Environmental Engineering Reference
In-Depth Information
In
A
the adjacency matrix is specified. The vector
xy
contains the positions
representing the compartments in the plot. The
'-o'
string in the
gplot
-command
specifies how lines and nodes in the plot (
vertices
and
edges
in graph theory - see for
example: Chartrand
1977
) are represented in the figure. The
axis
-command defines
the limits of the coordinate system. The final
text
calls set the text-strings near to the
corresponding edges.
In order to complete a compartment model, fluxes need a mathematical quantifi-
cation. Formulae for such fluxes are more or less complex, which determines
the degree complexity at this point. In the following sub-chapters fluxes of different
mathematical complexity will be treated, starting with the simplest linear case.
Holzbecher et al. (
2005
) describe some other properties of the adjacency matrix,
especially in relation to the feedback property within compartment systems. In
the following we examine linear systems as most simple mathematical examples of
compartment models. Finally, there is to mention that Avila et al
.
(
2003
) present
the ECOLEGO toolbox for radiological risk assessment, which is a MATLAB
®
implementation based on the compartment idea. The model was used for modeling
the accumulation of radionuclides in the arctic Barents Sea (Dommasnes et al.
2001
). A simplified version of the food chain as a graph is shown in Fig.
18.4
Harp seal
Polar cod
Zooplankton:
copepods, amphipods, euphausiids
Phytoplankton
Fig. 18.4
Graph,
representing the foodchain in
the Barents Sea; simplified by
E.H. from Dommasnes et al.
(
2001
)
Water
