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We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Levy searcher.
Non-Markovian diffusion of excitons in layered perovskites and transition metal dichalcogenides
(2022)
The diffusion of excitons in perovskites and transition metal dichalcogenides shows clear anomalous, subdiffusive behaviour in experiments.
In this paper we develop a non-Markovian mobile-immobile model which provides an explanation of this behaviour through paired theoretical and simulation approaches.
The simulation model is based on a random walk on a 2D lattice with randomly distributed deep traps such that the trapping time distribution involves slowly decaying power-law asymptotics.
The theoretical model uses coupled diffusion and rate equations for free and trapped excitons, respectively, with an integral term responsible for trapping.
The model provides a good fitting of the experimental data, thus, showing a way for quantifying the exciton diffusion dynamics.