where x is the position vector of solution, Y(n)(t) is the position vector
of a particle depending on the time (t), N is the total number of
particles, F(n)(t) is the force monopole strength equal to the hydrodynamic
drag on the nth particle and D(n)(x) is the Gaussian envelope
function. The Gaussian envelope function for the nth particle
can be explained using the length scale (rn) of the nth particle