Sunday, December 29, 2013

Snowflakes (is Christmas time after all, and I live in a boreal place)

Christmas time remembered me to give a look to snow crystal formation literature and models. To my surprise, a definitive (thermodynamic) theory of their formation does not exist. This is what can be deduced form the review paper by the K.G. Libbrecht (2005).  Even if in two subsequent papers (2012 and 2013) he tries to delineate a possible path towards a comprehensive theory. Actually the attention to Libbrecht paper was brought to me by a paper on a three-dimensional model of snow-fakes (fakes ;-), not flakes) by Gravner and Griffeath. For a classification of snow crystal, Magono paper, would be fine. I am looking forward to read them all (starting from the Libbrecht review and his two most recent papers, which seem to add something) and complete this post more appropriately eventually. For the moment, be happy with the bibliography.

Some of the  references could look strange (e.g. Fu et al., 2006). In that case, I was looking for literature in the area of fractal surfaces. Something else should be available.  In particular, I was looking for a papers by J. Nittman and  Eugene Stanley (a "star" among the "fractalists"). In any case, growth of this type of forms is pretty general and ubiquitous (as shown in many papers, and in particular, in Ben Jacob's ones).

I also indulged in adding some papers about snow crystal methamorphism. This is not the topic of the post, but for the moment I keep trace of them in here. Other papers were just added for getting some general reference to crystal growth (e.g. the Krug's one, and those looking to micro-meteorological aspects of the growth).

Interesting readings are also addressed in this older post.


Ben Jacob, E. (1993). From snowflake formation to growth of bacterial colonies: Part I. Diffusive patterning in azoic systems. Contemporary Physics, 34(5), 247–273. doi:10.1080/00107519308222085

Ben-Jacob, E. (1997). From snowflake formation to growth of bacterial colonies II: Cooperative formation of complex colonial patterns. Contemporary Physics, 38(3), 205–241. doi:10.1080/001075197182405

Chen, J. P., & Lamb, D. (1994). Simulation of Cloud Microphisical and Chemical Processes using a Multicomponent Framework. Part I: Description of the Microphysical Model. Journal of the Atmospheric Sciences, 51(18), 2613–2630.

Chen, S., & Baker, I. (2010). Evolution of individual snowflakes during metamorphism. Journal of Geophysical Research, 115(D21), D21114. doi:10.1029/2010JD014132

Fu, F., Liu, L., Yang, K., & Wang, L. (2006). The structure of the self-organized blogosphere. arXiv:Physics, 1–5.

Fukuta, N., & Takahashi, T. (1999). The Growth of Atmospheric Ice Crystals: A Summary of Findings in Vertical Supercooled Cloud Tunnel Studies. Journal of the Atmospheric Sciences, 56(12), 1963–1979. doi:10.1175/1520-0469(1999)056<1963:TGOAIC>2.0.CO;2

Gravner, J., & Griffeath, D. (2007). Modeling snow crystal growth III: three dimensional  snow fakes. arXiv:Physics, 1–39.

Gravner, J., & Griffeath, D. (2009a). Modeling snow-crystal growth: A three-dimensional mesoscopic approach. Physical Review E, 79(1), 011601. doi:10.1103/PhysRevE.79.011601

Krug, J. (2002). Four Lectures on the Physics of Crystal GrowtharXivcond-Math, 1–43.

Libbrecht, K. G. (2005). The physics of snow crystals. Reports on Progress in Physics. doi:10.1088/0034-4885/68/4/R03
Libbrecht, K. G. (2013a). Aerodynamical Effects in Snow Cristal Growthth. arXiv:Physics, 1–23.

Libbrecht, K. G. (2013b). Toward a Comprehensive Model of Snow Crystal Growth Dynamics: 2. Structure Dependent Attachment Kinetics near -5 C. arXivcond-Math, 1–13.

Magono, C., & Lee, C. W. (1966). Meterological Classification of Natural Snow Crystals. Journal Of the Faculty of Sciences, Hokkaido University, Japan, 2(4), 312–345.

Nelson, J. (2005). Branch Growth and Sidebranching in Snow Crystals. Crystal Growth & Design, 5(4), 1509–1525. doi:10.1021/cg049685v

Nittmann, J., & Stanley, H. E. (1987). Non-deterministic approach to anisotropic growth patterns with continuously tunable morphology: the fractal properties of some real snowflakes. Journal of Physics a: Mathematical Genereral

Nelson, J., & Knight, C. (1998). Snow Crystal Habit Changes Explained by Layer Nucleation. Journal of the Atmospheric Sciences, 55(8), 1452–1465. doi:10.1175/1520-0469(1998)055<1452:schceb>;2

Rango, A., P, W. W., & Erbe, E. F. (1996). Snow crystal imaging using scanning electron microscopy: I. Precipitated snow. Hydrological Sciences–Journal–Des Sciences Hydrologiques, 41(2), 219–233.

Rango, A., P, W. W., & Erbe, E. F. (1996b), Snow crystal imaging using scanning  electron microscopy: II. Metamorphosed snowHydrological Sciences–Journal–Des Sciences Hydrologiques41(2), 235–250.

Reiter, C. A. (2005). A local cellular model for snow crystal growth. Chaos Solitons & Fractals, 23(4), 1111–1119. doi:10.1016/j.chaos.2004.06.071

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