Piezoelectric-based apparatus for strain tuning

We report the design and construction of piezoelectric-based apparatus for applying continuously tuneable compressive and tensile strains to test samples. It can be used across a wide temperature range, including cryogenic temperatures. The achievable strain is large, so far up to 0.23% at cryogenic temperatures. The apparatus is compact and compatible with a wide variety of experimental probes. In addition, we present a method for mounting high-aspect-ratio samples in order to achieve high strain homogeneity.Comment: 8 pages, 8 figure

On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasi-normal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multi-mode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black hole spin and the energy emitted in each mode, will affect our ability to do black hole spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in press in Phys. Rev.

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies. In particular we determine the effects of radiation-reaction coupled to spin-orbit effects on the two-body equations of motion, and on the evolution of the spins. For a suitable definition of spin, we reproduce the standard equations of motion and spin-precession at the first post-Newtonian order. At 3.5PN order, we determine the spin-orbit induced reaction effects on the orbital motion, but we find that radiation damping has no effect on either the magnitude or the direction of the spins. Using the equations of motion, we find that the loss of total energy and total angular momentum induced by spin-orbit effects precisely balances the radiative flux of those quantities calculated by Kidder et al. The equations of motion may be useful for evolving inspiraling orbits of compact spinning binaries.Comment: 19 pages, small corrections, equivalent to published versio

Covers of acts over monoids II

In 1981 Edgar Enochs conjectured that every module has a flat cover and finally proved this in 2001. Since then a great deal of effort has been spent on studying different types of covers, for example injective and torsion free covers. In 2008, Mahmoudi and Renshaw initiated the study of flat covers of acts over monoids but their definition of cover was slightly different from that of Enochs. Recently, Bailey and Renshaw produced some preliminary results on the `other' type of cover and it is this work that is extended in this paper. We consider free, divisible, torsion free and injective covers and demonstrate that in some cases the results are quite different from the module case

Amplitudes and Spinor-Helicity in Six Dimensions

The spinor-helicity formalism has become an invaluable tool for understanding the S-matrix of massless particles in four dimensions. In this paper we construct a spinor-helicity formalism in six dimensions, and apply it to derive compact expressions for the three, four and five point tree amplitudes of Yang-Mills theory. Using the KLT relations, it is a straightforward process to obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we demonstrate this by writing down the gravitational three and four point amplitudes. Because there is no conserved helicity in six dimensions, these amplitudes describe the scattering of all possible polarization states (as well as Kaluza-Klein excitations) in four dimensions upon dimensional reduction. We also briefly discuss a convenient formulation of the BCFW recursion relations in higher dimensions.Comment: 26 pages, 2 figures. Minor improvements of the discussio

Higgs Mass from D-Terms: a Litmus Test

We explore supersymmetric theories in which the Higgs mass is boosted by the non-decoupling D-terms of an extended $U(1)_X$ gauge symmetry, defined here to be a general linear combination of hypercharge, baryon number, and lepton number. Crucially, the gauge coupling, $g_X$, is bounded from below to accommodate the Higgs mass, while the quarks and leptons are required by gauge invariance to carry non-zero charge under $U(1)_X$. This induces an irreducible rate, $\sigma$BR, for $pp \rightarrow X \rightarrow \ell\ell$ relevant to existing and future resonance searches, and gives rise to higher dimension operators that are stringently constrained by precision electroweak measurements. Combined, these bounds define a maximally allowed region in the space of observables, ($\sigma$BR, $m_X$), outside of which is excluded by naturalness and experimental limits. If natural supersymmetry utilizes non-decoupling D-terms, then the associated $X$ boson can only be observed within this window, providing a model independent `litmus test' for this broad class of scenarios at the LHC. Comparing limits, we find that current LHC results only exclude regions in parameter space which were already disfavored by precision electroweak data.Comment: 7 pages, 9 figure