Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Role of curvature and domain shape on Turing patterns   We consider pattern formation using reaction-diffusion equation on various
non-uniformly curved surfaces. We explore how, in general, curvature and, in
particular the domain shape would affect the pattern formation in these
geometries. As examples, we study stripe and spot patterns on a torus, and on
an ellipsoid. Our results show that the curvature and domain shape can control
the orientation of stripe pattern as well as the size and number of spots. Our
results also indicate that by controlling the curvature and shape, one can
drive the chemicals to a preferred region. Specifically on a torus, curvature
and shape can guide the chemicals more on to outer side than inner side. This
result may prove important in the studies of self-organization of molecules in
biological membranes.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics