H = T + Vattractor + Vradial + Vrepulsion + Vlink
T = Σi ½m|ṙi|² (kinetic energy)
Vattractor = (ga/2) Σp |rp - rtopic(p)|² (topic attraction)
Vradial = (gr/2) Σp (|rp| - R)² (sphere constraint)
Vrepulsion = gc Σi<j 1/|ri - rj| (Coulomb repulsion)
Vlink = (gl/n) Σ<a,p> |ra - rp|n (author-paper Ln norm)
â†p(x) creates publication at position x
â†a(x) creates author at position x
â†t(x) creates topic at position x
ga = Topic Pull (attractor strength)
gr = Surface (radial constraint)
gc = Repulsion (charge repulsion)
gl = Link (author-paper coupling)
n = Norm exponent (L2=harmonic, L3=cubic, L4=quartic, ...)
Enter potential energy expressions. Variables: r (distance), R (sphere radius = 350). Force F = -∇V computed automatically.
r
R
gₗ ×
r^2
r^3
r^4
gₐ ×
gᵣ ×
(r - R)^2
(r - R)^4
abs(r - R)^3
gᶜ ×
1/r
1/r^2
exp(-r/50)/r
gₐᵤ ×
0