Electron Distribution

    {  elec.mpl  }

    {  GAMS Model Library, http://www.gams.com/modlib/libhtml/elec.htm    }

    {  Distribution of electrons on a sphere,  NLP,  Size: 25x75  }



TITLE
    Elec;

OPTIONS
    ModelType=Nonlinear
    ParserType=Extended


INDEX
    i := 1..25;
    j := i;
    ut[i,j] WHERE (j > i);

DATA
!not allowed    Theta[i] := 2*pi;!*UNIFORM(0,1);
    A := 2*pi;
    B[i] := UNIFORM(0,1);
    Theta[i] := A*B;
    Phi[i] := pi*B;
    XInit[i] := cos(Theta)*sin(Phi);
    YInit[i] := sin(Theta)*sin(Phi);
    ZInit[i] := cos(Phi);

VARIABLES
    X[i] INITIAL XInit;
    Y[i] INITIAL YInit;
    Z[i] INITIAL ZInit;

MODEL

    MIN Potential = SUM(i,j IN ut: 1/((X[i]-X[i:=j])^2
                                    + (Y[i]-Y[i:=j])^2
                                    + (Z[i]-Z[i:=j])^2)^0.5);

SUBJECT TO

     Ball[i]:   X^2 + Y^2 + Z^2 = 1;

BOUNDS
     -1 <= X <= 1;
     -1 <= Y <= 1;
     -1 <= Z <= 1;

END