Seismic Response of Pile Supported Structures

Earthquake loads are applied to the foundation mainly through shear waves in the underlying soil. A method is presented for analyzing the alteration in the response of a structure by adding piling to the foundation. The method of computation consists of a series of transfer matrices which are used to form a stiffness matrix of the foundation system. Central to the computation is the modelling mode for the soil-pile interaction; several alternatives are presented. Observations regarding the effect of several design parameters, based on a numerical example, are discussed

Computation of Displacement and Spin Gravitational Memory in Numerical Relativity

We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS Collaboration's $\texttt{SpEC}$ code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using $\texttt{SpECTRE}$'s version of a Cauchy-characteristic extraction. We find that we can accurately resolve the strain's traditional $m=0$ memory modes and some of the $m\not=0$ oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary's inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Lastly, we find that signal-to-noise ratios of memory for LIGO, the Einstein Telescope (ET), and the Laser Interferometer Space Antenna (LISA) with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or Minimal Waveform models.Comment: 20 pages, 11 figures; 10.1103/PhysRevD.102.104007. Corrected a minor sign error in Eqs. 27, 40, 42, 43, and 5

Computation of displacement and spin gravitational memory in numerical relativity

We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS (Simulating eXtreme Spacetimes) Collaboration’s SpEC code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using SpECTRE’s version of a Cauchy-characteristic extraction. We find that we can accurately resolve the strain’s traditional m=0 memory modes and some of the m≠0 oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary’s inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Last, we find that signal-to-noise ratios of memory for LIGO, the Einstein Telescope, and the Laser Interferometer Space Antenna with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or minimal waveform models

Ineffectiveness of Pad\'e resummation techniques in post-Newtonian approximations

We test the resummation techniques used in developing Pad\'e and Effective One Body (EOB) waveforms for gravitational wave detection. Convergence tests show that Pad\'e approximants of the gravitational wave energy flux do not accelerate the convergence of the standard Taylor approximants even in the test mass limit, and there is no reason why Pad\'e transformations should help in estimating parameters better in data analysis. Moreover, adding a pole to the flux seems unnecessary in the construction of these Pad\'e-approximated flux formulas. Pad\'e approximants may be useful in suggesting the form of fitting formulas. We compare a 15-orbit numerical waveform of the Caltech-Cornell group to the suggested Pad\'e waveforms of Damour et al. in the equal mass, nonspinning quasi-circular case. The comparison suggests that the Pad\'e waveforms do not agree better with the numerical waveform than the standard Taylor based waveforms. Based on this result, we design a simple EOB model by modifiying the ET EOB model of Buonanno et al., using the Taylor series of the flux with an unknown parameter at the fourth post-Newtonian order that we fit for. This simple EOB model generates a waveform having a phase difference of only 0.002 radians with the numerical waveform, much smaller than 0.04 radians the phase uncertainty in the numerical data itself. An EOB Hamiltonian can make use of a Pad\'e transformation in its construction, but this is the only place Pad\'e transformations seem useful.Comment: 13 pages, 7 figures. added some reference

Characterizing Signal Loss in the 21 cm Reionization Power Spectrum: A Revised Study of PAPER-64

The Epoch of Reionization (EoR) is an uncharted era in our Universe's history during which the birth of the first stars and galaxies led to the ionization of neutral hydrogen in the intergalactic medium. There are many experiments investigating the EoR by tracing the 21cm line of neutral hydrogen. Because this signal is very faint and difficult to isolate, it is crucial to develop analysis techniques that maximize sensitivity and suppress contaminants in data. It is also imperative to understand the trade-offs between different analysis methods and their effects on power spectrum estimates. Specifically, with a statistical power spectrum detection in HERA's foreseeable future, it has become increasingly important to understand how certain analysis choices can lead to the loss of the EoR signal. In this paper, we focus on signal loss associated with power spectrum estimation. We describe the origin of this loss using both toy models and data taken by the 64-element configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER). In particular, we highlight how detailed investigations of signal loss have led to a revised, higher 21cm power spectrum upper limit from PAPER-64. Additionally, we summarize errors associated with power spectrum error estimation that were previously unaccounted for. We focus on a subset of PAPER-64 data in this paper; revised power spectrum limits from the PAPER experiment are presented in a forthcoming paper by Kolopanis et al. (in prep.) and supersede results from previously published PAPER analyses.Comment: 25 pages, 18 figures, Accepted by Ap

