Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self similarity and attraction in stochastic nonlinear
  reaction-diffusion systems   Similarity solutions play an important role in many fields of science: we
consider here similarity in stochastic dynamics. Important issues are not only
the existence of stochastic similarity, but also whether a similarity solution
is dynamically attractive, and if it is, to what particular solution does the
system evolve. By recasting a class of stochastic PDEs in a form to which
stochastic centre manifold theory may be applied we resolve these issues in
this class. For definiteness, a first example of self-similarity of the
Burgers' equation driven by some stochastic forced is studied. Under suitable
assumptions, a stationary solution is constructed which yields the existence of
a stochastic self-similar solution for the stochastic Burgers' equation.
Furthermore, the asymptotic convergence to the self-similar solution is proved.
Second, in more general stochastic reaction-diffusion systems stochastic centre
manifold theory provides a framework to construct the similarity solution,
confirm its relevance, and determines the correct solution for any compact
initial condition. Third, we argue that dynamically moving the spatial origin
and dynamically stretching time improves the description of the stochastic
similarity. Lastly, an application to an extremely simple model of turbulent
mixing shows how anomalous fluctuations may arise in eddy diffusivities. The
techniques and results we discuss should be applicable to a wide range of
stochastic similarity problems.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th