Exact post-critical particle mass spectra in a family of gelling systems

The critical behaviour of the coagulating systems, where the coagulation efficiency grows with the masses of colliding particles g and l as K(g, l) = gαlα (1/2 < α ≤ 1) is studied. The instantaneous sink that removes the particles with masses exceeding G is introduced which allows one to define the gel as a deposit of particles with masses between G + 1 and 2G. This system displays critical behaviour (the sol-gel transition) as G → ∞. The exact post-critical particle mass spectrum is shown to be an algebraic function of g times a growing exponent. All critical parameters of the systems are determined as the functions of α including the critical times. (fast track communication)