showing 2 related works from this author
Traveling Waves Emerging in a Diffusive Moving Filament System
2014
Starting from a minimal model for the actin cytoskeleton of motile cells we derive a spatially one dimensional model describing populations of right and left moving filaments with intrinsic velocity, diffusion and mutual alignment. For this model we derive traveling wave solutions whose speed and shape depend on the model parameters and the type of alignment. We discuss possible wave profiles obtained from analytical investigations as well as waves emerging in numerical simulations. In particular, we will explicitly comment on the observed wave speeds and how they are related to the model parameters. Moreover, some particularly interesting patterns being composed of several wave profiles ar…
Bifurcation of traveling waves in a Keller–Segel type free boundary model of cell motility
2018
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. The two key properties of this problem are (i) presence of the cross diffusion as in the classical Keller-Segel problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from a family of radially symmetric steady states. The traveling waves describe persistent motion without external cues or stimuli which is a signature of …