There are four key processes that dictate the behavior of the magnetic flux
concentrations that form the so-called 'magnetic carpet' of the quiet phot
osphere. These processes are emergence, cancellation, coalescence, and frag
mentation. Rates of emergence have been estimated from observations, but th
e rates of cancellation, coalescence, and fragmentation are much more diffi
cult to determine observationally. A model is set up to simulate an area of
magnetic carpet in the quiet Sun. In the model there are three imposed par
ameters: the rate of emergence of new flux, the distribution of emerged flu
x and the rate of fragmentation of flux concentrations. The rate of cancell
ation and the rate of coalescence are deduced from the model. From the simu
lations it is estimated that the average emergence rate of new flux in the
quiet Sun must be between 6x10(-6) and 10(-5) Mx cm(-2) s(-1) to maintain a
n absolute flux density of between 2.5 and 3 G. For this rate of emergence
a fragmentation rate of more than 12x10(-5) s(-1) is required to produce th
e observed exponential index for the number density of flux concentrations.
This is equivalent to each fragment canceling more than once every 200 min
utes. The rate of cancellation is calculated from the model and is found na
turally to be equivalent to the rate of emergence. However, it is found tha
t the frequency of cancellation is much greater than the frequency of emerg
ence. In fact, it is likely that there are several orders of magnitude more
cancellation events than emergence events. This implies that flux is injec
ted in relatively large concentrations whereas cancellation occurs though t
he disappearance of many small concentrations.