PAPER-64 Constraints On Reionization II: The Temperature Of The z=8.4 Intergalactic Medium

We present constraints on both the kinetic temperature of the intergalactic medium (IGM) at z=8.4, and on models for heating the IGM at high-redshift with X-ray emission from the first collapsed objects. These constraints are derived using a semi-analytic method to explore the new measurements of the 21 cm power spectrum from the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER), which were presented in a companion paper, Ali et al. (2015). Twenty-one cm power spectra with amplitudes of hundreds of mK^2 can be generically produced if the kinetic temperature of the IGM is significantly below the temperature of the Cosmic Microwave Background (CMB); as such, the new results from PAPER place lower limits on the IGM temperature at z=8.4. Allowing for the unknown ionization state of the IGM, our measurements find the IGM temperature to be above ~5 K for neutral fractions between 10% and 85%, above ~7 K for neutral fractions between 15% and 80%, or above ~10 K for neutral fractions between 30% and 70%. We also calculate the heating of the IGM that would be provided by the observed high redshift galaxy population, and find that for most models, these galaxies are sufficient to bring the IGM temperature above our lower limits. However, there are significant ranges of parameter space that could produce a signal ruled out by the PAPER measurements; models with a steep drop-off in the star formation rate density at high redshifts or with relatively low values for the X-ray to star formation rate efficiency of high redshift galaxies are generally disfavored. The PAPER measurements are consistent with (but do not constrain) a hydrogen spin temperature above the CMB temperature, a situation which we find to be generally predicted if galaxies fainter than the current detection limits of optical/NIR surveys are included in calculations of X-ray heating.Comment: companion paper to Ali et al. (2015), ApJ 809, 61; matches version accepted to ApJ; 11 pages, 7 figure

Numerical relativity surrogate model with memory effects and post-Newtonian hybridization

Numerical relativity simulations provide the most precise templates for the gravitational waves produced by binary black hole mergers. However, many of these simulations use an incomplete waveform extraction technique -- extrapolation -- that fails to capture important physics, such as gravitational memory effects. Cauchy-characteristic evolution (CCE), by contrast, is a much more physically accurate extraction procedure that fully evolves Einstein's equations to future null infinity and accurately captures the expected physics. In this work, we present a new surrogate model, NRHybSur3dq8$\_$CCE, built from CCE waveforms that have been mapped to the post-Newtonian (PN) BMS frame and then hybridized with PN and effective one-body (EOB) waveforms. This model is trained on 102 waveforms with mass ratios $q\leq8$ and aligned spins $\chi_{1z}, \, \chi_{2z} \in \left[-0.8, 0.8\right]$. The model spans the entire LIGO-Virgo-KAGRA (LVK) frequency band (with $f_{\text{low}}=20\text{Hz}$) for total masses $M\gtrsim2.25M_{\odot}$ and includes the $\ell\leq4$ and $(\ell,m)=(5,5)$ spin-weight $-2$ spherical harmonic modes, but not the $(3,1)$, $(4,2)$ or $(4,1)$ modes. We find that NRHybSur3dq8$\_$CCE can accurately reproduce the training waveforms with mismatches $\lesssim2\times10^{-4}$ for total masses $2.25M_{\odot}\leq M\leq300M_{\odot}$ and can, for a modest degree of extrapolation, capably model outside of its training region. Most importantly, unlike previous waveform models, the new surrogate model successfully captures memory effects.Comment: 14 pages, 11 figures. Accepted for publication in PR