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**Beerinkol** · 04-20-2012, 05:37 AM

Dear Bostonsankara,

I remembered this after reading your "I saw God today" post:

"Ice crystals form in the turbulent air with a famous blending of symmetry and chance, the special beauty of six-fold indeterminacy. As water freezes, crystals send out tips: the tips grow, their boundaries becoming unstable, and new tips shoot out from the sides. Snow flakes obey mathematical laws of surprising subtlety, and it was once impossible to predict precisely how fast a tip would grow, how narrow it would be, or how often it would branch. Generations of scientists sketched and cataloged the variegated patterns; plates and columns, crystals and poly crystals, needles and dendrites. The treatises treated crystal formation as a classification matter, for lack of a better approach.

Growth of such tips dendrites is now known as a highly non-linear unstable free boundary problem, meaning that models need to track a complex, wiggly boundary as it changes dynamically. When solidification proceeds from outside to inside, as in an ice tray in a fridge, the boundary generally remains stable and smooth, its speed controlled by the ability of the walls to draw away the heat. But when a crystal solidifies outward from an initial seed-as a snow flake does, grabbing water molecules while it falls through the moisture-laden air- the process becomes unstable. Any bit of boundary that gets out ahead of its neighbours gains an advantage in picking up new water molecules and therefore grows that much faster-the "lightning rod effect". New branches form and then subbranches".

The article proceeds to further explain how heat diffusion and surface tension play their roles in all this.

I had immense pleasure reading this as I see in all this not just God ( as you have seen) but I see him dancing, smiling, mocking at me and showing love and affection towards me which I do not know whether I deserve. After watching the crystals melt I remain deep in thought for a long time and then resign remembering the famous lines "yatha vacho nivartante, apraapya manasaa saha"

Cheers.

(For more of this please read "Chaos- the amazing science of the unpredictable" by James Gleick.)

04-20-2012, 05:37 AM	#19
Beerinkol Join Date Dec 2006 Posts 5,268 Senior Member	Dear Bostonsankara, I remembered this after reading your "I saw God today" post: "Ice crystals form in the turbulent air with a famous blending of symmetry and chance, the special beauty of six-fold indeterminacy. As water freezes, crystals send out tips: the tips grow, their boundaries becoming unstable, and new tips shoot out from the sides. Snow flakes obey mathematical laws of surprising subtlety, and it was once impossible to predict precisely how fast a tip would grow, how narrow it would be, or how often it would branch. Generations of scientists sketched and cataloged the variegated patterns; plates and columns, crystals and poly crystals, needles and dendrites. The treatises treated crystal formation as a classification matter, for lack of a better approach. Growth of such tips dendrites is now known as a highly non-linear unstable free boundary problem, meaning that models need to track a complex, wiggly boundary as it changes dynamically. When solidification proceeds from outside to inside, as in an ice tray in a fridge, the boundary generally remains stable and smooth, its speed controlled by the ability of the walls to draw away the heat. But when a crystal solidifies outward from an initial seed-as a snow flake does, grabbing water molecules while it falls through the moisture-laden air- the process becomes unstable. Any bit of boundary that gets out ahead of its neighbours gains an advantage in picking up new water molecules and therefore grows that much faster-the "lightning rod effect". New branches form and then subbranches". The article proceeds to further explain how heat diffusion and surface tension play their roles in all this. I had immense pleasure reading this as I see in all this not just God ( as you have seen) but I see him dancing, smiling, mocking at me and showing love and affection towards me which I do not know whether I deserve. After watching the crystals melt I remain deep in thought for a long time and then resign remembering the famous lines "yatha vacho nivartante, apraapya manasaa saha" Cheers. (For more of this please read "Chaos- the amazing science of the unpredictable" by James Gleick.)
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