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

Equivariant formality of isotropic torus actions

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus. We then classify all pairs $(G,S)$ such that $G$ is compact connected Lie and the embedded circular subgroup $S$ acts equivariantly formally on $G/S$. In the process we provide what seems to be the first published proof of the structure (known to Leray and Koszul) of the cohomology rings $H^*(G/S;\mathbb Q)$.Comment: Completely revised. Many proofs simplified, including reduction to toral isotropy and classification of reflected circles. An error in the reduction to the semisimple case is corrected. New: a reduction to the compact case; partial reductions if the groups are disconnected or compact but not Lie. Citations to literature improved. To be published in the Journal of Homotopy and Related Structure

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

Orbitally Excited Baryons in Large N_c QCD

We present a model-independent analysis of the mass spectrum of nonstrange l=1 baryons in large N_c QCD. The 1/N_c expansion is used to select and order a basis of effective operators that spans the nine observables (seven masses and two mixing angles). Comparison to the data provides support for the validity of the 1/N_c expansion, but also reveals that only a few nontrivial operators are strongly preferred. We show that our results have a consistent interpretation in a constituent quark model with pseudoscalar meson exchange interactions.Comment: 4 pages LaTeX. Invited parallel session talk presented at the XVth Particles and Nuclei International Conference (PANIC99), June 10, 1999, Uppsala, Swede

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

Equivariant formality of istropy actions

Let $G$ be a compact connected Lie group and $K$ a connected Lie subgroup. In this paper, we collect an assortment of results on equivariant formality of the isotropy action of $K$ on $G/K$ and thus improving those from previous work. We show that if the isotropy action of $K$ on $G/K$ is equivariantly formal, then $G/K$ is formal in the sense of rational homotopy theory. This enables us to strengthen Shiga-Takahashi's theorem to a cohomological characterization of equivariant formality of isotropy actions. Using an analogue of equivariant formality in $K$-theory introduced by the second author and shown to be equivalent to equivariant formality in the usual sense, we provide a representation theoretic characterization of equivariant formality of isotropy actions, and give a new, uniform proof of equivariant formality for previously known examples of homogeneous spaces.Comment: Accepted by Journal of the London Mathematical Society. Slightly different from the journal version in terms of formatting and wording. 26 page

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 $(\pi,\pi)$ 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

The Borel equivariant cohomology of real Grassmannians

Recent work of Chen He has determined through GKM methods the Borel equivariant cohomology with rational coefficients of the isotropy action on a real Grassmannian and an real oriented Grassmannian through GKM methods. In this expository note, we propound a less involved approach, due essentially to Vitali Kapovitch, to computing equivariant cohomology rings $H^*_K(G/H)$ for $G,K,H$ connected Lie groups, and apply it to recover the equivariant cohomology of the Grassmannians. The bulk is setup and commentary; once one believes in the model, the proof itself is under a page.Comment: 10-page expository note. Comments welcom