We study the behaviour of fermions localized on moving kinks as these collide with either antikinks or spacetime boundaries. We numerically solve for the evolution of the scalar kinks and the bound (i.e. localized) fermion modes, and calculate the number of fermions transfered to the antikink and boundary in terms of Bogoliubov coefficients. Interpreting the boundary as the brane on which we live, this models the ability of fermions on branes incoming from the bulk to ``stick'' on the world brane, even when the incoming branes bounce back into the bulk.
Saffin, P. M., & Tranberg, A. (2007). Particle transfer in braneworld collisions. Journal of High Energy Physics, 2007(8), https://doi.org/10.1088/1126-6708/2007/08/072