Monotone Volume Formulas for Geometric Flows

We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latter being non-decreasing along the flow. In the case where S=Ric is the Ricci curvature of M, the result corresponds to Perelman's well-known reduced volume monotonicity for the Ricci flow. Some other examples are given in the second section of this article, the main examples and motivation for this work being List's extended Ricci flow system, the Ricci flow coupled with harmonic map heat flow and the mean curvature flow in Lorentzian manifolds with nonnegative sectional curvatures. With our approach, we find new monotonicity formulas for these flows.Comment: v2: final version (as published

Top down, bottom up structured programming and program structuring

New design and programming techniques for shuttle software. Based on previous Apollo experience, recommendations are made to apply top-down structured programming techniques to shuttle software. New software verification techniques for large software systems are recommended. HAL, the higher order language selected for the shuttle flight code, is discussed and found to be adequate for implementing these techniques. Recommendations are made to apply the workable combination of top-down, bottom-up methods in the management of shuttle software. Program structuring is discussed relevant to both programming and management techniques

Spherical Redshift Distortions

Peculiar velocities induce apparent line of sight displacements of galaxies in redshift space, distorting the pattern of clustering in the radial versus transverse directions. On large scales, the amplitude of the distortion yields a measure of the dimensionless linear growth rate $\beta \approx \Omega^{0.6}/b$, where $\Omega$ is the cosmological density and $b$ the linear bias factor. To make the maximum statistical use of the data in a wide angle redshift survey, and for the greatest accuracy, the spherical character of the distortion needs to be treated properly, rather than in the simpler plane parallel approximation. In the linear regime, the redshift space correlation function is described by a spherical distortion operator acting on the true correlation function. It is pointed out here that there exists an operator, which is essentially the logarithmic derivative with respect to pair separation, which both commutes with the spherical distortion operator, and at the same time defines a characteristic scale of separation. The correlation function can be expanded in eigenfunctions of this operator, and these eigenfunctions are eigenfunctions of the distortion operator. Ratios of the observed amplitudes of the eigenfunctions yield measures of the linear growth rate $\beta$ in a manner independent of the shape of the correlation function. More generally, the logarithmic derivative $\partial/\partial\ln r$ with respect to depth $r$, along with the square $L^2$ and component $L_z$ of the angular momentum operator, form a complete set of commuting operators for the spherical distortion operator acting on the density. The eigenfunctions of this complete set of operators are spherical waves about the observer, with radial part lying in logarithmic real or Fourier space.Comment: 15 pages, with 1 embedded EPS figur

The interior structure of rotating black holes 1. Concise derivation

This paper presents a concise derivation of a new set of solutions for the interior structure of accreting, rotating black holes. The solutions are conformally stationary, axisymmetric, and conformally separable. Hyper-relativistic counter-streaming between freely-falling collisionless ingoing and outgoing streams leads to mass inflation at the inner horizon, followed by collapse. The solutions fail at an exponentially tiny radius, where the rotational motion of the streams becomes comparable to their radial motion. The papers provide a fully nonlinear, dynamical solution for the interior structure of a rotating black hole from just above the inner horizon inward, down to a tiny scale.Comment: Version 1: 8 pages, 3 figures. Version 2: Extensively revised to emphasize the derivation of the solution rather than the solution itself. 11 pages, 4 figures. Version 3: Minor changes to match published version. Mathematica notebook available at http://jila.colorado.edu/~ajsh/rotatinginflationary/rotatinginflationary.n

The power spectrum of galaxies in the 2dF 100k redshift survey

We compute the real-space power spectrum and the redshift-space distortions of galaxies in the 2dF 100k galaxy redshift survey using pseudo-Karhunen-Loeve eigenmodes and the stochastic bias formalism. Our results agree well with those published by the 2dFGRS team, and have the added advantage of producing easy-to-interpret uncorrelated minimum-variance measurements of the galaxy-galaxy, galaxy-velocity and velocity-velocity power spectra in 27 k-bands, with narrow and well-behaved window functions in the range 0.01h/Mpc < k < 0.8h/Mpc. We find no significant detection of baryonic wiggles, although our results are consistent with a standard flat Omega_Lambda=0.7 ``concordance'' model and previous tantalizing hints of baryonic oscillations. We measure the galaxy-matter correlation coefficient r > 0.4 and the redshift-distortion parameter beta=0.49+/-0.16 for r=1 (beta=0.47+/- 0.16 without finger-of-god compression). Since this is an apparent-magnitude limited sample, luminosity-dependent bias may cause a slight red-tilt in the power spectum. A battery of systematic error tests indicate that the survey is not only impressive in size, but also unusually clean, free of systematic errors at the level to which our tests are sensitive. Our measurements and window functions are available at http://www.hep.upenn.edu/~max/2df.html together with the survey mask, radial selection function and uniform subsample of the survey that we have constructed.Comment: Replaced to match accepted MNRAS version, with new radial/angular systematics plot and sigma8 typo corrected. High-res figures, power spectra, windows and our uniform galaxy subsample with mask at http://www.hep.upenn.edu/~max/2df.html or from [email protected]. 26 journal pages, 28 fig

