Introduction - Towards Autonomous Soft Matter Systems - page 7

Fig. 1.4 Clockwise from top left Spatiotemporal patterns such as spirals and travelling waves
in catalytic reactions, the Belousov-Zhabotinsky reaction, aggregating social amoeba and Min-
oscillations in bacteria (Images taken from [ 3 , 25 ])
constants k i ( i = 1, 2) set the temporal scale. When the reaction-diffusion dynam-
ics occur in a closed volume such that the confinement is smaller than the typical
wavelength of the spatial pattern, the spatial dynamics are suppressed. The closed
volume can be considered homogeneous in the diffusive limit and the dynamics
within the volume appear as strictly temporal oscillations. We enclose the Belousov-
Zhabotinsky (BZ) reaction in emulsion droplets of a few tens to hundreds of microns
diameter to form chemical oscillators. In Chap. 5 , we describe the properties of these
oscillators and their synchronization behaviour mediated by coupling across bilayer
membranes as those described in the previous part.
Similarly, co-ordinatedmotion (swarming) leads to pattern formation of a different
type at various length scales as seen in Fig. 1.5 . Different kinds of interactions—
biochemical, hydrodynamic and volume exclusion—mediate the co-ordination
between the movements of various individuals. While in bird and animal flocks there
can be visual and olfactory cues, swimming at the microscale is dominated by chem-
ical and hydrodynamic interactions. However, unlike the reaction-diffusion mecha-
nism for oscillators, there are no general principles known, yet, that are applicable
in a wide range of swarming behaviour, particularly due to complicated interactions.
Therefore, it is important to study the relative roles of the physical and biochemical
interactions in isolation. Theoretical studies of such systems have typically abstracted
the individual unit, be it bird, beast or microbe, to a point like self propelled particle
[ 23 , 29 ]. This approach of treating flocks as large collections of particles naturally