I have coded a simulation where **$n$ equal charges** are randomly placed **on** the surface of the conducting **sphere**. I added a damping term proportional to velocity so that the charges arrange in a stable configuration. Then the graphics of polyhedron with charges as vertices is displayed.

It **works for** every number of charges **less than 78**. It takes my computer around 20 seconds for 77 but for **78 or greater it just freezes**.

Below is the code. Under each defined function there is a description of what it does

Is there a way to fix it?

Thanks in advance.

```
NaključnaTNaKrogli(r_: 1) := {
{x, y, z} = {RandomReal({-1, 1}), RandomReal({-1, 1}),
RandomReal({-1, 1})};
If(x^2 + y^2 + z^2 < 1,
r {x, y, z}/Sqrt(x^2 + y^2 + z^2),
NaključnaTNaKrogli(r))
}((1));
(*returns random point on the sphere of radius r, centered at {0,0,0}*)
l(vektor_) := Sqrt(vektor.vektor);
(*returns magnitude(length) of a vector*)
L(sez_) := l /@ sez;
Strešca(vektor_) := vektor/l(vektor);
STREŠCA(sez_) := sez/L(sez);
sez(CapitalDelta)r(sezr_, n_, i_) :=
ConstantArray(sezr((i)), n - 1) - Delete(sezr, i);
(*returns list of vectors from i'th charge to all other charges in
sezr. n=Length(sezr)*)
F(sezr_, n_, i_, c_) := {
s = sez(CapitalDelta)r(sezr, n, i);
c Total(s/L(s)^3)
}((1));
(*returns list of force vectors of other charges on i'th charge in
sezr. c is q^2/(4Subscript((Pi)(Epsilon), 0))*)
Seza(sezr_, n_, c_, m_, k_, sezV_) := {
rstre = STREŠCA(sezr);
sezF =
Reap(
Do(
Sow(
F(sezr, n, j, c)
)
, {j, n})
)((2))((1));
(sezF - rstre (Total /@ (rstre sezF)) - k sezV)/m
}((1));
(*returns list of acceloration vectors of charges. sezV is a list of
velocities of charges*)
Pol(n_) := {
vmax = 1;
amax = 1;
sezr = Reap(
Do(
Sow(NaključnaTNaKrogli())
, n)
)((2))((1));
sezv = ConstantArray({0, 0, 0}, n);
seza = ConstantArray({0, 0, 0}, n);
t = 1/60;
dt = 1/60;
While(
(Not(
IntegerQ(
t))) (Or) ((Max(L(sezv)) > vmax) (And) (Max(L(seza)) >
amax)),
seza = Seza(sezr, n, 100, 1, 1, sezv);
sezv += seza dt;
sezr += sezv dt;
sezr /= L(sezr);
t += dt;
);
<< TetGenLink`;
{coords, incidences} = TetGenConvexHull(sezr);
Show(
Graphics3D({
EdgeForm(),
FaceForm(Cyan),
GraphicsComplex(coords, Polygon(incidences))}),
Background -> Black,
Boxed -> False
)
}((1));
(*returns graphics of polihedron with charges in end state as
vertecies*)
Pol(78)
```