  This study employed grain dynamic models to examine the density distribution
of debris discs, and discussed the effects of the collisional time-intervals of
asteroidal bodies, the maximum grain sizes, and the chemical compositions of
the dust grains of the models, in order to find out whether a steady out-moving
flow with an 1/R profile could be formed. The results showed that a model with
new grains every 100 years, a smaller maximum grain size, and a composition
C400 has the best fit to the 1/R profile because: (1) the grains have larger
values of beta on average,therefore, they can be blown out easily; (2) the new
grains are generated frequently enough to replace those have been blown out.
With the above two conditions, some other models can have a steady out-moving
flow with an approximate 1/R profile. However, those models in which new grains
are generated every 1000 years have density distributions far from the profile
of a continuous out-moving flow. Moreover, the analysis on the signatures of
planets in debris discs showed that there are no indications when a planet is
in a continuous out-moving flow, however, the signatures are obvious in a
debris disc with long-lived grains.
