Abstract:
Volume exclusion interactions play a key role in many biological systems. In particular, it seems to be the key to explaining spontaneous alignment of anisotropic particles, for example, alignment of myxobacteria or fibers in a network. Most individual-based models impose this type of alignment in their equations. Here we do not wish to impose this type of alignment, but to investigate how it might emerge from volume exclusion interactions. To carry this out, volume exclusion interactions will be modelled via a soft anisotropic repulsion potential (which are vastly used in the literature of liquid crystals). We will present an individual-based model based on this potential and derive the corresponding kinetic and macroscopic equations. This approach allows us to understand how alignment emerges from volume exclusion and how it also affects not only the orientation of the particles, but also their positions.