Timeline for Shape of snowflakes
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2022 at 13:18 | answer | added | Fallen Apart | timeline score: 0 | |
| Mar 6, 2022 at 12:00 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed
|
| Jan 1, 2014 at 0:15 | comment | added | Joseph O'Rourke | See also this MSE question: Horizontal drift of snowflake. | |
| Mar 14, 2012 at 13:56 | history | edited | Michał Oszmaniec |
edited tags
|
|
| Mar 14, 2012 at 12:12 | history | edited | user6976 | CC BY-SA 3.0 |
edited body
|
| Dec 24, 2011 at 22:31 | answer | added | Daniel Litt | timeline score: 12 | |
| Dec 24, 2011 at 12:17 | comment | added | user6976 | I looked at the papers suggested by Igor Rivin. I think it is indeed close to what I wanted. Also his answer was first, so I have accepted it. | |
| Dec 24, 2011 at 12:12 | vote | accept | CommunityBot | moved from User.Id=6976 by developer User.Id=69903 | |
| Dec 24, 2011 at 12:11 | vote | accept | CommunityBot | moved from User.Id=6976 by developer User.Id=69903 | |
| Dec 24, 2011 at 12:11 | |||||
| Dec 24, 2011 at 8:00 | comment | added | user6976 | @jc: Thank you! This is also how limits of spaces "grow" into fractals. But the chemical reason from Daniel's comment should be a minimizer reason? Thus the reason why the molecules are glued the way they are glued should be "because it minimizes some energy functional". Right? I do not think the article you mention gives any reason for this except that "the experiments show that". Perhaps I missed something, I am not very good at reading chemistry/physics papers. | |
| Dec 24, 2011 at 5:35 | comment | added | j.c. | I think their shapes are more akin to the random fractals arising from diffusion-limited aggregation, where molecules diffusing in "from infinity" attach to a seed. I think this paper psoup.math.wisc.edu/papers/h2l.pdf by the group that created the pictures that Joseph O'Rourke linked to below is probably the best current explanation for snowflakes, and has a similar philosophy starting from growth rather than minimization - create a random growth model (on a lattice, even) with certain physically motivated properties and one finds shapes that match well the real life snowflakes. | |
| Dec 24, 2011 at 5:24 | comment | added | j.c. | The review that Daniel Litt linked to explains that the shapes of snowflakes are the outcome of a complicated growth process, involving the competition of between the rates of diffusion and attachment of water molecules and heat transport, among other things. In particular, as snowflakes are formed very far from the equilibrium state of water and ice, their overall shapes won't be the minimizers of any natural thermodynamic energy functional, or even randomly perturbed versions of such, in the way that large facets of crystals might be. | |
| Dec 23, 2011 at 20:27 | comment | added | user6976 | @Daniel: This may not be what I want since I wanted an explanation, not a description. An example of an explanation could be something like this: "consider the following `energy' functional ..., the shapes that minimize that functional are snowflakes." | |
| Dec 23, 2011 at 20:18 | history | edited | user6976 | CC BY-SA 3.0 |
added 546 characters in body
|
| Dec 23, 2011 at 20:12 | comment | added | Daniel Litt | ...snowflake with appropriately chosen parameters is not a bad model at all. | |
| Dec 23, 2011 at 20:12 | comment | added | Daniel Litt | Water crystallizes in a hexagonal lattice, so small snowflakes are just hexagons. For reasons of surface chemistry that I don't really understand, water molecules are more likely to attach at a vertex than in the middle of an edge, so as the hexagons get large the vertices grow faster than the edges, creating a non-convex figure with 12 edges. Iterating this procedure (growing faster at vertices than at edges) gives a snowflake--for a picture of this, see pg. 884 here: its.caltech.edu/~atomic/publist/rpp5_4_R03.pdf (the whole article is pretty interesting. So really, the Koch... | |
| Dec 23, 2011 at 20:11 | answer | added | Joseph O'Rourke | timeline score: 18 | |
| Dec 23, 2011 at 20:08 | answer | added | Igor Rivin | timeline score: 16 | |
| Dec 23, 2011 at 19:57 | history | edited | user6976 |
edited tags
|
|
| Dec 23, 2011 at 19:51 | history | asked | user6976 | CC BY-SA 3.0 |