// InitVelocity initializes particle velocities selected from a random distribution.
// Ensures that the net momentum of the system is zero and scales the average kinetic energy to match a given temperature.
func InitVelocity(N int, T0 float64, M float64) [][3]float64 {
V := make([][3]float64, N)
rand.Seed(1)
netP := [3]float64{0, 0, 0}
netE := 0.0
for n := 0; n < N; n++ {
for i := 0; i < 3; i++ {
newP := rand.Float64() - 0.5
netP[i] += newP
netE += newP * newP
V[n][i] = newP
}
}
netP = vector.Scale(netP, 1.0/float64(N))
vscale := math.Sqrt(3.0 * float64(N) * T0 / (M * netE))
for i, v := range V {
correctedV := vector.Scale(vector.Difference(v, netP), vscale)
V[i] = correctedV
}
return V
}
// InitPositionCubic initializes particle positions in a simple cubic configuration.
func InitPositionCubic(N int, L float64) [][3]float64 {
R := make([][3]float64, N)
Ncube := 1
for N > Ncube*Ncube*Ncube {
Ncube++
}
rs := L / float64(Ncube)
roffset := (L - rs) / 2
i := 0
for x := 0; x < Ncube; x++ {
x := float64(x)
for y := 0; y < Ncube; y++ {
y := float64(y)
for z := 0; z < Ncube; z++ {
z := float64(z)
pos := vector.Scale([3]float64{x, y, z}, rs)
offset := [3]float64{roffset, roffset, roffset}
R[i] = vector.Difference(pos, offset)
i++
}
}
}
return R
}
// Displacement calculates the smallest vector pointing from a to b in a cell with periodic boundary conditions.
func Displacement(a, b [3]float64, L float64) [3]float64 {
r := vector.Difference(b, a)
return PutInBox(r, L)
}