Carbone Anna, Chiaia Bernardino M, Frigo Barbara, Türk Christian
Physics Department and CNISM, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036103. doi: 10.1103/PhysRevE.82.036103. Epub 2010 Sep 7.
Snow is a porous disordered medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of an assemblage of grains, ice matrix, initially arranged over a random load bearing skeleton. The quantitative relationship between density and morphological characteristics of different snow microstructures is still an open issue. In this work, a three-dimensional fractal description of density corresponding to different snow microstructure is put forward. First, snow density is simulated in terms of a generalized Menger sponge model. Then, a fully three-dimensional compact stochastic fractal model is adopted. The latter approach yields a quantitative map of the randomness of the snow texture, which is described as a three-dimensional fractional Brownian field with the Hurst exponent H varying as continuous parameters. The Hurst exponent is found to be strongly dependent on snow morphology and density. The approach might be applied to all those cases where the morphological evolution of snow cover or ice sheets should be conveniently described at a quantitative level.
雪是一种由空气和三种水相（冰、水汽和液体）组成的多孔无序介质。冰相由一组颗粒、冰基质组成，最初排列在一个随机的承重骨架上。不同雪微观结构的密度与形态特征之间的定量关系仍然是一个未解决的问题。在这项工作中，提出了一种对应于不同雪微观结构的密度的三维分形描述。首先，根据广义门格尔海绵模型模拟雪密度。然后，采用一个完全三维紧凑随机分形模型。后一种方法产生了雪质地随机性的定量图，其被描述为一个三维分数布朗场，其中赫斯特指数H作为连续参数变化。发现赫斯特指数强烈依赖于雪的形态和密度。该方法可能适用于所有那些需要在定量水平上方便地描述积雪或冰盖形态演变的情况。
