76,709 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=
Identifying Nearby UHECR Accelerators using UHE (and VHE) Photons
Ultra-high energy photons (UHE, E > 10^19 eV) are inevitably produced during
the propagation of 10^20 eV protons in extragalactic space. Their short
interaction lengths (<20 Mpc) at these energies, combined with the impressive
sensitivity of the Pierre Auger Observatory detector to these particles, makes
them an ideal probe of nearby ultra-high-energy cosmic ray (UHECR) sources. We
here discuss the particular case of photons from a single nearby (within 30
Mpc) source in light of the possibility that such an object might be
responsible for several of the UHECR events published by the Auger
collaboration. We demonstrate that the photon signal accompanying a cluster of
a few > 6x10^19 eV UHECRs from such a source should be detectable by Auger in
the near future. The detection of these photons would also be a signature of a
light composition of the UHECRs from the nearby source.Comment: 4 pages, 2 figures, accepted for publication in PR
Analysis of enhanced diffusion in Taylor dispersion via a model problem
We consider a simple model of the evolution of the concentration of a tracer,
subject to a background shear flow by a fluid with viscosity in an
infinite channel. Taylor observed in the 1950's that, in such a setting, the
tracer diffuses at a rate proportional to , rather than the expected
rate proportional to . We provide a mathematical explanation for this
enhanced diffusion using a combination of Fourier analysis and center manifold
theory. More precisely, we show that, while the high modes of the concentration
decay exponentially, the low modes decay algebraically, but at an enhanced
rate. Moreover, the behavior of the low modes is governed by finite-dimensional
dynamics on an appropriate center manifold, which corresponds exactly to
diffusion by a fluid with viscosity proportional to
The Intergalactic Propagation of Ultra-High Energy Cosmic Ray Nuclei: An Analytic Approach
It is likely that ultra-high energy cosmic rays contain a significant
component of heavy or intermediate mass nuclei. The propagation of ultra-high
energy nuclei through cosmic radiation backgrounds is more complicated than
that of protons and its study has required the use of Monte Carlo techniques.
We present an analytic method for calculating the spectrum and the composition
at Earth of ultra-high energy cosmic rays which start out as heavy nuclei from
their extragalactic sources. The results obtained are in good agreement with
those obtained using numerical methods.Comment: accepted for publication in Phys Rev
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