Fig. 2

Gauss’s theorem. In blue, the flux calculated as the surface integral of the vector field \(\overrightarrow {\mathbf{W}}\) obtained from commuters going to work. In red, the volume integral of ∇\(\overrightarrow {\mathbf{W}}\). a Results in London for a circle of radius R centered at Waterloo Bridge. b A square perimeter around London with the same center and side 2R. In the figure, we show half the side as the x-axis variable to maintain the geographical scales similar to those of the circle radius. The same for Paris with a circle (c) and a square (d) centered at the Passage du Grand Cerf in the 2nd Arrondissement