Investigation of long-term asymptotics of the probability of occurrence of particles diffusing in cylindrical pores with traps

Numerical simulation of trapping of particles diffusing in media with pores has been carried out. Traps are randomly distributed over the surface of pores having a cylindrical shape. The dynamics of particle capture on traps and trap filling have been studied. In general, the decrease of particles is exponentially decreasing with a characteristic time due to the concentration of traps. For the first time, the appearance of extended plateaus of the distribution function over long periods was discovered. The appearance of these plateaus is due to the fact that large areas arise in which either there are no traps due to fluctuations, or these traps are already filled with diffusing particles. In numerical modeling, it manifests itself in the form of steps of the particle distribution function due to the lack of grip on traps. The statistical characteristics of staggered distributions - interval lengths, length distribution functions - are investigated.