22,891 research outputs found
The equivariant K-theory of isotropy actions
We compute the equivariant K-theory with integer coefficients of an
equivariantly formal isotropy action, subject to natural hypotheses which cover
the three major classes of known examples. The proof proceeds by constructing a
map of spectral sequences from Hodgkin's K\"unneth spectral sequence in
equivariant K-theory to that in Borel cohomology. A new characterization of
equivariant formality appears as a consequence of this construction, and we are
now able to show that weak equivariant formality in the sense of
Harada--Landweber is equivalent with integer coefficients to surjectivity of
the forgetful map under a standard hypothesis.
The main structure theorem is formally similar to that for Borel equivariant
cohomology, which appears in the author's dissertation/dormant book project and
whose proof is finally made accessible in an appendix. The most generally
applicable corollary of the main theorem for rational coefficients depends on a
strengthening of the characterization of equivariant formality due to Shiga and
Takahashi, which appears as a second appendix.Comment: 22 pages. Comments extremely welcome
Computational fluid dynamics in a marine environment
The introduction of the supercomputer and recent advances in both Reynolds averaged, and large eddy simulation fluid flow approximation techniques to the Navier-Stokes equations, have created a robust environment for the exploration of problems of interest to the Navy in general, and the Naval Underwater Systems Center in particular. The nature of problems that are of interest, and the type of resources needed for their solution are addressed. The goal is to achieve a good engineering solution to the fluid-structure interaction problem. It is appropriate to indicate that a paper by D. Champman played a major role in developing the interest in the approach discussed
Magnetic Excitations of Stripes and Checkerboards in the Cuprates
We discuss the magnetic excitations of well-ordered stripe and checkerboard
phases, including the high energy magnetic excitations of recent interest and
possible connections to the "resonance peak" in cuprate superconductors. Using
a suitably parametrized Heisenberg model and spin wave theory, we study a
variety of magnetically ordered configurations, including vertical and diagonal
site- and bond-centered stripes and simple checkerboards. We calculate the
expected neutron scattering intensities as a function of energy and momentum.
At zero frequency, the satellite peaks of even square-wave stripes are
suppressed by as much as a factor of 34 below the intensity of the main
incommensurate peaks. We further find that at low energy, spin wave cones may
not always be resolvable experimentally. Rather, the intensity as a function of
position around the cone depends strongly on the coupling across the stripe
domain walls. At intermediate energy, we find a saddlepoint at for
a range of couplings, and discuss its possible connection to the "resonance
peak" observed in neutron scattering experiments on cuprate superconductors. At
high energy, various structures are possible as a function of coupling strength
and configuration, including a high energy square-shaped continuum originally
attributed to the quantum excitations of spin ladders. On the other hand, we
find that simple checkerboard patterns are inconsistent with experimental
results from neutron scattering.Comment: 11 pages, 13 figures, for high-res figs, see
http://physics.bu.edu/~yaodx/spinwave2/spinw2.htm
Magnetic Excitations of Stripes Near a Quantum Critical Point
We calculate the dynamical spin structure factor of spin waves for weakly
coupled stripes. At low energy, the spin wave cone intensity is strongly peaked
on the inner branches. As energy is increased, there is a saddlepoint followed
by a square-shaped continuum rotated 45 degree from the low energy peaks. This
is reminiscent of recent high energy neutron scattering data on the cuprates.
The similarity at high energy between this semiclassical treatment and quantum
fluctuations in spin ladders may be attributed to the proximity of a quantum
critical point with a small critical exponent .Comment: 4+ pages, 5 figures, published versio
Series expansions for the third incomplete elliptic integral via partial fraction decompositions
We find convergent double series expansions for Legendre's third incomplete
elliptic integral valid in overlapping subdomains of the unit square. Truncated
expansions provide asymptotic approximations in the neighbourhood of the
logarithmic singularity if one of the variables approaches this point
faster than the other. Each approximation is accompanied by an error bound. For
a curve with an arbitrary slope at our expansions can be rearranged
into asymptotic expansions depending on a point on the curve. For reader's
convenience we give some numeric examples and explicit expressions for
low-order approximations.Comment: The paper has been substantially updated (hopefully improved) and
divided in two parts. This part is about third incomplete elliptic integral.
10 page
An investigation of particle mixing in a gas-fluidized bed
Mechanism for particle movement in gas-fluidized beds was studied both from the theoretical and experimental points of view. In a two-dimensional fluidized bed particle trajectories were photographed when a bubble passed through
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