Seismic gravity-gradient noise in interferometric gravitational-wave detectors

When ambient seismic waves pass near and under an interferometric gravitational-wave detector, they induce density perturbations in the Earth, which in turn produce fluctuating gravitational forces on the interferometer’s test masses. These forces mimic a stochastic background of gravitational waves and thus constitute a noise source. This seismic gravity-gradient noise has been estimated and discussed previously by Saulson using a simple model of the Earth’s ambient seismic motions. In this paper, we develop a more sophisticated model of these motions, based on the theory of multimode Rayleigh and Love waves propagating in a multilayer medium that approximates the geological strata at the LIGO sites, and we use this model to reexamine seismic gravity gradients. We characterize the seismic gravity-gradient noise by a transfer function, T(f )≡x̃(f )/W̃(f ), from the spectrum of rms seismic displacements averaged over vertical and horizontal directions, W̃(f ), to the spectrum of interferometric test-mass motions, x̃(f )≡Lh̃(f ); here L is the interferometer arm length, h̃(f ) is the gravitational-wave noise spectrum, and f is frequency. Our model predicts a transfer function with essentially the same functional form as that derived by Saulson, T≃4πGρ(2πf )-2β(f ), where ρ is the density of Earth near the test masses, G is Newton’s constant, and β(f )≡γ(f )Γ(f )β′(f ) is a dimensionless reduced transfer function whose components γ≃1 and Γ≃1 account for a weak correlation between the interferometer’s two corner test masses and a slight reduction of the noise due to the height of the test masses above the Earth’s surface. This paper’s primary foci are (i) a study of how β′(f )≃β(f ) depends on the various Rayleigh and Love modes that are present in the seismic spectrum, (ii) an attempt to estimate which modes are actually present at the two LIGO sites at quiet times and at noisy times, and (iii) a corresponding estimate of the magnitude of β′(f ) at quiet and noisy times. We conclude that at quiet times β′≃0.35–0.6 at the LIGO sites, and at noisy times β′≃0.15–1.4. (For comparison, Saulson’s simple model gave β=β′=1/sqrt[3]=0.58.) By folding our resulting transfer function into the “standard LIGO seismic spectrum,” which approximates W̃(f ) at typical times, we obtain the gravity-gradient noise spectra. At quiet times this noise is below the benchmark noise level of “advanced LIGO interferometers” at all frequencies (though not by much at ∼10 Hz); at noisy times it may significantly exceed the advanced noise level near 10 Hz. The lower edge of our quiet-time noise constitutes a limit, beyond which there would be little gain from further improvements in vibration isolation and thermal noise, unless one can also reduce the seismic gravity gradient noise. Two methods of such reduction are briefly discussed: monitoring the Earth’s density perturbations near each test mass, computing the gravitational forces they produce, and correcting the data for those forces; and constructing narrow moats around the interferometers’ corner and end stations to shield out the fundamental-mode Rayleigh waves, which we suspect dominate at quiet times

Kinetic roughening of vicinal Si(001)

The kinetic roughening behavior of vicinal Si(001) surfaces is studied with scanning tunneling microscopy. By analyzing the height-height correlation function of the Si layers that have been grown we found, in the case of islands growth, an algebraic roughening behavior with a roughness exponent of 0.68 ± 0.05. In the step flow mode, however, we found non-algebraic roughening behavior

Spreading pressures of water and n-propanol on polymer surfaces

Spreading pressures of water and n-propanol on polytetrafluoroethylene (PTFE), polystyrene (PS), polymethylmethacrylate (PMMA), polycarbonate (PC), and glass are determined from ellipsometrically measured adsorption isotherms by graphical integration, yielding for water 9, 37, 26, 33, and 141 erg · cm−2 on PTFE, PS, PMMA, PC, and glass, respectively, while for n-propanol 5, 38, 26, 23, and 37 erg · cm−2, respectively. The spreading pressures for water as well as n-propanol are comparable to values previously obtained from contact angle data with water, water/n-propanol mixtures and α-bromonaphthalene using the geometric mean equation. This method yielded spreading pressures of 9, 14, 30, 27, and 70 erg · cm−2 for PTFE, PS, PMMA, PC, and glass, respectively. The numerical correspondence between the spreading pressures for water and n-propanol determined ellipsometrically with the values derived from contact angles indicates the necessity as well as the validity of taking the spreading pressures of water/n-propanol mixtures into account as a constant, if surface free energies of high energy substrata are approximated by contact angle measurements

Momentum flow in black-hole binaries. I. Post-Newtonian analysis of the inspiral and spin-induced bobbing

