Improved Determination of Bimodal Size Distributions from Measurements with Diffusional Size Classification

The size distribution of the unattached fraction of the short-lived radon progeny is reported in the literature to have a bimodal structure. Due to the weak size resolution of diffusional size classification, a wide variety of bimodal size distributions yields similar measurement results, obstructing the reconstruction of size distribution parameters from measured data. For example, it could be shown that although 2 of the commonly used nonlinear approximation algorithms per formed well for the reconstruction of a monomodal size distribution, the reproduc tion of parameters of a bimodal size distribution was unsatisfactory. In conse quence, a "random walk" approach is presented. The basic idea for this approach consists of probing the complete parameter space as an ideal method for locating the best set of parameters. Additionally, 2 steps are introduced for the reduction of computation time to render the ideal approach to an applicable method. The range of geometric standard deviations for the calculation was restricted to values between 1 and 5. The range of median diameters was limited according to the penetration functions of the diffusional samplers. This restricted volume of param eter space was subdivided into 10⁴ cells. During the calculation, cells with exceptionally large values of the minimization functional were eliminated from further computation. Compared to the results of EM and Simplex algorithms, this ''random walk'' method was able to retrieve parameters of both monomodal and bimodal size distributions with improved accuracy.