Role of spin in the calculation of Hubbard U and Hund's J parameters from first principles

The density functional theory (DFT)+$U$ method is a pragmatic and effective approach for calculating the ground-state properties of strongly-correlated systems, and linear response calculations are widely used to determine the requisite Hubbard parameters from first principles. We provide a detailed treatment of spin within this linear response approach, demonstrating that the conventional Hubbard $U$ formula, unlike the conventional DFT+$U$ corrective functional, incorporates interactions that are off-diagonal in the spin indices and places greater weight on one spin channel over the other. We construct alternative definitions for Hubbard and Hund's parameters that are consistent with the contemporary DFT+$U$ functional, expanding upon the minimum-tracking linear response method. This approach allows Hund's $J$ and spin-dependent $U$ parameters to be calculated with the same ease as for the standard Hubbard $U$. Our methods accurately reproduce the experimental band gap, local magnetic moments, and the valence band edge character of manganese oxide, a canonical strongly-correlated system. We also apply our approach to a complete series of transition-metal complexes [M(H$_2$O)$_6$]$^{n+}$ (for M = Ti to Zn), showing that Hubbard corrections on oxygen atoms are necessary for preserving bond lengths, and demonstrating that our methods are numerically well-behaved even for near-filled subspaces such as in zinc. However, spectroscopic properties appear beyond the reach of the standard DFT+$U$ approach. Collectively, these results shed new light on the role of spin in the calculation of the corrective parameters $U$ and $J$, and point the way towards avenues for further development of DFT+$U$-type methods

A Full PFPF Shell Model Study of a~=~48 Nuclei

Exact diagonalizations with a minimally modified realistic force lead to detailed agreement with measured level schemes and electromagnetic transitions in $^{48}$Ca, $^{48}$Sc, $^{48}$Ti, $^{48}$V, $^{48}$Cr and $^{48}$Mn. Gamow-Teller strength functions are systematically calculated and reproduce the data to within the standard quenching factor. Their fine structure indicates that fragmentation makes much strength unobservable. As a by-product, the calculations suggest a microscopic description of the onset of rotational motion. The spectroscopic quality of the results provides strong arguments in favour of the general validity of monopole corrected realistic forces, which is discussed.Comment: 30 pages, LaTeX with epsf.sty, 14 Postscript figures included and compressed using uufiles. Completely new version of previous preprint nucl-th/9307001. FTUAM-93/01, CRN/PT 93-3

Matrix permeability of reservoir rocks, Ngatamariki geothermal field, Taupo Volcanic Zone, New Zealand

The Taupo Volcanic Zone (TVZ) hosts 23 geothermal fields, seven of which are currently utilised for power generation. Ngatamariki geothermal field (NGF) is one of the latest geothermal power generation developments in New Zealand (commissioned in 2013), located approximately 15 km north of Taupo. Samples of reservoir rocks were taken from the Tahorakuri Formation and Ngatamariki Intrusive Complex, from five wells at the NGF at depths ranging from 1354 to 3284 m. The samples were categorised according to whether their microstructure was pore or microfracture dominated. Image analysis of thin sections impregnated with an epoxy fluorescent dye was used to characterise and quantify the porosity structures and their physical properties were measured in the laboratory. Our results show that the physical properties of the samples correspond to the relative dominance of microfractures compared to pores. Microfracture-dominated samples have low connected porosity and permeability, and the permeability decreases sharply in response to increasing confining pressure. The pore-dominated samples have high connected porosity and permeability, and lower permeability decrease in response to increasing confining pressure. Samples with both microfractures and pores have a wide range of porosity and relatively high permeability that is moderately sensitive to confining pressure. A general trend of decreasing connected porosity and permeability associated with increasing dry bulk density and sonic velocity occurs with depth; however, variations in these parameters are more closely related to changes in lithology and processes such as dissolution and secondary veining and re-crystallisation. This study provides the first broad matrix permeability characterisation of rocks from depth at Ngatamariki, providing inputs for modelling of the geothermal system. We conclude that the complex response of permeability to confining pressure is in part due to the intricate dissolution, veining, and recrystallization textures of many of these rocks that lead to a wide variety of pore shapes and sizes. While the laboratory results are relevant only to similar rocks in the Taupo Volcanic Zone, the relationships they highlight are applicable to other geothermal fields, as well as rock mechanic applications to, for example, aspects of volcanology, landslide stabilisation, mining, and tunnelling at depth

A framework for power analysis using a structural equation modelling procedure

BACKGROUND: This paper demonstrates how structural equation modelling (SEM) can be used as a tool to aid in carrying out power analyses. For many complex multivariate designs that are increasingly being employed, power analyses can be difficult to carry out, because the software available lacks sufficient flexibility. Satorra and Saris developed a method for estimating the power of the likelihood ratio test for structural equation models. Whilst the Satorra and Saris approach is familiar to researchers who use the structural equation modelling approach, it is less well known amongst other researchers. The SEM approach can be equivalent to other multivariate statistical tests, and therefore the Satorra and Saris approach to power analysis can be used. METHODS: The covariance matrix, along with a vector of means, relating to the alternative hypothesis is generated. This represents the hypothesised population effects. A model (representing the null hypothesis) is then tested in a structural equation model, using the population parameters as input. An analysis based on the chi-square of this model can provide estimates of the sample size required for different levels of power to reject the null hypothesis. CONCLUSIONS: The SEM based power analysis approach may prove useful for researchers designing research in the health and medical spheres

