Direct reconstruction of dark energy

An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With so few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy parameter space. We present a new non-parametric method which can accurately reconstruct a wide variety of dark energy behaviour with no prior assumptions about it. It is simple, quick and relatively accurate, and involves no expensive explorations of parameter space. The technique uses principal component analysis and a combination of information criteria to identify real features in the data, and tailors the fitting functions to pick up trends and smooth over noise. We find that we can constrain a large variety of w(z) models to within 10-20 % at redshifts z<1 using just SNAP-quality data.Comment: 5 pages, 4 figures. v2 has added refs plus minor changes. To appear in PR

Soliton Solutions to the Einstein Equations in Five Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS$_{5}/\Gamma$, but have less energy than AdS$_{5}/\Gamma$. We present evidence that these solutions are the lowest-energy states within their asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title changed by journal from original title "Eguchi-Hanson Solitons

New Reducible Five-brane Solutions in M-theory

We construct new M-theory solutions of M5 branes that are a realization of the fully localized ten dimensional NS5/D6 and NS5/D5 brane intersections. These solutions are obtained by embedding self-dual geometries lifted to M-theory. We reduce these solutions down to ten dimensions, obtaining new D-brane systems in type IIA/IIB supergravity. The worldvolume theories of the NS5-branes are new non-local, non-gravitational, six dimensional, T-dual little string theories with eight supersymmetries.Comment: 19 pages, 4 figures, two paragraphs added in conclusions, typos correcte

The cosmological gravitational wave background from primordial density perturbations

We discuss the gravitational wave background generated by primordial density perturbations evolving during the radiation era. At second-order in a perturbative expansion, density fluctuations produce gravitational waves. We calculate the power spectra of gravitational waves from this mechanism, and show that, in principle, future gravitational wave detectors could be used to constrain the primordial power spectrum on scales vastly different from those currently being probed by large-scale structure. As examples we compute the gravitational wave background generated by both a power-law spectrum on all scales, and a delta-function power spectrum on a single scale.Comment: 8 Page

Eguchi-Hanson Solitons in Odd Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.Comment: 26 pages, Late

Randomized Extended Kaczmarz for Solving Least-Squares

We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by Strohmer and Vershynin.Comment: 19 Pages, 5 figures; code is available at https://github.com/zouzias/RE

Subsonic high-angle-of-attack aerodynamic characteristics of a cone and cylinder with triangular cross sections and a cone with a square cross section

Experiments were conducted in the 12-Foot Pressure Wind Tunnel at Ames Research Center on three models with noncircular cross sections: a cone having a square cross section with rounded corners and a cone and cylinder with triangular cross sections and rounded vertices. The cones were tested with both sharp and blunt noses. Surface pressures and force and moment measurements were obtained over an angle of attack range from 30 deg to 90 deg and selected oil-flow experiments were conducted to visualize surface flow patterns. Unit Reynolds numbers ranged from 0.8x1,000,000/m to 13.0x1,000,000/m at a Mach number of 0.25, except for a few low-Reynolds-number runs at a Mach number of 0.17. Pressure data, as well as force data and oil-flow photographs, reveal that the three dimensional flow structure at angles of attack up to 75 deg is very complex and is highly dependent on nose bluntness and Reynolds number. For angles of attack from 75 deg to 90 deg the sectional aerodynamic characteristics are similar to those of a two dimensional cylinder with the same cross section