Model-Independent Plotting of the Cosmological Scale Factor As a Function of Lookback Time

In this work we describe a model-independent method of developing a plot of scale factor a(t) versus lookback time tL from the usual Hubble diagram of modulus data against redshift. This is the first plot of this type. We follow the model-independent methodology of Daly & Djorgovski used for their radio-galaxy data. Once the a(t)data plot is completed, any model can be applied and will display as described in the standard literature. We then compile an extensive data set to z = 1.8 by combining Type Ia supernovae (SNe Ia) data from SNLS3 of Conley et al., high-z SNe data of Riess et al., and radio-galaxy data of Daly & Djorgovski to validate the new plot. We first display these data on a standard Hubble diagram to confirm the best fit for ΛCDM cosmology, and thus validate the joined data set. The scale factor plot is then developed from the data and the ΛCDM model is again displayed from a least-squares fit. The fit parameters are in agreement with the Hubble diagram fit confirming the validity of the new plot. Of special interest is the transition time of the universe, which in the scale factor plot will appear as an inflection point in the data set. Noise is more visible in this presentation, which is particularly sensitive to inflection points of any model displayed in the plot, unlike on a modulus-z diagram, where there are no inflection points and the transition-z is not at all obvious by inspection. We obtain a lower limit of z ⩾ 0.6. It is evident from this presentation that there is a dearth of SNe data in the range z = 1–2, exactly the range necessary to confirm a ΛCDM transition-z around z = 0.76. We then compare a toy model wherein dark matter is represented as a perfect fluid with an equation of state p = −(1/3) ρ to demonstrate the plot sensitivity to model choice. Its density varies as 1/t2 and it enters the Friedmann equations as Ωdark/t2, replacing only the Ωdark/a3 term. The toy model is a close match to ΛCDM, but separates from it on the scale factor plot for similar ΛCDM density parameters. It is described in the Appendix. A more complete transition time analysis will be presented in a future paper

Two transducer formula for more precise determination of ultrasonic phase velocity from standing wave measurements

A two transducer correction formula valid for both solid and liquid specimens is presented. Using computer simulations of velocity measurements, the accuracy and range of validity of the results are discussed and are compared with previous approximations

Model-Independent Plotting of the Cosmological Scale Factor As a Function of Lookback Time

In this work we describe a model-independent method of developing a plot of scale factor a(t) versus lookback time tL from the usual Hubble diagram of modulus data against redshift. This is the first plot of this type. We follow the model-independent methodology of Daly & Djorgovski used for their radio-galaxy data. Once the a(t)data plot is completed, any model can be applied and will display as described in the standard literature. We then compile an extensive data set to z = 1.8 by combining Type Ia supernovae (SNe Ia) data from SNLS3 of Conley et al., high-z SNe data of Riess et al., and radio-galaxy data of Daly & Djorgovski to validate the new plot. We first display these data on a standard Hubble diagram to confirm the best fit for ΛCDM cosmology, and thus validate the joined data set. The scale factor plot is then developed from the data and the ΛCDM model is again displayed from a least-squares fit. The fit parameters are in agreement with the Hubble diagram fit confirming the validity of the new plot. Of special interest is the transition time of the universe, which in the scale factor plot will appear as an inflection point in the data set. Noise is more visible in this presentation, which is particularly sensitive to inflection points of any model displayed in the plot, unlike on a modulus-z diagram, where there are no inflection points and the transition-z is not at all obvious by inspection. We obtain a lower limit of z ⩾ 0.6. It is evident from this presentation that there is a dearth of SNe data in the range z = 1–2, exactly the range necessary to confirm a ΛCDM transition-z around z = 0.76. We then compare a toy model wherein dark matter is represented as a perfect fluid with an equation of state p = −(1/3) ρ to demonstrate the plot sensitivity to model choice. Its density varies as 1/t2 and it enters the Friedmann equations as Ωdark/t2, replacing only the Ωdark/a3 term. The toy model is a close match to ΛCDM, but separates from it on the scale factor plot for similar ΛCDM density parameters. It is described in the Appendix. A more complete transition time analysis will be presented in a future paper

Towards a Flat-Bottom Hole Standard for Thermal Imaging

Transient thermal imaging has not as yet found a niche among industrial NDE methodologies even though the field has been active since the mid 1980’s. Difficulty with image interpretation is perhaps the primary reason. An ambiguous image leads to false calls and lack of confidence. Ultrasonics, on the other hand appears not to generally suffer from these issues for a simple reason — the term “flat-bottom hole” (FBH) is second nature in the field. Such standards encourage quantitative imaging. The present work provides a deeper insight into certain invariances in 1-D and 2-D heat flow that permit the use of flatbottom hole standards to quantify thermal imaging yielding reproducible and interpretable images of flaws. The very simple theoretical basis for these effects will be described with emphasis placed on the thermal images obtained and the accuracy of the quantitative results. We describe recent work both at GE-CRD and UTRC in the area of thermal standards evaluation

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

A cyclic universe with colour fields

The topology of the universe is discussed in relation to the singularity problem. We explore the possibility that the initial state of the universe might have had a structure with 3-Klein bottle topology, which would lead to a model of a nonsingular oscillating (cyclic) universe with a well-defined boundary condition. The same topology is assumed to be intrinsic to the nature of the hypothetical primitive constituents of matter (usually called preons) giving rise to the observed variety of elementary particles. Some phenomenological implications of this approach are also discussed.Comment: 21 pages, 9 figures; v.4: final versio

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Observation of Discrete Oscillations In a Model-Independent Plot of Cosmological Scale Factor Versus Lookback Time and Scalar Field Model

We have observed damped longitudinal cosmological-scale oscillations in a unique model-independent plot of scale factor against lookback time for Type Ia supernovae data. We found several first-derivative relative maxima/minima spanning the range of reported transition redshifts. These extrema comprise two full cycles with a period of approximately 0.15 Hubble times (H0=68 km s−1 Mpc−1). This period corresponds to a fundamental frequency of approximately seven cycles over the Hubble time. Transition-z values quoted in the literature generally fall near these minima and may explain the reported wide spread up to the predicted ΛCDM value of approximately z = 0.77. We also observe second and third harmonics of the fundamental. The scale factor data is analyzed several different ways, including smoothing, Fourier transform, and autocorrelation. We propose a cosmological scalar field harmonic oscillator model for the observation. On this timescale, for a quantum scalar field, the scalar field mass is extraordinarily small at 3 × 10-32 eV. Our scalar field density parameter precisely replaces the ΛCDM dark matter density parameter in the Friedmann equations, resulting in essentially identical data fits, and its present value matches the Planck value. Thus the wave is fundamentally a dark matter wave. We therefore posit that this scalar field manifests itself as the dark matter