Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model of pattern formation in marsh ecosystems with nonlocal
  interactions   Smooth cordgrass Spartina alterniflora is a grass species commonly found in
tidal marshes. It is an ecosystem engineer, capable of modifying the structure
of its surrounding environment through various feedbacks. The scale-dependent
feedback between marsh grass and sediment volume is particularly of interest.
Locally, the marsh vegetation attenuates hydrodynamic energy, enhancing
sediment accretion and promoting further vegetation growth. In turn, the
diverted water flow promotes the formation of erosion troughs over longer
distances. This scale-dependent feedback may explain the characteristic
spatially varying marsh shoreline, commonly observed in nature. We propose a
mathematical framework to model grass-sediment dynamics as a system of
reaction-diffusion equations with an additional nonlocal term quantifying the
short-range positive and long-range negative grass-sediment interactions. We
use a Mexican-hat kernel function to model this scale-dependent feedback. We
perform a steady state biharmonic approximation of our system and derive
conditions for the emergence of spatial patterns, corresponding to a spatially
varying marsh shoreline. We find that the emergence of such patterns depends on
the spatial scale and strength of the scale-dependent feedback, specified by
the width and amplitude of the Mexican-hat kernel function.

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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math