Tamagawa Numbers for Motives with (Non-Commutative) Coefficients

Let $M$ be a motive which is defined over a number field and admits an action of a finite dimensional semisimple \bq-algebra $A$. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at $0$ of the $A$-equivariant $L$-function of $M$. This conjecture simultaneously generalizes and refines the Tamagawa number conjecture of Bloch, Kato, Fontaine, Perrin-Riou et al. and also the central conjectures of classical Galois module theory as developed by Fröhlich, Chinburg, M. Taylor et al. The precise formulation of our conjecture depends upon the choice of an order \A in $A$ for which there exists a `projective \A-structure' on $M$. The existence of such a structure is guaranteed if \A is a maximal order, and also occurs in many natural examples where \A is non-maximal. In each such case the conjecture with respect to a non-maximal order refines the conjecture with respect to a maximal order. We develop a theory of determinant functors for all orders in $A$ by making use of the category of virtual objects introduced by Deligne

Contemporary Seismicity in and Around the Yakima Fold-and-Thrust Belt in Eastern Washington

We examined characteristics of routinely cataloged seismicity from 1970 to the present in and around the Yakima fold-and-thrust belt (YFTB) in eastern Washington to determine if the characteristics of contemporary seismicity provide clues about regional-scale active tectonics or about more localized, near-surface processes. We employed new structural and hydrologic models of the Columbia River basalts (CRB) and found that one-third to one-half of the cataloged earthquakes occur within the CRB and that these CRB earthquakes exhibit significantly more clustered, and swarmlike, behavior than those outside. These results and inferences from published studies led us to hypothesize that clustered seismicity is likely associated with hydrologic changes in the CRB, which hosts the regional aquifer system. While some general features of the regional groundwater system support this hypothesis, seismicity patterns and mapped long-term changes in groundwater levels and present-day irrigation neither support nor refute it. Regional tectonic processes and crustal-scale structures likely influence the distribution of earthquakes both outside and within the CRB as well. We based this inference on qualitatively assessed alignments between the dominant northwest trends in the geologic structure and the seismicity generally and between specific faults and characteristics of the 2009 Wooded Island swarm and aseismic slip, which is the only cluster studied in detail and the most vigorous since regional monitoring began.USGS-NAGTGeological Science

Cluster Winds Blow along Supercluster Axes

Within Abell galaxy clusters containing wide-angle tailed radio sources, there is evidence of a ``prevailing wind'' which directs the WAT jets. We study the alignment of WAT jets and nearby clusters to test the idea that this wind may be a fossil of drainage along large-scale supercluster axes. We also test this idea with a study of the alignment of WAT jets and supercluster axes. Statistical test neighbours indicate no alignment of WAT jets towards nearest clusters, but do indicate approximately 98% confidence in alignment with the long axis of the supercluster in which the cluster lies. We find a preferred scale for such superclusters of order 25 Mpc $h^{-1}$.Comment: Latex, 5 pages, with 5 postscript figures. To be published in MNRAS. Slight revisions to coincide with journal text. Linked to color image at http://kusmos.phsx.ukans.edu/~melott/images/A2634SUW.jp

Noise reduction tests of large-scale-model externally blown flap using trailing-edge blowing and partial flap slot covering

Noise data were obtained with a large-scale cold-flow model of a two-flap, under-the-wing, externally blown flap proposed for use on future STOL aircraft. The noise suppression effectiveness of locating a slot conical nozzle at the trailing edge of the second flap and of applying partial covers to the slots between the wing and flaps was evaluated. Overall-sound-pressure-level reductions of 5 db occurred below the wing in the flyover plane. Existing models of several noise sources were applied to the test results. The resulting analytical relation compares favorably with the test data. The noise source mechanisms were analyzed and are discussed

Effects of perforated flap surfaces and screens on acoustics of a large externally blown flap model

Various model geometries and combinations of perforated flap surfaces and screens mounted close to the flap surfaces were studied for application to jet-flap noise attenuation for externally blown flap, under-the-wing aircraft. The efforts to reduce jet-flap interaction noise were marginally successful. Maximum attenuations of less than 4 db in overall sound pressure level were obtained in the flyover plane. Noise reductions obtained in the low-to-middle-frequency ranges (up to 7 db) were generally offset by large increases in high-frequency noise (up to 20 db)

Optical binding mechanisms: a conceptual model for Gaussian beam traps

Optical binding interactions between laser-trapped spherical microparticles are familiar in a wide range of trapping configurations. Recently it has been demonstrated that these experiments can be accurately modeled using Mie scattering or coupled dipole models. This can help confirm the physical phenomena underlying the inter-particle interactions, but does not necessarily develop a conceptual understanding of the effects that can lead to future predictions. Here we interpret results from a Mie scattering model to obtain a physical description which predict the behavior and trends for chains of trapped particles in Gaussian beam traps. In particular, it describes the non-uniform particle spacing and how it changes with the number of particles. We go further than simply \emph{demonstrating} agreement, by showing that the mechanisms ``hidden'' within a mathematically and computationally demanding Mie scattering description can be explained in easily-understood terms.Comment: Preprint of manuscript submitted to Optics Expres

On equivariant characteristic ideals of real classes

Let $p$ be an odd prime, $F/{\Bbb Q}$ an abelian totally real number field, $F_\infty/F$ its cyclotomic ${\Bbb Z}_p$-extension, $G_\infty = Gal (F_\infty / {\Bbb Q}),$ ${\Bbb A} = {\Bbb Z}_p [[G_\infty]].$ We give an explicit description of the equivariant characteristic ideal of $H^2_{Iw} (F_\infty, {\Bbb Z}_p(m))$ over ${\Bbb A}$ for all odd $m \in {\Bbb Z}$ by applying M. Witte's formulation of an equivariant main conjecture (or "limit theorem") due to Burns and Greither. This could shed some light on Greenberg's conjecture on the vanishing of the $\lambda$-invariant of $F_\infty/F.