Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive

Interactive volumetric segmentation for textile micro-tomography data using wavelets and nonlocal means

This work addresses segmentation of volumetric images of woven carbon fiber textiles from micro-tomography data. We propose a semi-supervised algorithm to classify carbon fibers that requires sparse input as opposed to completely labeled images. The main contributions are: (a) design of effective discriminative classifiers, for three-dimensional textile samples, trained on wavelet features for segmentation; (b) coupling of previous step with nonlocal means as simple, efficient alternative to the Potts model; and (c) demonstration of reuse of classifier to diverse samples containing similar content. We evaluate our work by curating test sets of voxels in the absence of a complete ground truth mask. The algorithm obtains an average 0.95 F1 score on test sets and average F1 score of 0.93 on new samples. We conclude with discussion of failure cases and propose future directions toward analysis of spatiotemporal high-resolution micro-tomography images

Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove

Trace element geochemistry of peridotites from the Izu-Bonin-Mariana Forearc, Leg 125

Trace element analyses (first-series transition elements, Ti, Rb, Sr, Zr, Y, Nb, and REE) were carried out on whole rocks and minerals from 10 peridotite samples from both Conical Seamount in the Mariana forearc and Torishima Forearc Seamount in the Izu-Bonin forearc using a combination of XRF, ID-MS, ICP-MS, and ion microprobe. The concentrations of incompatible trace elements are generally low, reflecting the highly residual nature of the peridotites and their low clinopyroxene content (n ratios in the range of 0.05-0.25; several samples show possible small positive Eu anomalies. LREE enrichment is common to both seamounts, although the peridotites from Conical Seamount have higher (La/Ce)n ratios on extended chondrite-normalized plots, in which both REEs and other trace elements are organized according to their incompatibility with respect to a harzburgitic mantle. Comparison with abyssal peridotite patterns suggests that the LREEs, Rb, Nb, Sr, Sm, and Eu are all enriched in the Leg 125 peridotites, but Ti and the HREEs exhibit no obvious enrichment. The peridotites also give positive anomalies for Zr and Sr relative to their neighboring REEs. Covariation diagrams based on clinopyroxene data show that Ti and the HREEs plot on an extension of an abyssal peridotite trend to more residual compositions. However, the LREEs, Rb, Sr, Sm, and Eu are displaced off this trend toward higher values, suggesting that these elements were introduced during an enrichment event. The axis of dispersion on these plots further suggests that enrichment took place during or after melting and thus was not a characteristic of the lithosphere before subduction. Compared with boninites sampled from the Izu-Bonin-Mariana forearc, the peridotites are significantly more enriched in LREEs. Modeling of the melting process indicates that if they represent the most depleted residues of the melting events that generated forearc boninites they must have experienced subsolidus enrichment in these elements, as well as in Rb, Sr, Zr, Nb, Sm, and Eu. The lack of any correlation with the degree of serpentinization suggests that low-temperature fluids were not the prime cause of enrichment. The enrichment in the high-field-strength elements also suggests that at least some of this enrichment may have involved melts rather than aqueous fluids. Moreover, the presence of the hydrous minerals magnesio-hornblende and tremolite and the common resorption of orthopyroxene indicate that this high-temperature peridotite-fluid interaction may have taken place in a water-rich environment in the forearc following the melting event that produced the boninites. The peridotites from Leg 125 may therefore contain a record of an important flux of elements into the mantle wedge during the initial formation of forearc lithosphere. Ophiolitic peridotites with these characteristics have not yet been reported, perhaps because the precise equivalents to the serpentinite seamounts have not been analyzed

Complete phase diagram of the spin-1/2 J1J_{1}-J2J_{2}-J3J_{3} model (with J3=J2J_{3}=J_{2}) on the honeycomb lattice

We use the coupled cluster method to investigate the ground-state (GS) properties of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ model on the honeycomb lattice, with nearest-neighbor exchange coupling $J_1$ plus next-nearest-neighbor ($J_2$) and next-next-nearest-neighbor ($J_3$) exchanges of equal strength. In particular we find a direct first-order phase transition between the N\'eel-ordered antiferromagnetic phase and the ferromagnetic phase at a value $J_{2}/J_{1} = -1.17 \pm 0.01$ when $J_{1}>0$, compared to the corresponding classical value of -1. We find no evidence for any intermediate phase. From this and our previous CCM studies of the model we present its full zero-temperature GS phase diagram.Comment: 4 pages, 4 figure

Challenges of ultra large scale integration of biomedical computing systems

The NCRI Informatics Initiative is overseeing the implementation of an informatics framework for the UK cancer research community. The framework advocates an integrated multidisciplinary method of working between scientific and medical communities. Key to this process is community adoption of high quality acquisition, storage, sharing and integration of diverse data elements to improve knowledge of the causes, prevention and treatment of cancer. The integration of the complex data and meta-data used by these multiple communities is a significant challenge and there are technical, resource-based and sociological issues to be addressed. In this paper we review progress aimed at establishing the framework and outline key challenges in ultra large scale integration of biomedical computing systems

Spinful bosons in an optical lattice

We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized S=1 chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.Comment: Minor revisions and clarification

Antarctic Sea Ice variations 1973 - 1975

Variations in the extent and concentration of sea ice cover on the Southern Ocean are described for the three-year period 1973-75 using information derived from the Nimbus-5 passive microwave imager