  Comet C/2013 A1 (Siding Spring) will have a close encounter with Mars on
October 19, 2014. We model the dynamical evolution of dust grains from the time
of their ejection from the comet nucleus to the Mars close encounter, and
determine the flux at Mars. Constraints on the ejection velocity from Hubble
Space Telescope observations indicate that the bulk of the grains will likely
miss Mars, although it is possible that a few-percent of grains with higher
velocities will reach Mars, peaking approximately 90--100 minutes after the
close approach of the nucleus, and consisting mostly of millimeter-radius
grains ejected from the comet nucleus at a heliocentric distance of
approximately 9~AU or larger. At higher velocities, younger grains from
sub-millimeter to several millimeter can reach Mars too, although an even
smaller fraction of grains is expected have these velocities, with negligible
effect on the peak timing. Using NEOWISE observations of the comet, we can
estimate that the maximum fluence will be of the order of $10^{-7}$
grains/m$^2$. We include a detailed analysis of how the expected fluence
depends on the grain density, ejection velocity, and size-frequency
distribution, to account for current model uncertainties and in preparation of
possible refined model values in the near future.
