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

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Abstract

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
Publisher:	IOP Publishing
ISSN:	1742-6596
Date:	2011
Volume:	Vol.333
Page Range:	012005
Identification Number:	10.1088/1742-6596/333/1/012005
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Related URLs:	Other Repository
References:	[1] G. L. Stephens, J. Climate 18, 237 (2005). [2] E. Bodenschatz, S. P. Malinowski, R. A. Shaw, and F. Stratmann, Science 327, 970 (2010). [3] H. Siebert, K. Lehmann, M. Wendisch, H. Franke, R. Maser, D. Schell, E. Wei Saw, and R. A. Shaw, Bull. Am. Meteorol. Soc. 87, 1727 (2006). [4] W. C. Reade and L. R. Collins, J. Fluid Mech. 415, 45 (2000). [5] L.-P. Wang, O. Ayala, B. Rosa, and G. W. Grabowski, New J. Phys. 10, 075013 (2008). [6] H. Wright and D. Ramkrishna, Comput. Chem. Eng. 16, 1019 (1992). [7] R. Onishi, K. Matsuda, K. Takahashi, K. Ryoichi, and S. Komori, Int. J. Multiphas. Flow 37, 125 (2011). [8] M. V. Smoluchowski, Z. Phys. Chem. 91, 129 (1917). [9] F. Leyvraz, Phys. Reports 383, 95 (Aug. 2003). [10] M. Ernst, in Fractals in Physics, edited by L. Pietronero and E. Tosatti (North Holland, Amsterdam, 1986) p. 289. [11] M. Lee, Icarus 143, 74 (2000). [12] G. Falkovich, A. Fouxon, and M. G. Stepanov, Nature 419, 151 (2002). [13] P. van Dongen, J. Phys. A: Math. Gen. 20, 1889 (1987). [14] R. C. Ball, C. Connaughton, T. H. M. Stein, and O. Zaboronski, “Instantaneous gelation in the Smoluchowski coagulation equation revisited,” (2010), arXiv:1012.4431v1 [cond-mat.stat-mech]. [15] P. C. Hansen, in Computational Inverse Problems in Electrocardiology, edited by P. Johnston (WIT Press, 2001) pp. 119–142. [16] S. Bhattacharjee and F. Seno, J. Phys. A–Math. Gen. 34, 6375 (2001).
URI:	http://wrap.warwick.ac.uk/id/eprint/44446

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