Integral formulation of null-collision Monte Carlo algorithms

•Null-collisions are discussed in integral terms instead of kinetic ones.•Negative null-collision coefficients are allowed.•A full meshless multiple-scattering algorithm example is provided.•The meaning of all free algorithmic parameters is closely discussed.

At the kinetic level, the meaning of null-collisions is straightforward: they correspond to pure-forward scattering events. We here discuss their technical significance in integral terms. We first consider a most standard null-collision Monte Carlo algorithm and show how it can be rigorously justified starting from a Fredholm equivalent to the radiative transfer equation. Doing so, we also prove that null-collision algorithms can be slightly modified so that they deal with unexpected occurrences of negative values of the null-collision coefficient (when the upper bound of the heterogeneous extinction coefficient is nonstrict). We then describe technically, in full details, the resulting algorithm, when applied to the evaluation of the local net-power density within a bounded, heterogeneous, multiple scattering and emitting/absorbing medium. The corresponding integral formulation is then explored theoretically in order to distinguish the statistical significance of introducing null-collisions from that of the integral-structure underlying modification.