Arrested development of active suspensions in liquid crystals: traveling waves

Many microorganisms must navigate complex biological fluid environments. To study such challenging systems, liquid crystals (LCs) have emerged as a model anisotropic, viscoelastic fluid. Recent experiments using bacteria in LCs have shown an alluring interplay between bulk fluid elasticity and flows generated by active stresses. We will present analytical and numerical results on bifurcations and arrested states in a model active suspension in a nematic LC. In addition, we identify weakly and strongly deformed traveling wave solutions in motile suspensions, with numerics and theoretical results showing close agreement.