Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 316 / 3 / d / Solution

If $Q_D^{\ast }\propto D^b$, part (b) givesThe mass in one logarithmic size interval scales as $D^3[Dn(D)]\propto D^{4-\alpha }$. A steady collisional cascade requires the mass destroyed per unit time, and hence the mass flux through every logarithmic interval, to be independent of $D$. Its exponent is thereforeSolving gives