Metachronal waves in concentrations of swimming {\it Turbatrix aceti} nematodes and an oscillator chain model for their synchronized behavior

At high concentration, free swimming nematodes known as vinegar eels ({\it Tubatrix aceti}), collectively exhibit metachronal waves near a boundary. We find that the frequency of the collective traveling wave is lower than that of the freely swimming organisms. We explore models based on a chain of oscillators with nearest neighbor interactions that inhibit oscillator phase velocity. The phase of each oscillator represents the phase of the motion of the eel's head back and forth about its mean position. A strongly interacting directed chain model mimicking steric interactions between organisms robustly gives traveling wave states and can approximately match the observed wavelength and oscillation frequency of the observed traveling wave. We predict body shapes assuming that waves propagate down the eel body at a constant speed. The phase oscillator model that minimizes eel head overlaps also reduces close interactions throughout the eel bodies.