Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 32: Microswimmers I (joint session DY/BP/CPP)

DY 32.4: Talk

Tuesday, March 13, 2018, 14:45–15:00, BH-N 243

Clearing out a Maze: Chemotaxis and Percolation — Tanja Schilling¹ and •Thomas Voigtmann^2,3 — ¹Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany — ²Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany — ³Department of Physics, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany

We study chemotactic motion in a random environment of obstacles by means of a lattice model that bears resemblance to the arcade game PAC-MAN®: A random walker moves on the percolating cluster of a square lattice, with steps that are biased towards the food that is initially placed on the accessible lattice sites and that is then consumed by the walker. Anomalous diffusion emerges, and is best described by a power-law with a non-trivial dynamical exponent that depends continuously on the propensity of the walker to move towards food. Although its food propensity biases the walker to explore previously unvisited sites more easily than the unbiased random walk, and thus intuitively serves to stretch out the walker’s trajectories in comparison to the non-chemotactic case, the asymptotic growth of the mean-squared displacement is weaker. We suggest that getting lost in the culs-de-sac is a mechanism to explain why the chemotactic exploration of a maze thus becomes less effective than the pure diffusive one.

[1] T. Schilling and Th. Voigtmann, J. Chem. Phys. (in press, 2017); arXiv:1607.01123.