Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform asymptotic approximation of diffusion to a small target:
  generalized reaction models   The diffusion of a reactant to a binding target plays a key role in many
biological processes. The reaction-radius at which the reactant and target may
interact is often a small parameter relative to the diameter of the domain in
which the reactant diffuses. We develop uniform in time asymptotic expansions
in the reaction-radius of the full solution to the corresponding diffusion
equations for two separate reactant-target interaction mechanisms: the Doi or
volume reactivity model, and the Smoluchowski-Collins-Kimball partial
absorption surface reactivity model. In the former, the reactant and target
react with a fixed probability per unit time when within a specified
separation. In the latter, upon reaching a fixed separation, they
probabilistically react or the reactant reflects away from the target.
Expansions of the solution to each model are constructed by projecting out the
contribution of the first eigenvalue and eigenfunction to the solution of the
diffusion equation, and then developing matched asymptotic expansions in
Laplace-transform space. Our approach offers an equivalent, but alternative,
method to the pseudo-potential approach we previously employed in [Isaacson and
Newby 2013] for the simpler Smoluchowski pure absorption reaction mechanism. We
find that the resulting asymptotic expansions of the diffusion equation
solutions are identical with the exception of one parameter: the diffusion
limited reaction rates of the Doi and partial absorption models. This
demonstrates that for biological systems in which the reaction-radius is a
small parameter, properly calibrated Doi and partial absorption models may be
functionally equivalent.

23
The categories of this paper are: solv-int
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat