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\subsection{Radiative properties of a cloud of porous ceria particles under solar irradiation}  We now calculate the radiative properties of clouds of particles made up of monodisperse, cold, uniformly distributed particles. The incident   Representations of the three particle types can be found in Figure \ref{fig:particletypes} \ref{fig:problem_setup}  The radiative transfer equation has been solved in one dimension using the Monte Carlo method.   Calculations were validated against single scattering measurements and theoretical calculations of bidirectional reflectivity and transmissivity of polystyrene spheres as a function incidence angle\cite{Hottel_1970}.