65,371 research outputs found
Rapid behavioral transitions produce chaotic mixing by a planktonic microswimmer
Despite their vast morphological diversity, many invertebrates have similar
larval forms characterized by ciliary bands, innervated arrays of beating cilia
that facilitate swimming and feeding. Hydrodynamics suggests that these bands
should tightly constrain the behavioral strategies available to the larvae;
however, their apparent ubiquity suggests that these bands also confer
substantial adaptive advantages. Here, we use hydrodynamic techniques to
investigate "blinking," an unusual behavioral phenomenon observed in many
invertebrate larvae in which ciliary bands across the body rapidly change
beating direction and produce transient rearrangement of the local flow field.
Using a general theoretical model combined with quantitative experiments on
starfish larvae, we find that the natural rhythm of larval blinking is
hydrodynamically optimal for inducing strong mixing of the local fluid
environment due to transient streamline crossing, thereby maximizing the
larvae's overall feeding rate. Our results are consistent with previous
hypotheses that filter feeding organisms may use chaotic mixing dynamics to
overcome circulation constraints in viscous environments, and it suggests
physical underpinnings for complex neurally-driven behaviors in early-divergent
animals.Comment: 20 pages, 4 figure
Geometric Proofs of Horn and Saturation Conjectures
We provide a geometric proof of the Schubert calculus interpretation of the
Horn conjecture, and show how the saturation conjecture follows from it. The
geometric proof gives a strengthening of Horn and saturation conjectures. We
also establish transversality theorems for Schubert calculus in non-zero
characteristic.
Some parts of the version posted in Nov 2002 (concerning explicit invariants
constructed from Schubert calculus) have been removed from this version. They
have appeared separately in IMRN 2004, no. 69, pages 3709--3721 " Invariant
theory of GL(n) and Intersection theory of Grassmannians"Comment: 36 pages, accepted for publication in the Journal of Algebraic
Geometr
Geometric Proof of a Conjecture of Fulton
We give a geometric proof of a conjecture of W. Fulton on the multiplicities
of irreducible representations in a tensor product of irreducible
representations for GL(r).Comment: 10 pages, no figure
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