From the collision frequency, f c o l l , given by kinetic theory the total number of hard sphere collisions in a cell during a time τ τ is M c o l l = 1 2 ( N c − − 1 ) F N f c o l l τ τ = N c ( N c − − 1 ) F N π π d 2 ⟨ ⟨ v r ⟩ ⟩ τ τ 2 V c where d is the particle diameter and V c is the volume of the cell. Since collision candidates go through a rejection sampling procedure the ratio of total accepted to total candidates for hard sphere particles is M c o l l M c a n d = ⟨ ⟨ v r ⟩ ⟩ v r max The number of collision candidates selected in a cell over a time step τ τ is M c a n d = N c ( N c − − 1 ) F N π π d 2 v r max τ τ 2 V c This approach for determining the number of collisions is known as the No-Time-Counter (NTC) method. If v r max is set excessively high then the algorithm processes the same number of collisions (on average) but the simulation is inefficient because many candidates are rejected.