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I didn't realize that. It sounds like the same situation with astronomical simulations. General Relativity is too complicated so everyone uses Newtonian mechani

by nonbel 10y ago

I didn't realize that. It sounds like the same situation with astronomical simulations. General Relativity is too complicated so everyone uses Newtonian mechanics plus a fudge factor. I think it is odd that the two most cherished scientific theories are not actually used in practice to compare with data. Also, this got me wondering how they did this simulation, which lead me to this site: http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html There is a lot of code.. but after a quick look at it I see Netwonian mechanics. From analytic_gravity.h: void GravAccel_StaticIsothermalSphere() { double ISO_M200=95.21; double ISO_R200=160.0; double ISO_Eps=0.1; double ISO_FRACTION=0.9; double r, m, dx, dy, dz; int i; for(i = FirstActiveParticle; i >= 0; i = NextActiveParticle[i]) { dx = P[i].Pos[0]; dy = P[i].Pos[1]; dz = P[i].Pos[2]; r = sqrt(dx * dx + dy * dy + dz * dz); if(r > ISO_R200) m = ISO_M200; else m = ISO_M200 * r / ISO_R200; m *= ISO_FRACTION; if(r > 0) { P[i].GravAccel[0] += -All.G * m * dx / r / (r * r + ISO_Eps * ISO_Eps); P[i].GravAccel[1] += -All.G * m * dy / r / (r * r + ISO_Eps * ISO_Eps); P[i].GravAccel[2] += -All.G * m * dz / r / (r * r + ISO_Eps * ISO_Eps); } } }

dekhn 10y ago
Yes, both astrophysics codes and MD are basically "n-body approximations" https://en.wikipedia.org/wiki/N-body_simulation https://en.wikipedia.org/wiki/N-body_simulation although if I understand correctly universal simulations do explicitly model general relatively Personally I find the "particle mesh". If you model the N-body calculation this way, you can solve for the field (potential) by converting to fourier space, doing some FFTs (which computers are really, really good at), then converting back to real space. This works in both astro and molecular simulations, really well.
- semi-extrinsic 10y ago
  Fourier methods are good, but only when your potential is decaying slowly. If it decays fast, like van der Waals interaction which are plentiful in MD, you just have to do the plain n-body approx.
  - dekhn 10y ago
    In MD, it's a combination of VDW and electrostatic. Typically VDW is just a cutoff (VDW forces beyond 8A are neglible), and electrostatic is handled by particle-mesh ewald. I worked on DNA and RNA, which have strong electrostatic interactions and my thesis work showed PME was critical for stability.
    - semi-extrinsic 10y ago
      This was what I was trying to say. Actually, this assumes atomistic MD where you have electrostatics. I've done some work with coarse-grained MD, where you've averaged out the electrostatics and you just have VDW.

by nonbel 10y ago

dekhn 10y ago

Yes, both astrophysics codes and MD are basically "n-body approximations" https://en.wikipedia.org/wiki/N-body_simulation https://en.wikipedia.org/wiki/N-body_simulation although if I understand correctly universal simulations do explicitly model general relatively Personally I find the "particle mesh". If you model the N-body calculation this way, you can solve for the field (potential) by converting to fourier space, doing some FFTs (which computers are really, really good at), then converting back to real space. This works in both astro and molecular simulations, really well.

semi-extrinsic 10y ago
Fourier methods are good, but only when your potential is decaying slowly. If it decays fast, like van der Waals interaction which are plentiful in MD, you just have to do the plain n-body approx.
- dekhn 10y ago
  In MD, it's a combination of VDW and electrostatic. Typically VDW is just a cutoff (VDW forces beyond 8A are neglible), and electrostatic is handled by particle-mesh ewald. I worked on DNA and RNA, which have strong electrostatic interactions and my thesis work showed PME was critical for stability.
  - semi-extrinsic 10y ago
    This was what I was trying to say. Actually, this assumes atomistic MD where you have electrostatics. I've done some work with coarse-grained MD, where you've averaged out the electrostatics and you just have VDW.