Open Access
Table A.1
List of symbols and notation.
| symbol | quantity |
|---|---|
| n | pixel count for each axis |
| s | pixel width |
| L = ns | system size |
| N | particle count |
| i = 1…N | particle index |
| t | time |
| ω | orbital angular frequency |
| r = xi + yj + zk | coordinate vector |
| r | distance |
| b | width of isothermal |
| k | wave vector |
| k = |k| | length of the vector |
| mi | mass of particle i |
| ri(t) | position of particle i |
 |
velocity of particle i |
 |
acceleration of particle i |
| R(t) | center of mass |
| P | total momentum |
| L | total angular momentum |
| Epot, Ekin | potential, kinetic energy |
| E = Epot + Ekin | total energy |
| M | total mass |
| ϕ(r, t) | MOND potential |
| ψ(x, y, t) | deflection potential |
| gM(r, t) = −∇ϕ | Milgromian gravity |
| gN(r, t) | Newtonian gravity |
| F(r, t) = gN + H | vector field |
| H(r, t) | magnetic component of F |
| c | speed of light |
| a0 = 1.2 10−10ms−2 | Milgrom’s constant |
| G | Newton’s constant |
| Λ | cosmological constant |
| a(t) | cosmological scale factor |
| x = gM/a0 | strength of MOND force |
| y = F/a0 | strength of surface density |
| μ(x) = y/x | interpolation function |
| v(y) = x/y | reciprocal interpolation |
| ρB(r, t) | baryonic matter density |
| ρD(r, t) | dark matter density |
| ρA(r, t) = ρB + ρD | apparent matter density |
| σ(x, y, t) | surface mass density |
| ∆t | time step |
| ℱ | 3d FT operator |
 |
3d FT of (r) |
| i, j, k | standard basis vectors |
| i, j, k | pixel coordinate index |
| ξ, η, ζ | random floating-points |
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