3 ms·

This is just an occurrence of the principle of least action. Systems exhibiting "hyperuniformity" just arrange themselves in order to minimize their potential.

This is just an occurrence of the principle of least action. Systems exhibiting "hyperuniformity" just arrange themselves in order to minimize their potential. This is pretty standard stuff in engineering, and is the basis for finite element simulations of structural mechanics and fluid dynamics problems.

pfd1986 10y ago
That is not strictly true. Most systems "minimizing their potential" exhibit a crystalline, ordered arrangement. Hyperuniform patterns are definitely a result of an optimization, but in this case it is a more complicated one than a 'potential energy'.
- jsnsjsfnts 10y ago
  No, gradients can exist in the steady state system depending on the boundary conditions. Additional irregularities can be accounted for by what would ordinarily be considered "discretization error," since the problems considered in the article are discrete structures rather than continuous PDE's.
- trhway 10y ago
  >Most systems "minimizing their potential" exhibit a crystalline, ordered arrangement. crystalline structures have lower entropy compensated by increase in the entropy of the environment due to heat being transferred out of crystalline structure during its formation. It is kind of intuitively obvious that hyperuniform(random) forest have higher entropy than crystalline style ordered forest would have. I don't see connection to environment (like heat transfer in crystal case) that would allow to compensate for decrease of entropy in an ordered forest.
  - TheOtherHobbes 10y ago
    Trees are a kind of literal poisson disk. Because trees capture light and nutrients, there's a minimum viable spacing between them which enforces some separation. But seed distribution either clusters around each tree, or looks for gaps, depending on the seeding strategy. So I'm not surprised you get a hyperuniform distribution. It's not truly random, because there's a pull towards maximum packing density in one direction, balanced by a push towards a spatial expansion distribution around each tree in the other. Intuitively, I'd suspect this pull/push balance explains most hyperuniform distributions.
    - jsnsjsfnts 10y ago
      >I'd suspect this pull/push balance explains most hyperuniform distributions Also known as the principle of least action
  - pfd1986 10y ago
    That is a good point. But without getting too technical (although I'd love too if wanted), there are 2 caveats with your thought: 1. Order does not need heat transfer. Flying birds form a V-shaped pattern (to minimize drag, whatever), fish "order" into a packed school instead of being random, a honeycomb is hexagonal. Those are (near) optional solutions for constraints. There is an analogy with crystal formation but the math is not totally clear. 2. Crystals can have higher entropy than disordered states. Actually, a (crystalline) dense packing of Brownian spheres have higher entropy than a random close packing of spheres.
    - goodmachine 10y ago
      Interesting. Please feel free to get more technical.
      - pfd1986 10y ago
        About the 2nd point there is this video you can watch which might do better than anything I can type: https://www.youtube.com/watch?v=chS8dpGB0E0 https://www.youtube.com/watch?v=chS8dpGB0E0
        goodmachine 10y ago
        Thanks!
jacobolus 10y ago
So are the authors of all these papers just idiots, or what? https://scholar.google.com/scholar?cites=1079648018171535627 https://scholar.google.com/scholar?cites=1079648018171535627

pfd1986 10y ago

That is not strictly true. Most systems "minimizing their potential" exhibit a crystalline, ordered arrangement. Hyperuniform patterns are definitely a result of an optimization, but in this case it is a more complicated one than a 'potential energy'.

jsnsjsfnts 10y ago
No, gradients can exist in the steady state system depending on the boundary conditions. Additional irregularities can be accounted for by what would ordinarily be considered "discretization error," since the problems considered in the article are discrete structures rather than continuous PDE's.
trhway 10y ago
>Most systems "minimizing their potential" exhibit a crystalline, ordered arrangement. crystalline structures have lower entropy compensated by increase in the entropy of the environment due to heat being transferred out of crystalline structure during its formation. It is kind of intuitively obvious that hyperuniform(random) forest have higher entropy than crystalline style ordered forest would have. I don't see connection to environment (like heat transfer in crystal case) that would allow to compensate for decrease of entropy in an ordered forest.
- TheOtherHobbes 10y ago
  Trees are a kind of literal poisson disk. Because trees capture light and nutrients, there's a minimum viable spacing between them which enforces some separation. But seed distribution either clusters around each tree, or looks for gaps, depending on the seeding strategy. So I'm not surprised you get a hyperuniform distribution. It's not truly random, because there's a pull towards maximum packing density in one direction, balanced by a push towards a spatial expansion distribution around each tree in the other. Intuitively, I'd suspect this pull/push balance explains most hyperuniform distributions.
  - jsnsjsfnts 10y ago
    >I'd suspect this pull/push balance explains most hyperuniform distributions Also known as the principle of least action
- pfd1986 10y ago
  That is a good point. But without getting too technical (although I'd love too if wanted), there are 2 caveats with your thought: 1. Order does not need heat transfer. Flying birds form a V-shaped pattern (to minimize drag, whatever), fish "order" into a packed school instead of being random, a honeycomb is hexagonal. Those are (near) optional solutions for constraints. There is an analogy with crystal formation but the math is not totally clear. 2. Crystals can have higher entropy than disordered states. Actually, a (crystalline) dense packing of Brownian spheres have higher entropy than a random close packing of spheres.
  - goodmachine 10y ago
    Interesting. Please feel free to get more technical.
    - pfd1986 10y ago
      About the 2nd point there is this video you can watch which might do better than anything I can type: https://www.youtube.com/watch?v=chS8dpGB0E0 https://www.youtube.com/watch?v=chS8dpGB0E0
      - goodmachine 10y ago
        Thanks!

jacobolus 10y ago

So are the authors of all these papers just idiots, or what? https://scholar.google.com/scholar?cites=1079648018171535627 https://scholar.google.com/scholar?cites=1079648018171535627