Evolution of shock parameters in the simulation with ﹩{ \mathcal N }={10}^{39}﹩: upstream Lorentz factor γ _u, shock compression factor q ≡ κ _d/κ _u, and radiative parameter χ. Red dotted curves show the analytical results for γ _u(r), q(r), χ(r) derived in Section 5 (Equations (75), (92), and (94)). The simulation neglected the precursor effect (Section 5.5).