Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on the inverse Smoluchowski problem for cluster-cluster
  aggregation   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.

14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph