Matrix Transfer Function Design for Flexible Structures: An Application

The application of matrix transfer function design techniques to the problem of disturbance rejection on a flexible space structure is demonstrated. The design approach is based on parameterizing a class of stabilizing compensators for the plant and formulating the design specifications as a constrained minimization problem in terms of these parameters. The solution yields a matrix transfer function representation of the compensator. A state space realization of the compensator is constructed to investigate performance and stability on the nominal and perturbed models. The application is made to the ACOSSA (Active Control of Space Structures) optical structure

A Superfield for Every Dash-Chromotopology

The recent classification scheme of so-called adinkraic off-shell supermultiplets of N-extended worldline supersymmetry without central charges finds a combinatorial explosion. Completing our earlier efforts, we now complete the constructive proof that all of these trillions or more of supermultiplets have a superfield representation. While different as superfields and supermultiplets, these are still super-differentially related to a much more modest number of minimal supermultiplets, which we construct herein.Comment: 13 pages, integrated illustration

New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields

A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting the Weyl tensor to type D produces a set of equations which can be solved, and a range of new techniques are introduced to simplify the problem. Imposing the further condition that the solution is asymptotically flat yields the Kerr solution uniquely. The implications of this result for the no-hair theorem are discussed. The techniques developed here have many other applications, which are described in the conclusions.Comment: 30 pages, no figure

Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry

A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.Comment: 13 Figure

Early Dark Energy Cosmologies

We propose a novel parameterization of the dark energy density. It is particularly well suited to describe a non-negligible contribution of dark energy at early times and contains only three parameters, which are all physically meaningful: the fractional dark energy density today, the equation of state today and the fractional dark energy density at early times. As we parameterize Omega_d(a) directly instead of the equation of state, we can give analytic expressions for the Hubble parameter, the conformal horizon today and at last scattering, the sound horizon at last scattering, the acoustic scale as well as the luminosity distance. For an equation of state today w_0 < -1, our model crosses the cosmological constant boundary. We perform numerical studies to constrain the parameters of our model by using Cosmic Microwave Background, Large Scale Structure and Supernovae Ia data. At 95% confidence, we find that the fractional dark energy density at early times Omega_early < 0.06. This bound tightens considerably to Omega_early < 0.04 when the latest Boomerang data is included. We find that both the gold sample of Riess et. al. and the SNLS data by Astier et. al. when combined with CMB and LSS data mildly prefer w_0 < -1, but are well compatible with a cosmological constant.Comment: 6 pages, 3 figures; references added, matches published versio

Energetic and Environmental Constraints on the Community Structure of Benthic Microbial Mats in Lake Fryxell, Antarctica.

Ecological communities are regulated by the flow of energy through environments. Energy flow is typically limited by access to photosynthetically active radiation (PAR) and oxygen concentration (O2). The microbial mats growing on the bottom of Lake Fryxell, Antarctica, have well-defined environmental gradients in PAR and (O2). We analyzed the metagenomes of layers from these microbial mats to test the extent to which access to oxygen and light controls community structure. We found variation in the diversity and relative abundances of Archaea, Bacteria and Eukaryotes across three (O2) and PAR conditions: high (O2) and maximum PAR, variable (O2) with lower maximum PAR, and low (O2) and maximum PAR. We found distinct communities structured by the optimization of energy use on a millimeter-scale across these conditions. In mat layers where (O2) was saturated, PAR structured the community. In contrast, (O2) positively correlated with diversity and affected the distribution of dominant populations across the three habitats, suggesting that meter-scale diversity is structured by energy availability. Microbial communities changed across covarying gradients of PAR and (O2). The comprehensive metagenomic analysis suggests that the benthic microbial communities in Lake Fryxell are structured by energy flow across both meter- and millimeter-scales

Quadratic Lagrangians and Topology in Gauge Theory Gravity

We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals contribute to the classical field equations. An identity is found for the invariants that is valid for non-symmetric Riemann tensors, generalizing the usual GR expression for the topological invariants. The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten independent quadratic terms are constructed from the Riemann tensor, and the topological invariants reduce these to eight possible independent terms for a quadratic Lagrangian. The resulting field equations for the parity non-violating terms are presented. Our derivations of these results are considerably simpler that those found in the literature