Toward a better understanding of helicopter stability derivatives

An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the unsable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation

Abelian homotopy Dijkgraaf-Witten theory

We construct a version of Dijkgraaf-Witten theory based on a compact abelian Lie group within the formalism of Turaev's homotopy quantum field theory. As an application we show that the 2+1-dimensional theory based on U(1) classifies lens spaces up to homotopy type.Comment: 23 pages, 1 figur

Why does the Jeans Swindle work?

When measuring the mass profile of any given cosmological structure through internal kinematics, the distant background density is always ignored. This trick is often refereed to as the "Jeans Swindle". Without this trick a divergent term from the background density renders the mass profile undefined, however, this trick has no formal justification. We show that when one includes the expansion of the Universe in the Jeans equation, a term appears which exactly cancels the divergent term from the background. We thereby establish a formal justification for using the Jeans Swindle.Comment: 5 pages, 2 figures, Accepted for publication in MNRAS Letter

Multiple-channel generalization of Lellouch-Luscher formula

We generalize the Lellouch-Luscher formula, relating weak matrix elements in finite and infinite volumes, to the case of multiple strongly-coupled decay channels into two scalar particles. This is a necessary first step on the way to a lattice QCD calculation of weak decay rates for processes such as D -> pi pi and D -> KK. We also present a field theoretic derivation of the generalization of Luscher's finite volume quantization condition to multiple two-particle channels. We give fully explicit results for the case of two channels, including a form of the generalized Lellouch-Luscher formula expressed in terms of derivatives of the energies of finite volume states with respect to the box size. Our results hold for arbitrary total momentum and for degenerate or non-degenerate particles.Comment: 16 pages, 2 figures. v3: Added references, clarified relation to and corrected comments about previous work, and minor stylistic improvements. v4: Minor clarifications added, typos fixed, references updated---matches published versio

The need for a second black hole at the Galactic center

Deep infra-red observations and long-term monitoring programs have provided dynamical evidence for a supermassive black hole of mass 3.e6 solar masses associated with the radio source Sagitarrius A* at the center of our Galaxy. The brightest stars orbiting within 0.1 parsecs of the black hole appear to be young, massive main sequence stars, n spite of an environment near the black hole that is hostile to star formation. We discuss mechanisms by which stars born outside the central parsec can sink towards the black hole and conclude that the drag coming from plausible stellar populations does not operate on the short timescales required by the stellar ages. We propose that these stars were dragged in by a second black hole of mass of 1.e3-1.e4 solar masses, which would be classified as an intermediate-mass black hole. We discuss the implications for the stellar populations and the kinematics in the Galactic center. Finally we note that continued astrometric monitoring of the central radio source offers the prospect for a direct detection of such objects.Comment: 5 pages, 2 postscript figures, submitted to ApJ letters The introduction section has been updated since submission to Ap