Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions.

At high concentration, free swimming nematodes known as vinegar eels (Turbatrix 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 repulsion 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 impedes eel head overlaps also reduces close interactions throughout the eel bodies.

Ricochets on Asteroids: Experimental study of low velocity grazing impacts into granular media.

Spin off events and impacts can eject boulders from an asteroid surface and rubble pile asteroids can accumulate from debris following a collision between large asteroids. These processes produce a population of gravitational bound objects in orbit that can impact an asteroid surface at low velocity and with a distribution of impact angles. We present laboratory experiments of low velocity spherical projectiles into a fine granular medium, sand. We delineate velocity and impact angles giving ricochets, those giving projectiles that roll-out from the impact crater and those that stop within their impact crater. With high speed camera images and fluorescent markers on the projectiles we track spin and projectile trajectories during impact. We find that the projectile only reaches a rolling without slipping condition well after the marble has reached peak penetration depth. The required friction coefficient during the penetration phase of impact is 4-5 times lower than that of the sand suggesting that the sand is fluidized near the projectile surface during penetration. We find that the critical grazing impact critical angle dividing ricochets from roll-outs, increases with increasing impact velocity. The critical angles for ricochet and for roll-out as a function of velocity can be matched by an empirical model during the rebound phase that balances a lift force against gravity. We estimate constraints on projectile radius, velocity and impact angle that would allow projectiles on asteroids to ricochet or roll away from impact, finally coming to rest distant from their initial impact sites.

Excitation of Tumbling in Phobos and Deimos.

Mass-spring model simulations are used to investigate past spin states of a viscoelastic Phobos and Deimos. From an initially tidally locked state, we find crossing of a spin-orbit resonance with Mars or a mean motion resonance with each other does not excite tumbling in Phobos or Deimos. However, once tumbling our simulations show that these moons can remain so for an extended period and during this time their orbital eccentricity can be substantially reduced. We attribute the tendency for simulations of an initially tumbling viscoelastic body to drop into spin-synchronous state at very low eccentricity to the insensitivity of the tumbling chaotic zone volume to eccentricity. After a tumbling body enters the spin synchronous resonance, it can exhibit long lived non-principal axis rotation and this too can prolong the period of time with enhanced tidally generated energy dissipation. The low orbital eccentricities of Phobos and Deimos could in part be due to spin excitation by nearly catastrophic impacts rather than tidal evolution following orbital resonance excitation.