A brief overview is presented of a new Caltech/Cornell research program that is exploring the nonlinear dynamics of curved spacetime in binary black-hole collisions and mergers, and of an initial project in this program aimed at elucidating the flow of linear momentum in binary black holes (BBHs). The “gauge-dependence” (arbitrariness) in the localization of linear momentum in BBHs is discussed, along with the hope that the qualitative behavior of linear momentum will be gauge-independent. Harmonic coordinates are suggested as a possibly preferred foundation for fixing the gauge associated with linear momentum. For a BBH or other compact binary, the Landau-Lifshitz formalism is used to define the momenta of the binary’s individual bodies in terms of integrals over the bodies’ surfaces or interiors, and define the momentum of the gravitational field (spacetime curvature) outside the bodies as a volume integral over the field’s momentum density. These definitions will be used in subsequent papers that explore the internal nonlinear dynamics of BBHs via numerical relativity. This formalism is then used, in the 1.5 post-Newtonian approximation, to explore momentum flow between a binary’s bodies and its gravitational field during the binary’s orbital inspiral. Special attention is paid to momentum flow and conservation associated with synchronous spin-induced bobbing of the black holes, in the so-called “extreme-kick configuration” (where two identical black holes have their spins lying in their orbital plane and antialigned)

Can the US Minimum Data Set Be Used for Predicting Admissions to Acute Care Facilities?

This paper is intended to give an overview of Knowledge Discovery in Large Datasets (KDD) and data mining applications in healthcare particularly as related to the Minimum Data Set, a resident assessment tool which is used in US long-term care facilities. The US Health Care Finance Administration, which mandates the use of this tool, has accumulated massive warehouses of MDS data. The pressure in healthcare to increase efficiency and effectiveness while improving patient outcomes requires that we find new ways to harness these vast resources. The intent of this preliminary study design paper is to discuss the development of an approach which utilizes the MDS, in conjunction with KDD and classification algorithms, in an attempt to predict admission from a long-term care facility to an acute care facility. The use of acute care services by long term care residents is a negative outcome, potentially avoidable, and expensive. The value of the MDS warehouse can be realized by the use of the stored data in ways that can improve patient outcomes and avoid the use of expensive acute care services. This study, when completed, will test whether the MDS warehouse can be used to describe patient outcomes and possibly be of predictive value

Can the US Minimum Data Set Be Used for Predicting Admissions to Acute Care Facilities?

This paper is intended to give an overview of Knowledge Discovery in Large Datasets (KDD) and data mining applications in healthcare particularly as related to the Minimum Data Set, a resident assessment tool which is used in US long-term care facilities. The US Health Care Finance Administration, which mandates the use of this tool, has accumulated massive warehouses of MDS data. The pressure in healthcare to increase efficiency and effectiveness while improving patient outcomes requires that we find new ways to harness these vast resources. The intent of this preliminary study design paper is to discuss the development of an approach which utilizes the MDS, in conjunction with KDD and classification algorithms, in an attempt to predict admission from a long-term care facility to an acute care facility. The use of acute care services by long term care residents is a negative outcome, potentially avoidable, and expensive. The value of the MDS warehouse can be realized by the use of the stored data in ways that can improve patient outcomes and avoid the use of expensive acute care services. This study, when completed, will test whether the MDS warehouse can be used to describe patient outcomes and possibly be of predictive value

Electron Microprobe Chemical Dating of Uraninite as a Reconnaissance Tool for Leucogranite Geochronology

We suggest that electron microprobe techniques may be employed to date Tertiary samples of uraninite (UO~2~), which can contain very high concentrations of radiogenic Pb after only a few million of years of U and Th decay. Although uraninite is regarded as a rare accessory mineral, it is relatively abundant in leucogranitic rocks such as those found in the Himalayan orogen. We apply the U-Th-total Pb electron microprobe chemical dating method to a uraninite crystal from a ca. 18.3 Ma dike of the Mugu granite from the Upper Mustang region of central Nepal. With this technique, we calculate a mean chemical date that is consistent with isotope-dilution thermal ionization mass spectrometry (ID-TIMS) U-Pb dates obtained from seven other uraninite grains and a monazite crystal from the same sample. Electron microprobe chemical dating yields results that typically will be an order of magnitude less precise than conventional dates: in the specific case of the Mugu granite, single point chemical dates each have ca. 1.5 Ma 2[sigma] (95%) confidence level uncertainties. However, the mean chemical date of 15 point analyses of the crystal we study has a 2SE (2 standard error) uncertainty of ca. 400 ka, comparable to uncertainties obtained with ID-TIMS. These results show that electron microprobe chemical dating of uraninite has substantial promise as a reconnaissance tool for the geochronology of young granitic rocks. The electron microprobe work also reveals substantial chemical complexity within uraninite that must be taken into account. The analyzed crystal displays a texturally and chemically distinctive core and rim that suggests episodic growth. Concentration gradients in U, Th, and Y across the boundary imply diffusive modification. We estimate the diffusivity of U, Th, and Y in uraninite at ca. 700 °C to be > 10-7 cm2 s-1. In contrast, Pb shows no distinctive concentration gradient across the core-rim boundary, implying that Pb has a much higher diffusivity in uraninite than U, Th, or Y. We estimate that Pb loss of as much as ca. 8.9% has occurred in the uraninite grains we analyzed by ID-TIMS