113,385 research outputs found
Cubic structures, equivariant Euler characteristics and lattices of modular forms
We use the theory of cubic structures to give a fixed point Riemann-Roch
formula for the equivariant Euler characteristics of coherent sheaves on
projective flat schemes over Z with a tame action of a finite abelian group.
This formula supports a conjecture concerning the extent to which such
equivariant Euler characteristics may be determined from the restriction of the
sheaf to an infinitesimal neighborhood of the fixed point locus. Our results
are applied to study the module structure of modular forms having Fourier
coefficients in a ring of algebraic integers, as well as the action of diamond
Hecke operators on the Mordell-Weil groups and Tate-Shafarevich groups of
Jacobians of modular curves.Comment: 40pp, Final version, to appear in the Annals of Mathematic
Dispersion of biased swimming microorganisms in a fluid flowing through a tube
Classical Taylor-Aris dispersion theory is extended to describe the transport
of suspensions of self-propelled dipolar cells in a tubular flow. General
expressions for the mean drift and effective diffusivity are determined exactly
in terms of axial moments, and compared with an approximation a la Taylor. As
in the Taylor-Aris case, the skewness of a finite distribution of biased
swimming cells vanishes at long times. The general expressions can be applied
to particular models of swimming microorganisms, and thus be used to predict
swimming drift and diffusion in tubular bioreactors, and to elucidate competing
unbounded swimming drift and diffusion descriptions. Here, specific examples
are presented for gyrotactic swimming algae.Comment: 20 pages, 4 figures. Published version available at
http://rspa.royalsocietypublishing.org/content/early/2010/02/09/rspa.2009.0606.short?rss=
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