Geoscience Reference
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By studying the following natural problems, it was shown that they exhibit the
Turing nonequilibrium mechanisms of spatial patterns formations, with clustering
and fractal boundaries behavior - the author has been studying since 2003 the
subjects contained in items (3), (13), and (14):
1. Mutual interference between predators (Alonso et al.
2002
)
2. The dynamics of nutrient cycling and food webs (DeAngelis
1992
)
3. Kinetic modeling of microbial-driven redox chemistry of subsurface envi-
ronments, with coupling transport, microbial metabolism, and geochemistry
(Hunter et al.
1998
)
4. Predator-prey dynamics in environments rich and poor in nutrients (McCauley
and Murdoch
1990
)
5. The occurrence and activity of sulfate-reducing bacteria (producing hydrogen
sulfide gas, H
2
S) in the bottom sediments of the Gulf of Gdansk (Mudryk et al.
2000
)
6. The cycling of iron and manganese in surface sediments, with the coupled
transport and reaction of carbon (C), oxygen (O
2
), nitrogen (N
2
), sulfur (S),
iron (Fe), and manganese (Mn) (Van Capellen and Chang
1996
)
7. Linear understanding of a huge aquatic ecosystem model using a group-
collecting sensitive study (Köhler and Wirtz
2002
)
8. Phenomenological pattern recognition in the dynamical structures of marine-
estuarine tidal sediments from the German Wadden Sea (Kropp and Klenke
1997
)
9. Global terrestrial distribution of nitrous oxide (N
2
O) production and N inputs in
freshwater (rivers, lakes, and ponds), estuarine, and coastal marine ecosystems
(Seitzinger and Kroeze
1998
)
10. Dynamic response of deep-sea sediments to seasonal variations (Soetaert et al.
1996
)
11. A multicomponent reactive transport model of early diagenesis, with applica-
tion to redox cycling in coastal marine sediments (Wang and Van Capellen
1996
)
12. The control of biogeochemical cycling by mobility and metabolic strategies of
microbes in the sediments (Wirtz
2003
)
13. Instabilities and pattern formation in simple ecosystem models (Baurmann et al.
2003
)
14. Stable squares and other oscillatory Turing patterns in a diffusion-reaction
model (Yang et al.
2004
)
We then can see clearly that the dynamical evolutions of the LLV models
(which are based on nonlinear reactive and other processes between species on
a lattice) lead toward structures with clustering and fractal boundaries behavior.
And we know from above that the evolutions of the Turing structures (based on the
formation of patterns in nonequilibrium mixing of the mechanisms of diffusion and
nonlinear reactive kinetics, between natural objects) also lead toward structures with
clustering and fractal boundaries behavior (Kropp et al.
1997
). So, the LLV model is
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