On the Use of Nonlinear Boundary-Value Problems to Estimate the Cloud-Formation Potential of Aerosol Particles

This paper investigates the transient growth of aerosol particles in a humid environment. It seeks to explore the dependence of the fraction of droplet-forming particles on statistical properties of the distribution of dry particle diameters, as well as on the rate of temperature decay associated with vertical motion through the atmosphere. Low-dimensional, autonomous models are investigated using basic tools of dynamical systems analysis that establish the parameter-dependent existence and stability of families of equilibrium distributions of wet particle diameters. In the fully nonautonomous case, an original heuristic parameterization of the fraction of droplet-forming particles is derived in terms of a scalar, nonlinear boundary-value problem. To address the failure of the heuristic parameterization to account for the potential of a dynamic reversal of growth following an initial increase in particle diameter, a finely resolved, high-dimensional boundary-value formulation for the aerosol dynamics is i...

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