Soft biological materials like cytoskeletal gels, cell extracts and actomyosin solutions
are often challenging to model as they continuously burn energy e.g. in the form of ATP,
and this drives them out of equilibrium even in steady state.
I will focus on two particular examples of such soft active matter.
First I will present 3-dimensional dynamic Monte-Carlo simulations
of the propulsion of a colloidal obstacle via the polymerisation of an actin comet (see e.g. movies in
Then I will introduce a lattice Boltzmann method to simulate the equations
of motion of an active gel or active liquid crystal (a coarser continuum
description which holds e.g. for a solution of microtubules and molecular
motors). I will show that an active gel can sustain spontaneous flow in
steady state, and if time permits I will discuss some preliminary numerical studies on
its rheological properties