Taming Lévy flights in confined crowded geometries.
We study two-dimensional diffusive motion of a tracer particle in restricted, crowded anisotropic geometries. The underlying medium is formed from a monolayer of elongated molecules [Cieśla J. Chem. Phys. 140, 044706 (2014)] of known concentration. Within this mesh structure, a tracer molecule is allowed to perform a Cauchy random walk with uncorrelated steps. Our analysis shows that the presence of obstacles significantly influences the motion, which in an obstacle-free space would be of a superdiffusive type. At the same time, the selfdiffusive process reveals different anomalous properties, both at the level of a single trajectory realization and after the ensemble averaging. In particular, due to obstacles, the sample mean squared displacement asymptotically grows sublinearly in time, suggesting a non-Markov character of motion. Closer inspection of survival probabilities indicates, however, that the underlying diffusion is memoryless over long time scales despite a strong inhomogeneity of the motion induced by the orientational ordering.
M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland.
Michał
M
Cieśla
M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland.
Bartłomiej
B
Dybiec
Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.
Igor
I
Sokolov
M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland.
Ewa
E
Gudowska-Nowak
D016880:Anisotropy; D004058:Diffusion; D008958:Models, Molecular; D009038:Motion; D013269:Stochastic Processes