Lattice Models of Bacterial Turbulence

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There is something truly fascinating about coordinated behaviour of living organisms. Be it the simple pleasure of watching geometrical patterns or a deeper, almost philosophical, satisfaction of observing order appear from chaos, collective motion in schools of fish and flocks of birds or insects, so successfully popularised by Sir David Attenborough, appeals equally to the general public and scientists alike. Studies of how this behaviour comes about transformed our understanding of animal behaviour, biology of groups of organisms, and social interactions. Surprisingly, such phenomena have had a strong impact on statistical and soft matter physics by stimulating the development of what is now called the field of active matter. In the attempt to distill what aspects of such collective behaviour can be attributed to physical interactions, there emerged a new direction in non-equilibrium physics that seeks to understand the unique states of matter formed by particles that extract energy from their environment and transform it into self-propulsion.In this proposal we focus on dilute solutions of swimming bacteria - an archetypal model for swimming microorganisms. Such solutions often exhibit a unique dynamical state, known as "bacterial turbulence". At very low densities, bacterial suspensions appear featureless and disordered, while at higher, yet still sufficiently low densities, collective motion sets in on the scale of the system. We propose a high-risk, high-gain research programme that will establish a novel class of lattice models describing collective motion in microscopic self-propelled particles suspended in a fluid. Similar in spirit to other non-equilibrium lattice models, our model is simple enough to allow for detailed studies into the exact nature of collective motion.If successful, the model will gain the status similar to, say, the Ising model in condensed matter physics, and will establish itself as a new archetypal class of active matter systems, ultimately enriching our understanding of non-equilibrium physics and fascinating collective phenomena in nature.