Quantitative immuno-mass spectrometry imaging of skeletal muscle dystrophin

Emerging and promising therapeutic interventions for Duchenne muscular dystrophy (DMD) are confounded by the challenges of quantifying dystrophin. Current approaches have poor precision, require large amounts of tissue, and are difficult to standardize. This paper presents an immuno-mass spectrometry imaging method using gadolinium (Gd)-labeled anti-dystrophin antibodies and laser ablation-inductively coupled plasma-mass spectrometry to simultaneously quantify and localize dystrophin in muscle sections. Gd is quantified as a proxy for the relative expression of dystrophin and was validated in murine and human skeletal muscle sections following k-means clustering segmentation, before application to DMD patients with different gene mutations where dystrophin expression was measured up to 100 µg kg−1 Gd. These results demonstrate that immuno-mass spectrometry imaging is a viable approach for pre-clinical to clinical research in DMD. It rapidly quantified relative dystrophin in single tissue sections, efficiently used valuable patient resources, and may provide information on drug efficacy for clinical translation

A Comparison Of New Calculations Of The Yearly 10Be Production In The Earths Polar Atmosphere By Cosmic Rays With Yearly 10Be Measurements In Multiple Greenland Ice Cores Between 1939 And 1994 - A Troubling Lack Of Concordance Paper #2

We have compared the yearly production rates of 10Be by cosmic rays in the Earths polar atmosphere over the last 50-70 years with 10Be measurements from two separate ice cores in Greenland. These ice cores provide measurements of the annual 10Be concentration and 10Be flux levels during this time. The scatter in the ice core yearly data vs. the production data is larger than the average solar 11 year production variations that are being measured. The cross correlation coefficients between the yearly 10Be production and the ice core 10Be measurements for this time period are <0.4 in all comparisons between ice core data and 10Be production, including 10Be concentrations, 10Be fluxes and in comparing the two separate ice core measurements. In fact, the cross correlation between the two ice core measurements, which should be measuring the same source, is the lowest of all, only ~0.2. These values for the correlation coefficient are all indicative of a "poor" correlation. The regression line slopes for the best fit lines between the 10Be production and the 10Be measurements used in the cross correlation analysis are all in the range 0.4-0.6. This is a particular problem for historical projections of solar activity based on ice core measurements which assume a 1:1 correspondence. We have made other tests of the correspondence between the 10Be predictions and the ice core measurements which lead to the same conclusion, namely that other influences on the ice core measurements, as large as or larger than the production changes themselves, are occurring. These influences could be climatic or instrumentally based. We suggest new ice core measurements that might help in defining more clearly what these influences are and-if possible-to correct for them.Comment: 24 pages, 6 figure

Minimization of phonon-tunneling dissipation in mechanical resonators

Micro- and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavors. Their performance is in many cases limited by the deleterious effects of mechanical damping. Here, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators. We begin by introducing an efficient numerical solver, based on the "phonon-tunneling" approach, capable of predicting the design-limited damping of high-quality mechanical resonators. Further, through careful device engineering, we isolate support-induced losses and perform the first rigorous experimental test of the strong geometric dependence of this loss mechanism. Our results are in excellent agreement with theory, demonstrating the predictive power of our approach. In combination with recent progress on complementary dissipation mechanisms, our phonon-tunneling solver represents a major step towards accurate prediction of the mechanical quality factor.Comment: 12 pages, 4 figure

Integrated Spectroscopy of Bulge Globular Clusters and Fields. II. Implications for stellar population models and elliptical galaxies

Synthetic Lick indices (e.g. Mg_2, Fe, etc.) of Simple Stellar Population (SSP) models are calibrated for the first time up to solar metallicity with a sample of Milky Way globular clusters (GCs) which includes the metal rich GCs of the Galactic bulge. This metallicity range is relevant to elliptical galaxies. It is shown that the Bulge GCs and integrated light follow the same correlation between Mg and Fe indices of elliptical galaxies, showing weaker Fe indices at given Mg indices with respect to models that assume solar-scaled abundances. This similarity is the robust empirical evidence for enhanced alpha/Fe ratios in the stellar populations of elliptical galaxies, since the globular clusters are independently known to be alpha-enhanced. The uniqueness of this alpha-overabundance solution is checked by exploring the whole range of model ingredients. We argue that the standard models reproduce the Mg-Fe correlation at low metallicities because the stellar templates used in the synthesis are the alpha-enhanced stars of the galactic Halo. These same models, however, fail to recover the Mg-Fe pattern of Bulge clusters and ellipticals at high metallicities because the high-metallicity templates are disk stars, which are not alpha-enhanced. The new SSP models by Thomas, Maraston & Bender (2002) which incorporate the dependence on alpha/Fe reproduce the Mg and Fe indices of GCs at all metallicities, with alpha/Fe=+0.3, which is in agreement with spectroscopic abundance determinations. The Balmer indices (Hbeta, Hdelta, Hgamma) are very well calibrated, provided the Horizontal Branch morphology is taken into account. In particular, we reproduce the Balmer lines of NGC 6388 and NGC 6441, which are metal-rich GCs with a tail of warm Horizontal Branch stars. {Abridged}Comment: 19 pages, 13 figures, Astronomy and Astrophysics in press. Only minor changes after the referee repor