Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

Deep-sea hydrocarbon seep gastropod Bathynerita naticoidea responds to cues from the habitat-providing mussel Bathymodiolus childressi

Bathynerita naticoidea (Gastropoda: Neritidae) is a numerically dominant heterotrophic gastropod found at hydrocarbon seep sites on the upper Louisiana slope of the Gulf of Mexico. Snails of this species are commonly associated with beds of the methanotrophic mussel Bathymodiolus childressi (Bivalvia: Mytilidae), and their population structure mirrors that of the mussels they are found among. Previous studies have shown that these snails feed on bacteria and decomposing periostracum on the B. childressi shell. We predicted that B. naticoidea might be attracted to cues specific to its preferred habitat, such as dissolved methane, mucus from conspecific snails, or metabolites produced by B. childressi mussels. To examine this, we used a flow‐through Y‐maze system to investigate the behavior of B. naticoidea exposed to these potential cues. We found that the nerite is not attracted to methane, but is strongly attracted to seawater conditioned with B. childressi. The attractant appears to be specific to this type of mussel, and is not a soluble cue produced by conspecific snails.