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Project C.3: Spatio-temporal pattern formation in reaction-diffusion-advection-mechanics (RDAM) systems
So far, in the RDAM model for Physarum
polycephalum we have considered non-moving protoplasmic droplets
corresponding to fixed boundary conditions. Therein, we could
reproduce the whole variety of experimentally observed spatio-temporal
patterns ranging from anti-phase oscillations over standing and
rotating traveling waves to irregular, seemingly chaotic patterns.
Now we will take into account that droplet boundaries are soft and should also be affected by external forces. This will allow to describe moving droplets and should contribute substantially to the understanding of the interplay between internal force generation and cell motility on substrates. Phase-field methods will be applied as effective computational alternative to the sharp interface limit within the free-boundary approach that we have used in the description of localized spots and moving wave segments in reaction-diffusion systems.
In the two-phase model, we will study how different properties of the viscoelastic phase, e.g. nonlinear elasticity or a different constitutive law, and chemical reactions between the stress-regulating species influence the generation and the dynamics of mechano-chemical waves.
Project leaders: Prof. Dr. H. Engel , Prof. Dr. M. Bär