Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spatial pattern formation induced by Gaussian white noise   The ability of Gaussian noise to induce ordered states in dynamical systems
is here presented in an overview of the main stochastic mechanisms able to
generate spatial patterns. These mechanisms involve: (i) a deterministic local
dynamics term, accounting for the local rate of variation of the field
variable, (ii) a noise component (additive or multiplicative) accounting for
the unavoidable environmental disturbances, and (iii) a linear spatial coupling
component, which provides spatial coherence and takes into account diffusion
mechanisms. We investigate these dynamics using analytical tools, such as
mean-field theory, linear stability analysis and structure function analysis,
and use numerical simulations to confirm these analytical results.

20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th