Framed vertex operator algebras, codes and the moonshine module

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1/2 are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.Comment: Latex, 54 page

Final report on PCRV thermal cylinder axial tendon failures

The post-test examination of the failed tendons from the PCRV thermal cylinder experiment has been concluded. Failures in the wires are attributed to stress-corrosion cracking. The cause of tendon failures has not been unequivocably established, but they may have been due to nitrates in the duct. The wires employed in the manufacture of the tendons will crack in less than 72 hr in a 0.2 M solution of ammonium nitrate at 70$sup 0$C. The quality of the wires is poor, and surface cracks were detected. These could have acted as concentrating sites for both stress and the deleterious contaminants. It is believed that the factors that led to the failures in the thermal cylinder experiment were unique. An improper formulation of the epoxy resin did not provide the tendon anchor plate seal that was desired; indeed, the improper formulation is responsible for the high level of nitrogen in the ducts of the failed tendons. (auth

Brownian motion exhibiting absolute negative mobility

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility).Comment: 4 pages, 3 figures, to be published in PR

Global cost and weight evaluation of fuselage keel design concepts

The Boeing program entitled Advanced Technology Composite Aircraft Structure (ATCAS) is focused on the application of affordable composite technology to pressurized fuselage structure of future aircraft. As part of this effort, a design study was conducted on the keel section of the aft fuselage. A design build team (DBT) approach was used to identify and evaluate several design concepts which incorporated different material systems, fabrication processes, structural configurations, and subassembly details. The design concepts were developed in sufficient detail to accurately assess their potential for cost and weight savings as compared with a metal baseline representing current wide body technology. The cost and weight results, along with an appraisal of performance and producibility risks, are used to identify a globally optimized keel design; one which offers the most promising cost and weight advantages over metal construction. Lastly, an assessment is given of the potential for further cost and weight reductions of the selected keel design during local optimization

G(2) quivers

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered

On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine

We consider the relationship between the conjectured uniqueness of the Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible $Z_n$ meromorphic orbifold constructions of ${\cal V}^\natural$ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster group $M$ together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give ${\cal V}^\natural$ itself or the Leech theory. This constraint on the meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0

The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys

The collisionless accretion shock at the outer boundary of a galaxy cluster should primarily heat the ions instead of electrons since they carry most of the kinetic energy of the infalling gas. Near the accretion shock, the density of the intracluster medium is very low and the Coulomb collisional timescale is longer than the accretion timescale. Electrons and ions may not achieve equipartition in these regions. Numerical simulations have shown that the Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can be biased if non-equipartition effects are not properly taken into account. Using a set of hydrodynamical simulations, we have calculated three potential systematic biases in the Y-mass relations introduced by non-equipartition effects during the cross-calibration or self-calibration when using the galaxy cluster abundance technique to constraint cosmological parameters. We then use a semi-analytic technique to estimate the non-equipartition effects on the distribution functions of Y (Y functions) determined from the extended Press-Schechter theory. Depending on the calibration method, we find that non-equipartition effects can induce systematic biases on the Y functions, and the values of the cosmological parameters Omega_8, sigma_8, and the dark energy equation of state parameter w can be biased by a few percent. In particular, non-equipartition effects can introduce an apparent evolution in w of a few percent in all of the systematic cases we considered. Techniques are suggested to take into account the non-equipartition effect empirically when using the cluster abundance technique to study precision cosmology. We conclude that systematic uncertainties in the Y-mass relation of even a few percent can introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical Journal, abstract abridged slightly. Typos corrected in version

Advanced Technology Composite Fuselage - Repair and Damage Assessment Supporting Maintenance

Under the NASA-sponsored contracts for Advanced Technology Composite Aircraft Structures (ATCAS) and Materials Development Omnibus Contract (MDOC), Boeing is studying the technologies associated with the application of composite materials to commercial transport fuselage structure. Included in the study is the incorporation of maintainability and repairability requirements of composite primary structure into the design. This contractor report describes activities performed to address maintenance issues in composite fuselage applications. A key aspect of the study was the development of a maintenance philosophy which included consideration of maintenance issues early in the design cycle, multiple repair options, and airline participation in design trades. Fuselage design evaluations considered trade-offs between structural weight, damage resistance/tolerance (repair frequency), and inspection burdens. Analysis methods were developed to assess structural residual strength in the presence of damage, and to evaluate repair design concepts. Repair designs were created with a focus on mechanically fastened concepts for skin/stringer structure and bonded concepts for sandwich structure. Both a large crown (skintstringer) and keel (sandwich) panel were repaired. A compression test of the keel panel indicated the demonstrated repairs recovered ultimate load capability. In conjunction with the design and manufacturing developments, inspection methods were investigated for their potential to evaluate damaged structure and verify the integrity of completed repairs

A series of algebras generalizing the octonions and Hurwitz-Radon identity

International audienceWe study non-associative twisted group algebras over (ℤ2)n with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of quaternions. We study their properties, give several equivalent definitions and prove their uniqueness within some natural assumptions. We then prove a simplicity criterion. We present two applications of the constructed algebras and the developed technique. The first application is a simple explicit formula for the following famous square identity: (a21+⋯+a2N)(b21+⋯+b2ρ(N))=c21+⋯+c2N , where c k are bilinear functions of the a i and b j and where ρ(N) is the Hurwitz-Radon function. The second application is the relation to Moufang loops and, in particular, to the code loops. To illustrate this relation, we provide an explicit coordinate formula for the factor set of the Parker loop