33,951 research outputs found
Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems
The bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equation corresponding
to the affine Hecke algebra of type is a consistent system of
-difference equations which in some sense contains two families of
Cherednik's quantum affine Knizhnik-Zamolodchikov equations for meromorphic
functions with values in principal series representations of . In this paper
we extend this construction of BqKZ to the case where is the affine Hecke
algebra associated to an arbitrary irreducible reduced root system. We
construct explicit solutions of BqKZ and describe its correspondence to a
bispectral problem involving Macdonald's -difference operators.Comment: 31 page
Validity of Viscous Core Correction Models for Self-Induced Velocity Calculations
Viscous core correction models are used in free wake simulations to remove
the infinite velocities at the vortex centreline. It will be shown that the
assumption that these corrections converge to the Biot-Savart law in the far
field is not correct for points near the tangent line of a vortex segment.
Furthermore, the self-induced velocity of a vortex ring with a viscous core is
shown to converge to the wrong value. The source of these errors in the model
is identified and an improved model is presented that rectifies the errors. It
results in correct values for the self-induced velocity of a viscous vortex
ring and induced velocities that converge to the values predicted by the
Biot-Savart law for all points in the far field.Comment: 8 pages, 5 figure
On global deformation quantization in the algebraic case
We give a proof of Yekutieli's global algebraic deformation quantization
result which does not rely on the choice of local sections of the bundle of
affine coordinate systems. Instead we use an argument inspired by algebraic De
Rham cohomology.Comment: 60 pages; references added; relation to Hinich's work explaine
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