Active Brownian and inertial particles in disordered environments: short-time expansion of the mean-square displacement
Davide Breoni, Michael Schmiedeberg, Hartmut Löwen
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α = 3 and α = 4. We confirm our theoretical predictions by computer simulations. Moreover they are verifiable in experiments on self-propelled colloids in random environments.
It is increasingly becoming apparent that the physical concepts of forces and flows play an important role in understanding biological processes, from the spread of cancers to morphogenesis, thedevelopment of organisms. However, biological systems, such as cells, probe new ideas in that theyoperate out of thermodynamic equilibrium continually taking chemical energy from their surroundings, and using it to move and self-organise.
The term active matter has come to describe models of living systems where such a continuous influx of energy leads to striking collective behaviour like the chaotic flow patterns of active turbulence seen in collections of bacteria and self-propelled topological defects which are now thought to be relevant to some modes of biofilm formation. This paper is a numerical investigation of three-dimensional droplets composed of active matter and the ways in which their shapes change in response to the continuous input of energy. One striking observation is the continuous formation of finger-like protrusions, reminiscent of the collective motion of invading cancer cells. By changing the mechanical properties of the drop or the activity level, we find several different dynamical responses: for example the droplet surface can wrinkle in a way that resembles a walnut or the active forces can drive a dimple in the droplet to grow, leading to a cup-shape: such invagination is reminiscent of patterns seen during morphogenesis.
Understanding the behaviour of model systems, here a continuum model of active material, is an important step towards the goal of understanding the role of physical theories in the life sciences.
Morphology of active deformable 3D droplets
Liam J. Ruske, Julia M. Yeomans
We numerically investigate the morphology and disclination line dynamics of active nematic droplets in three dimensions. Although our model only incorporates the simplest possible form of achiral active stress, active nematic droplets display an unprecedented range of complex morphologies. For extensile activity finger-like protrusions grow at points where disclination lines intersect the droplet surface. For contractile activity, however, the activity field drives cup-shaped droplet invagination, run-and-tumble motion or the formation of surface wrinkles. This diversity of behaviour is explained in terms of an interplay between active anchoring, active flows and the dynamics of the motile dislocation lines. We discuss our findings in the light of biological processes such as morphogenesis, collective cancer invasion and the shape control of biomembranes, suggesting that some biological systems may share the same underlying mechanisms as active nematic droplets.