Dynamical self-consistent field-theory for active nematic liquid crystals: Nematic order and spatio-temporal structure in surface colonies of rod-like bacteria

We present a dynamical self-consistent field theory for interacting, self-propelled rods that we use to study fascinating time-dependent, inhomogeneous structures observed in surface colonies of twitching Pseudomonas aeruginosa bacteria. We apply an extremal principle to an exact dynamical functional integral derived from the microscopic, many-body dynamics of self-propelled rods moving in two-dimensions. This reduces the problem to that of a single self-propelled rod moving in response to self-consistent, mean-force and torque fields. We address the thorny problem of calculating rod-rod interactions in this mean-field approximation. For uniform systems in two-dimensions, we observe that a continuous isotropic-nematic phase transition occurs at a critical rod concentration. The value of the critical concentration is independent of the magnitude of the self-propulsive force. We discuss our preliminary simulations of inhomogeneous, dynamical structures formed in motile bacteria surface colonies.