Environmental Engineering Reference
In-Depth Information
cross the border of the system [inflow from the outside into the system (i.e. from a
source), outflow when it leaves the system (into a sink)].
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Controls
Controls are used to specify the extent of flows occurring between different
compartments. They are drawn as valves with influences from other parts of the
system that are drawn as light or dotted arrows. The dotted arrows represent the
causal structure, determining which parts of the system have an impact on other
parts.
Compartments, connections, and controls represent the functional units which
allow to specify dynamic systems. For convenience, additional graphical elements
are sometimes used in systems representation when a direct interfacing to a
mathematical formalization is intended.
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Sources and Sinks
The system border is indicated only implicitly in the form that flows come from
the outside into the system or leave the system to the outside. Sources are used if a
flow is represented that does not originate from within the system (i.e. an inflow to a
variable that does not originate from another variable). Sinks, usually displayed
with the same symbol as a source, are displayed when a flow originates from within
the system but does not ends in a systems compartment.
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Auxiliaries
In some cases it simplifies the representation by adding a symbol (e.g. a larger
circle) to represent expressions, which occur more than once in the specification of
different controls.
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Parameters
These are constant values that are used to specify controls. They can be visua-
lized by a specific symbol, frequently a small circle, from which influence(s) go to
one or more than one control.
The transition from a cause-effect diagram to a flow chart is made by an
assignment of the concepts appearing in the cause-effect diagram to either a
compartment, connection or control. Arrows from the cause-effect diagram are
distinguished whether representing flows or influences. The process to set up a
flow diagram is easier when the overall structure has already been considered in
terms of causes and effects, rather than starting at the beginning with the set-up of
a flow diagram without having systematized the relevant relations to be considered
beforehand.
For a correct systems representation, implicit rules emerge for flow charts. Flows
can only originate from sources or from compartments and end at sinks or compart-
ments. Influences can originate from parameters, auxiliaries, compartments or con-
trols. They can connect to auxiliaries and controls, but cannot end at compartments.
Figure
4.2
represents an example of a Lotka-Volterra flow chart.