  We present a new model of the $\beta$ Pictoris disk-and-planet system that
simulates both the planetesimal collisions and the dynamics of the resulting
dust grains, allowing us to model features and asymmetries in both thermal and
scattered light images of the disk. Our two-part model first simulates the
collisional and dynamical evolution of the planetesimals with the
Superparticle-Method Algorithm for Collisions in Kuiper belts (SMACK) and then
simulates the dynamical evolution of the resulting dust grains with a standard
Bulirsch-Stoer N-body integrator. Given the observed inclination and
eccentricity of the $\beta$ Pictoris b planet, the model neatly ties together
several features of the disk: the central hole in the submillimeter images, the
two-disk "x"-pattern seen in scattered light, and possibly even the clumpy gas
seen by ALMA. We also find that most of the dust in the $\beta$ Pictoris system
is likely produced outside the ring at 60-100 AU. Instead of a birth ring, this
disk has a "stirring ring" at 60-100 AU where the high-velocity collisions
produced by the secular wave launched by the planet are concentrated. The
two-disk x-pattern arises because collisions occur more frequently at the peaks
and troughs of the secular wave. The perturbations of the disk in this region
create an azimuthally and vertically asymmetric spatial distribution of
collisions, which could yield an azimuthal clump of gas without invoking
resonances or an additional planet.

Earth and Planetary Astrophysics