MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup

Kyungkeun Kang, Arnd Scheel and Angela Stevens


For spatially one-dimensional run-and-tumble dynamics with mass conservation we develop a coarse phase diagram, that discriminates between global decay to equidistributed constant states, existence of spatially non-trivial waves, and finite time blowup of solutions. Motivated by counter-migrating ripples of high and low population density and fruiting body formation in myxobacteria, we identify phase boundaries as particular critical tumbling dynamics that allow for switching between these spatio-temporal phases upon slight changes in mass densities or parameter values.


Related publications

2019 Repository Open Access
Kyungkeun Kang, Arnd Scheel and Angela Stevens

Global phase diagrams of run-and-tumble dynamics : equidistribution, waves, and blowup

In: Nonlinearity, 32 (2019) 6, pp. 2128-2146