaciology 48, 163 (2002).