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Debris discs are traditionally studied using two distinct types of numericalmodels: statistical particle-in-a-box codes to study their collisional and sizedistribution evolution, and dynamical N-body models to study their spatialstructure. The absence of collisions from N-body codes is in particular a majorshortcoming, as collisional processes are expected to significantly alter theresults obtained from pure N-body runs. We present a new numerical model, tostudy the spatial structure of perturbed debris discs at dynamical andcollisional steady-state. We focus on the competing effects betweengravitational perturbations by a massive body (planet or star), collisionalproduction of small grains, and radiation pressure placing these grains inpossibly dynamically unstable regions. We consider a disc of parent bodies atdynamical steady-state, from which small radiation-pressure-affected grains arereleased in a series of runs, each corresponding to a different orbitalposition of the perturber, where particles are assigned a collisionaldestruction probability. These collisional runs produce successive positionmaps that are then recombined, following a complex procedure, to producesurface density profiles for each orbital position of the perturbing body. Weapply our code to the case of a circumprimary disc in a binary. We findpronounced structures inside and outside the dynamical stability regions. Forlow $e_B$, the disc's structure is time varying, with spiral arms in thedynamically "forbidden" region precessing with the companion star. For high$e_B$, the disc is strongly asymmetric but time invariant, with a pronounceddensity drop in the binary's periastron direction. (better resolution versionof the paper at http://lesia.obspm.fr/perso/philippe-thebault/theb2011.pdf)

A new code to study structures in collisionally active, perturbed debris discs. Application to binaries