where the data a(r, t) are the measured evolution of the radial signal profiles, and c(s, f r ) is a differential size-andshape distribution, expressed most conveniently for the modeling of SV data in coordinates of sedimentation coefficient s and frictional ratio f r (Brown and Schuck 2006) . v(s, f r , r, t) are normalized solutions of the Lamm equation (Lamm 1929 )