Extended Variational Cluster Approximation

The variational cluster approximation (VCA) proposed by M. Potthoff {\it et al.} [Phys. Rev. Lett. {\bf 91}, 206402 (2003)] is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.Comment: 23 pages, 5 figures, statements about DCA corrected; published versio

Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups

In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem and the recent Nayar theorem on polynomial growth harmonic functions on lattices \mathds{Z}^n that does not use a representation formula for harmonic functions. We also calculate the precise dimension of the space of polynomial growth harmonic functions on finitely generated abelian groups. While the Cayley graph not only depends on the abelian group, but also on the choice of a generating set, we find that this dimension depends only on the group itself.Comment: 15 pages, to appear in Ann. Global Anal. Geo

Molecular hydrogen emission in the interstellar medium of the Large Magellanic Cloud

We present the detection and analysis of molecular hydrogen emission toward ten interstellar regions in the Large Magellanic Cloud. We examined low-resolution infrared spectral maps of twelve regions obtained with the Spitzer infrared spectrograph (IRS). The pure rotational 0--0 transitions of H$_2$ at 28.2 and 17.1${\,\rm \mu m}$ are detected in the IRS spectra for ten regions. The higher level transitions are mostly upper limit measurements except for three regions, where a 3$\sigma$ detection threshold is achieved for lines at 12.2 and 8.6${\,\rm \mu m}$. The excitation diagrams of the detected H$_2$ transitions are used to determine the warm H$_2$ gas column density and temperature. The single-temperature fits through the lower transition lines give temperatures in the range $86-137\,{\rm K}$. The bulk of the excited H$_2$ gas is found at these temperatures and contributes $\sim$5-17% to the total gas mass. We find a tight correlation of the H$_2$ surface brightness with polycyclic aromatic hydrocarbon and total infrared emission, which is a clear indication of photo-electric heating in photodissociation regions. We find the excitation of H$_2$ by this process is equally efficient in both atomic and molecular dominated regions. We also present the correlation of the warm H$_2$ physical conditions with dust properties. The warm H$_2$ mass fraction and excitation temperature show positive correlations with the average starlight intensity, again supporting H$_2$ excitation in photodissociation regions.Comment: Accepted for publication in MNRA

Molecular Dynamics Simulations of the Roller Nanoimprint Process: Adhesion and Other Mechanical Characteristics

Molecular dynamics simulations using tight-binding many body potential are carried out to study the roller imprint process of a gold single crystal. The effect of the roller tooth’s taper angle, imprint depth, imprint temperature, and imprint direction on the imprint force, adhesion, stress distribution, and strain are investigated. A two-stage roller imprint process was obtained from an imprint force curve. The two-stage imprint process included the imprint forming with a rapid increase of imprint force and the unloading stage combined with the adhesion stage. The results show that the imprint force and adhesion rapidly increase with decreasing taper angle and increasing imprint depth. The magnitude of the maximum imprint force and the time at which this maximum occurs are proportional to the imprint depth, but independent of the taper angle. In a comparison of the imprint mechanisms with a vertical imprint case, while high stress and strain regions are concentrated below the mold for vertical imprint, they also occur around the mold in the case of roller imprint. The regions were only concentrated on the substrate atoms underneath the mold in vertical imprint. Plastic flow increased with increasing imprint temperature

SDSS J143030.22-001115.1: A misclassified narrow-line Seyfert 1 galaxy with flat X-ray spectrum

We used multi-component profiles to model H$\beta$ and [O III]$\lambda \lambda$4959,5007 lines for SDSS J143030.22-001115.1, a narrow-line Seyfert 1 galaxy (NLS1) in a sample of 150 NLS1s candidates selected from the Sloan Digital Sky Survey (SDSS) Early Data Release (EDR). After subtracting the H$\beta$ contribution from narrow line regions (NLRs), we found that its full width half maximum (FWHM) of broad H$\beta$ line is nearly 2900 \kms, significantly larger than the customarily adopted criterion of 2000 \kms. With its weak Fe II multiples, we think that SDSS J143030.22-001115.1 can't be classified as a genuine NLS1. When we calculate the virial black hole masses of NLS1s, we should use the H$\beta$ linewidth after subtracting the H$\beta$ contribution from NLRs.Comment: 7 pages, 1 table, accepted by ChJA

A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality

Tumors and tumor-like lesions of the heart valves

Valvular tumors and tumor-like lesions may have similar morphological and clinical characteristics, and may place the patients at a high risk of stroke in different ways. From January 2004 to June 2008, 11 patients underwent surgery for a suspected valvular tumor. Valvular tumor and tumor-like lesions accounted for 0.32% of adult cardiac operations. Five (45.5%) valvular lesions were papillary fibroelastomas, one (9.1%) was myxoma, 2 (18.2%) were organized thrombi, and 3 (27.3%) were calcification lesions. There was a total of 5 (45.5%) atrioventricular valve lesions, 4 arising from the atrial side of the leaflets, and one from the ventricular side. All 5 (45.5%) semilunar valvular lesions were from the aortic valve. One (9.1%) lesion originated from the chorda tendinea of the mitral valve. All leaflet lesions were resected by a simple shave technique, and all the patients recovered favorably. Valvular tumor and tumor-like lesions are rare. Pre-operative differential diagnoses among these valvular lesions pose important clinical implications for appropriate treatment for the underlying diseases. Prompt therapeutic measures in view of the underlying diseases of the valvular lesions are essential to prevent potential embolic events

Chemical potential and symmetry energy for intermediate-mass fragment production in heavy ion reactions near the Fermi energy

Ratios of differential chemical potential values relative to the temperature, ({\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p})/T, extracted from isotope yields of 13 reaction systems at 40 MeV/nucleon are compared to those of a quantum statistical model to determine the temperature and symmetry energy values of the fragmenting system. The experimental ({\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p})/T values are extracted based on the modified Fisher model. Using the density value of \ensuremath{\rho}/{\ensuremath{\rho}}_{0}=0.56 from the previous analysis, the temperature and symmetry energy values of T=4.6\ifmmode\pm\else\textpm\fi{}0.4 MeV and {a}_{\mathrm{sym}}=23.6\ifmmode\pm\else\textpm\fi{}2.1 MeV are extracted in a framework of a quantum statistical model. These values agree well with those of the previous work, in which a self-consistent method was utilized with antisymmetrized molecular dynamics simulations. The extracted temperature and symmetry energies are discussed together with other experimental values published in literature

Harmonic analysis on the Möbius gyrogroup

In this paper we propose to develop harmonic analysis on the Poincaré ball $B_t^n$, a model of the n-dimensional real hyperbolic space. The Poincaré ball $B_t^n$ is the open ball of the Euclidean n-space $R^n$ with radius $t>0$, centered at the origin of $R^n$ and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in $\mathbb{R}^n$. For any $t>0$ and an arbitrary parameter $\sigma \in R$ we study the $(\sigma,t)$-translation, the $( \sigma,t)$-convolution, the eigenfunctions of the $(\sigma,t)$-Laplace-Beltrami operator, the $(\sigma,t)$-Helgason Fourier transform, its inverse transform and the associated Plancherel's Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic harmonic analysis. Moreover, when $t \rightarrow +\infty$ the resulting hyperbolic harmonic analysis on $B_t^n$ tends to the standard Euclidean harmonic analysis on $R^n$, thus unifying hyperbolic and Euclidean harmonic analysis. As an application we construct diffusive wavelets on $B_t^n$