Some remarks on the inverse Smoluchowski problem for cluster-cluster aggregation
Connaughton, Colm and Jones, Peter P.. (2011) Some remarks on the inverse Smoluchowski problem for cluster-cluster aggregation. Journal of Physics: Conference Series, Vol.333 . 012005. ISSN 1742-6596
WRAP_Connaughton_1104.4589v1.pdf - Submitted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://dx.doi.org/10.1088/1742-6596/333/1/012005
It is proposed to revisit the inverse problem associated with Smoluchowski's coagulation equation. The objective is to reconstruct the functional form of the collision kernel from observations of the time evolution of the cluster size distribution. A regularised least squares method originally proposed by Wright and Ramkrishna (1992) based on the assumption of self-similarity is implemented and tested on numerical data generated for a range of different collision kernels. This method expands the collision kernel as a sum of orthogonal polynomials and works best when the kernel can be expressed exactly in terms of these polynomials. It is shown that plotting an "L-curve" can provide an a-priori understanding of the optimal value of the regularisation parameter and the reliability of the inversion procedure. For kernels which are not exactly expressible in terms of the orthogonal polynomials it is found empirically that the performance of the method can be enhanced by choosing a more complex regularisation function.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Centre for Complexity Science
Faculty of Science > Mathematics
|Library of Congress Subject Headings (LCSH):||Coagulation -- Mathematical models, Cluster analysis|
|Journal or Publication Title:||Journal of Physics: Conference Series|
|Access rights to Published version:||Restricted or Subscription Access|
 G. L. Stephens, J. Climate 18, 237 (2005).
Actions (login required)