Effects of hard-core interaction on nearest neighbor distances at a single trap for random walks and for diffusion processes

Absence of depletion zone effects for the trapping reaction in complex networks

In the present work we examine in detail the formation of a depletion zone in the trapping reaction in networks, with a single perfect trap. We monitor the particle density rho(r) with respect to the distance r from the trap. We show using Monte Carlo simulations that the depletion zone is absent in regular, Erdos-Renyi (ER), and scale-free (SF) networks. The density profiles show significant differences for these cases. The particles are homogeneously distributed in regular and ER networks with the depletion effect appearing in very sparse ER networks. In SF networks we reveal the important role of the hubs, which due to their high random walk centrality are critical in the trapping reaction. In addition, the degree distribution plays a significant role in the distribution of the particles recovering the depletion zone formation for high gamma values. The mean connectivity of the network is found to play a significant role in both ER and SF networks.

Anomalous growth of the depletion zone in the photobleaching trapping reaction

We study the anomalous growth of the depletion zone at a single trap, as observed in a photobleaching trapping reaction in confined geometry. We provide experimental evidence for a nonuniversal growth of this depletion. We also find an early-time behavior of the depletion zone, owing to the finite size of the trap. Various laser powers are used in order to study the effects of trapping strength, interpreted theoretically in terms of an imperfect trap. The results are supported by numerical calculations. Comparison with other trapping reactions provides insight into finite-size traps.

Trapping reactions for mobile particles and a trap in the laboratory frame

We have used a stochastic model to obtain the exact spatial particle density profile for the trapping process A+B-->B in a one-dimensional lattice with a single trap, as seen from the laboratory frame. We obtain the profile for either perfect or imperfect reactions when A particles are immobile, but only for perfect absorption in the general case where both particles are mobile with different diffusivities. This profile is found to be similar to that seen from the reference system attached to the trap, the most noticeable difference being near the origin.