In the electrical circuit in Fig. 3,
when the manual switch is closed,
the inductor is connected
to the source and builds up a flux, 
, by drawing a current
(Fig. 4).
The diode is not active in this mode of operation.
When the switch is opened,
the current drawn by the inductor drops to 0,
causing its flux, , to discharge instantaneously.
The derivative nature of the constituent relation
,
results in an infinite negative (the flux changes
from a positive value to 0) voltage across the diode such that
is exceeded. The diode comes
on instantaneously and the mode of operation where the switch
was open and the diode inactive is never realized in real time.
If it were, the stored energy of the inductor
would be released instantaneously in a mode where the model
has no real representation, producing an incorrect energy balance
in the overall system. Consequently, there would be no flow of current
after the diode becomes active. This shows that the flux of the inductor
when the diode comes on should be computed based on the flux before
switching started, .
So, the consecutive mode
switch to 
has to occur before the state vector is
updated to its a posteriori value, 
.
Mathematically, this can be represented as
(3) 
where 
is a mythical mode [5].
It is clear that switching specifications have to be in terms of
a posteriori state variable values, 
, as shown by Fig. 3.
Figure 3: Physical system with discontinuities.
Figure 4: A series of mode switches may occur.
Consider a scenario where the diode requires a threshold current
to remain on. If the inductor has built
up a positive flux, the diode comes on when the switch opens. However,
if the flux in the inductor is too low to maintain the threshold
current, i.e., 
,
the diode goes off instantaneously, but when it is off,
the voltage drop exceeds the threshold
voltage again.
The model goes into a loop of instantaneous changes
(dashed arrow in Fig. 4) during which
real time does not progress or diverge, and this conflicts with the
notion that in the physical world time does not halt.