2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163881We propose a model for aggregation where particles are continuously growing by heterogeneous condensation in one dimension and solve it exactly. We show that the particle size spectra exhibit transition to dynamic scaling $c(x,t)\sim t^{-β}ϕ(x/t^z)$. The exponents $β$ and $z$ satisfy a generalized scaling relation $β=(1+q)z$ where the value of $q$ is fixed by a non-trivial conservation law. We have shown that the value of $(1+q)$ is always less than the value 2 of aggregation without condensation.6 pages, 3 figuresStatistical MechanicsDisordered Systems and Neural Networkstext