Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions of kinetic equations in an autocatalytic growth model   Kinetic equations are introduced for the transition-metal nanocluster
nucleation and growth mechanism, as proposed by Watzky and Finke. Equations of
this type take the form of Smoluchowski coagulation equations supplemented with
the terms responsible for the chemical reactions. In the absence of
coagulation, we find complete analytical solutions of the model equations for
the autocatalytic rate constant both proportional to the cluster mass, and the
mass-independent one. In the former case, $\xi_{k} = s_k(\xi_{1})\propto
\xi_{1}^{k}/k $ was obtained, while in the latter, the functional form of
$s_k(\xi_{1})$ is more complicated. In both cases, $\xi_{1}(t) =
h_{\mu}(M_{\mu}(t))$ is a function of the moments of the mass distribution.
Both functions, $s_k(\xi_{1})$ and $h_{\mu}(M_{\mu})$, depend on the assumed
mechanism of autocatalytic growth and monomer production, and not on other
chemical reactions present in a system.

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
2
The categories of this paper are: math