[math-fun] Entering a New Phase
http://www.lassp.cornell.edu/sethna/OrderParameters/BrokenSymmetry.html Interesting view: phase changes are about symmetry changes. One counterexample to this is glasses (amorphous solids). They can be solid or liquid but no symmetry changes that I know of. The fact glasses tend to have non-sharp melting points, as opposed to a lot of other phase changes with more sharply-defined changeovers, could be argued to support his view, though(?). Another way to look at it, which also supports his view, if the "freedom of motion" in a liquid IS a symmetry. Also, for many glasses, there is a crystalline ordered phase which can form, but takes ages to do so. If so we could argue this not really a counterexample. Must such an ordered phase exist with lower energy than the disordered phase? I claim "no" and as proof I point out that certain 2D tiling problems have min-energy state (i.e. tiling) corresponding to Turing machine valid computations... which can be arbitrarily infinitely messy.
On 12/26/2012 1:36 PM, Warren Smith wrote:
http://www.lassp.cornell.edu/sethna/OrderParameters/BrokenSymmetry.html
Interesting view: phase changes are about symmetry changes.
One counterexample to this is glasses (amorphous solids). They can be solid or liquid but no symmetry changes that I know of.
I don't think they are solid, they're just liquids with very high viscosity. Brent
The fact glasses tend to have non-sharp melting points, as opposed to a lot of other phase changes with more sharply-defined changeovers, could be argued to support his view, though(?). Another way to look at it, which also supports his view, if the "freedom of motion" in a liquid IS a symmetry.
Also, for many glasses, there is a crystalline ordered phase which can form, but takes ages to do so. If so we could argue this not really a counterexample.
Must such an ordered phase exist with lower energy than the disordered phase? I claim "no" and as proof I point out that certain 2D tiling problems have min-energy state (i.e. tiling) corresponding to Turing machine valid computations... which can be arbitrarily infinitely messy.
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It used to be widely claimed that (apparently solid) glass was known to be liquid, because old window panes are thicker at the bottom. As a boy, after I got my first toy of Silly Putty (in 1955. It was called "Nutty Putty"), which will slowly flow like a liquid but which can also break irregularly if struck with a hammer (like glass)* -- and learned it was a silicon compound, I was entirely convinced. But more recently I've read that this has been found to be a myth. Rather, it is said, glass windows, etc., are in fact solids. And, the old windows were sometimes thicker at the bottom only because they were made of blown glass, with much less precision. --Dan _________________________________________________________________________________ * It also bounced and could pick up the reverse image of something printed in a newspaper -- but you all probably knew that. I can't find any reference to the trade name "Nutty Putty", for some reason. Especially since it's a more memorable name than "Silly Putty", I'd expect that someone must have obtained the rights to that name. On 2012-12-26, at 1:54 PM, meekerdb wrote:
On 12/26/2012 1:36 PM, Warren Smith wrote:
http://www.lassp.cornell.edu/sethna/OrderParameters/BrokenSymmetry.html
Interesting view: phase changes are about symmetry changes.
One counterexample to this is glasses (amorphous solids). They can be solid or liquid but no symmetry changes that I know of.
I don't think they are solid, they're just liquids with very high viscosity.
On 12/26/2012 2:14 PM, Dan Asimov wrote:
It used to be widely claimed that (apparently solid) glass was known to be liquid, because old window panes are thicker at the bottom.
As a boy, after I got my first toy of Silly Putty (in 1955. It was called "Nutty Putty"), which will slowly flow like a liquid but which can also break irregularly if struck with a hammer (like glass)* -- and learned it was a silicon compound, I was entirely convinced.
But more recently I've read that this has been found to be a myth. Rather, it is said, glass windows, etc., are in fact solids. And, the old windows were sometimes thicker at the bottom only because they were made of blown glass, with much less precision.
Yes, I think that is a myth. But insofar as glass is amorphous there are arbitrarily small energy barriers against changes of configuration and so it is technically a liquid, even though in practical terms it's a solid. Brent Meeker
Silly Putty was once (tongue in cheek) refered to as 'studentene' because of its one-second memory. Being a student at that time, the name stuck. this link describes three states (not phases) as liquid, rubbery and glass: http://www.files.chem.vt.edu/chem-dept/marand/Lecture14.pdf mind you that the separation between rheology and theology is thinnish, Wouter. -----Original Message----- From: Dan Asimov Sent: Wednesday, December 26, 2012 11:14 PM To: math-fun Subject: Re: [math-fun] Entering a New Phase It used to be widely claimed that (apparently solid) glass was known to be liquid, because old window panes are thicker at the bottom. As a boy, after I got my first toy of Silly Putty (in 1955. It was called "Nutty Putty"), which will slowly flow like a liquid but which can also break irregularly if struck with a hammer (like glass)* -- and learned it was a silicon compound, I was entirely convinced. But more recently I've read that this has been found to be a myth. Rather, it is said, glass windows, etc., are in fact solids. And, the old windows were sometimes thicker at the bottom only because they were made of blown glass, with much less precision. --Dan _________________________________________________________________________________ * It also bounced and could pick up the reverse image of something printed in a newspaper -- but you all probably knew that. I can't find any reference to the trade name "Nutty Putty", for some reason. Especially since it's a more memorable name than "Silly Putty", I'd expect that someone must have obtained the rights to that name. On 2012-12-26, at 1:54 PM, meekerdb wrote:
On 12/26/2012 1:36 PM, Warren Smith wrote:
http://www.lassp.cornell.edu/sethna/OrderParameters/BrokenSymmetry.html
Interesting view: phase changes are about symmetry changes.
One counterexample to this is glasses (amorphous solids). They can be solid or liquid but no symmetry changes that I know of.
I don't think they are solid, they're just liquids with very high viscosity.
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participants (4)
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Dan Asimov -
meekerdb -
Warren Smith -
Wouter Meeussen