Nonlinear Torsional Wave Beams

An evolution equation with cubic nonlinearity is presented for a torsional wave beam in an isotropic elastic solid. Analytical solutions are presented for the fundamental and third harmonic in the far field of a uniform circular source. Numerical results are presented for harmonic beam patterns at an intermediate distance between the near and far fields, and for a torsional waveform with shocks.Applied Research Laboratorie

How Does Wind Project Performance Change with Age in the United States?

Wind-plant performance declines with age, and the rate of decline varies between regions. The rate of performance decline is important when determining wind-plant financial viability and expected lifetime generation. We determine the rate of age-related performance decline in the United States wind fleet by evaluating generation records from 917 plants. We find the rate of performance decline to be 0.53%/year for older vintages of plants and 0.17%/year for newer vintages of plants on an energy basis for the first 10 years of operation, which is on the lower end of prior estimates in Europe. Unique to the United States, we find a significant drop in performance by 3.6% after 10 years, as plants lose eligibility for the production tax credit. Certain plant characteristics, such as the ratio of blade length to nameplate capacity, influence the rate of performance decline. These results indicate that the performance decline rate can be partially managed and influenced by policy

Quantum walk with a four-dimensional coin

We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is implemented using the internal states of the photon: the polarization and two of the orbital angular momentum states. We demonstrate how to implement this physically and what components would be needed. We then illustrate some of the results that could be obtained by performing the experiment

HST Images and Spectra of the Remnant of SN 1885 in M31

Near UV HST images of the remnant of SN 1885 (S And) in M31 show a 0"70 +- 0"05 diameter absorption disk silhouetted against M31's central bulge, at SN 1885's historically reported position. The disk's size corresponds to a linear diameter of 2.5 +- 0.4 pc at a distance of 725 +- 70 kpc, implying an average expansion velocity of 11000 +- 2000 km/s over 110 years. Low-dispersion FOS spectra over 3200-4800 A; reveal that the absorption arises principally from Ca II H & K (equivalent width ~215 A;) with weaker absorption features of Ca I 4227 A; and Fe I 3720 A;. The flux at Ca II line center indicates a foreground starlight fraction of 0.21, which places SNR 1885 some 64 pc to the near side of the midpoint of the M31 bulge, comparable to its projected 55 pc distance from the nucleus. The absorption line profiles suggest an approximately spherically symmetric, bell-shaped density distribution of supernova ejecta freely expanding at up to 13100 +- 1500 km/s. We estimate Ca I, Ca II, and Fe I masses of 2.9(+2.4,-0.6) x 10^-4 M_o, 0.005(+0.016,-0.002) M_o, and 0.013(+0.010,-0.005) M_o respectively. If the ionization state of iron is similar to the observed ionization state of calcium, M_CaII/M_CaI = 16(+42,-5), then the mass of Fe II is 0.21(+0.74,-0.08) M_o, consistent with that expected for either normal or subluminous SN Ia.Comment: 8 pages, including 4 embedded EPS figures, emulateapj.sty style file. Color image at http://casa.colorado.edu/~mcl/sand.shtml . Submitted to Ap

Gas Absorption in the KH 15D System: Further Evidence for Dust Settling in the Circumbinary Disk

Na I D lines in the spectrum of the young binary KH 15D have been analyzed in detail. We find an excess absorption component that may be attributed to foreground interstellar absorption, and to gas possibly associated with the solids in the circumbinary disk. The derived column density is log N_NaI = 12.5 cm^-2, centered on a radial velocity that is consistent with the systemic velocity. Subtracting the likely contribution of the ISM leaves log N_NaI ~ 12.3 cm^-2. There is no detectable change in the gas column density across the "knife edge" formed by the opaque grain disk, indicating that the gas and solids have very different scale heights, with the solids being highly settled. Our data support a picture of this circumbinary disk as being composed of a very thin particulate grain layer composed of millimeter-sized or larger objects that are settled within whatever remaining gas may be present. This phase of disk evolution has been hypothesized to exist as a prelude to the formation of planetesimals through gravitational fragmentation, and is expected to be short-lived if much gas were still present in such a disk. Our analysis also reveals the presence of excess Na I emission relative to the comparison spectrum at the radial velocity of the currently visible star that plausibly arises within the magnetosphere of this still-accreting young star.Comment: Accepted for publication in ApJ, 23 pages, 6 figure