Abstract
In this paper, the particle size distribution is reconstructed using finite moments based on a converted spline-based method, in which the number of linear system of equations to be solved reduced from 4m × 4m to (m + 3) × (m + 3) for (m + 1) nodes by using cubic spline compared to the original method. The results are verified by comparing with the reference firstly. Then coupling with the Taylor-series expansion moment method, the evolution of particle size distribution undergoing Brownian coagulation and its asymptotic behavior are investigated.
Highlights
Particle size distribution (PSD) is one of the most important properties of aerosol particles, including transport, sedimentation, and so on [1]
This problem is distinguished between the three types for the monovariate case: the Hausdorff moment problem with the PSD supported on the closed interval [a, b], where [a, b] are the lower and upper limits of the domain of PSD; the Stieltjes moment problem with the PSD supported on [0, +∞); and the Hamburger moment problem with the PSD supported on (−∞, +∞) [8]
There exist several frequently used reconstruction methods in the literature mainly for the Hausdorff moment problem, including but not limited to parameter-fitting method, Kernel density function-based method, maximum entropy method, and spline-based method. e parameter-fitting method is to assume the PSD as a simple function, where the parameters in the function are determined by the given low-order moments [7]
Summary
Particle size distribution (PSD) is one of the most important properties of aerosol particles, including transport, sedimentation, and so on [1]. Using a given number of moments to reconstruct the PSD is known as the finite-moment problem or inverse problem in mathematical analysis [7]. E parameter-fitting method is to assume the PSD as a simple function (i.e., log-normal distribution or gamma distribution), where the parameters in the function are determined by the given low-order moments [7]. It is the fastest and easiest method but with drawbacks that need a priori knowledge about the solution and limited to simple shapes, even though a weighted sum of different simple functions can be used [9]. Compared to the original method, the number of linear system of equations to be solved is significantly reduced through substituting the continuous conditions. e correctness of this new treatment is verified by comparing with the reference results in [7]. en with the moments obtained by the Taylor-series expansion moment method (TEMOM) [16], the evolution of PSD due to Brownian coagulation and its asymptotic behavior are investigated
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