Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models

The effect of quantization on the FCIQMC sign problem

The sign problem in Full Configuration Interaction Quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.Comment: 4 pages w/ 2 page appendix, 2 figures, 1 tabl

Hadron spectroscopy from canonical partition functions

A spectroscopic method for staggered fermions based on thermodynamical considerations is proposed. The canonical partition functions corresponding to the different quark number sectors are expressed in the low temperature limit as polynomials of the eigenvalues of the reduced fermion matrix. Taking the zero temperature limit yields the masses of the lowest states. The method is successfully applied to the Goldstone pion and both dynamical and quenched results are presented showing good agreement with that of standard spectroscopy. Though in principle the method can be used to obtain the baryon and dibaryon masses, due to their high computational costs such calculations are practically unreachable.Comment: 13 pages, 4 figures. Spelling and grammatical errors are correcte

Photometry of SN 2002bo with template image subtraction

VRI photometry of the type Ia supernova 2002bo is presented. This SN exploded in a dusty region of the host galaxy NGC 3190, thus, subtraction of a template frame was necessary to obtain reliable photometry. We used a template frame of NGC 3190 taken during the course of our galaxy imaging project, fortunately, just a few days before SN 2002bo was discovered. The aim of this project is to collect template frames of nearby galaxies that are potential hosts of bright SNe. Subtraction of pre-SN images helped us to exclude the background light contamination of the host galaxy. The maximum occurred at JD 2452346, with maximal V brightness of 13.58. MLCS analysis led to T0(B)=JD 2452346.1 pm 0.8 (fiducial B-maximum), E(B-V)=0.24 pm 0.02, mu0=32.46 pm 0.06, Delta=-0.14 pm 0.04. E(B-V)=0.24(2) indicates a significant extinction in the host galaxy as the galactic reddening is negligible toward NGC 3190. The accepted value of Delta indicates that SN 2002bo was a slightly overluminous SN by about 0.14 relative to fiducial SN Type Ia. The distance turned out to be 31.0 pm 3 Mpc. In addition, the heavily obscured SN 2002cv was also detected on the I frame taken on JD 2452434 (June 8, 2002), and a variable star is found in the field, very close to the host galaxy.Comment: accepted by Astronomy and Astrophysic

Investigations of Ra+^+ properties to test possibilities of new optical frequency standards

The present work tests the suitability of the narrow transitions $7s \ ^2S_{1/2} \to 6d ^2D_{3/2}$and$7s ^2S_{1/2} \to 6d ^2D_{5/2}$in Ra$^+$for optical frequency standard studies. Our calculations of the lifetimes of the metastable$6d$states using the relativistic coupled-cluster theory suggest that they are sufficiently long for Ra$^+$ to be considered as a potential candidate for an atomic clock. This is further corroborated by our studies of the hyperfine interactions, dipole and quadrupole polarizabilities and quadrupole moments of the appropriate states of this system.Comment: Latex files, 5 pages, 1 figur

Origin of the high piezoelectric response in PbZr(1-x)TixO3

High resolution x-ray powder diffraction measurements on poled PbZr(1-x)TixO3 (PZT) ceramic samples close to the rhombohedral-tetragonal phase boundary (the so-called morphotropic phase boundary, MPB) have shown that for both rhombohedral and tetragonal compositions, the piezoelectric elongation of the unit cell does not occur along the polar directions but along those directions associated with the monoclinic distortion. This work provides the first direct evidence for the origin of the very high piezoelectricity in PZT.Comment: 4 pages, 4 EPS figures embedded. More specific title and abstract. To appear in Phys. Rev. Let

Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles

We compute the leading, strong-interaction contribution to the anomalous magnetic moment of the electron, muon and tau using lattice quantum chromodynamics (QCD) simulations. Calculations include the effects of $u$, $d$, $s$ and $c$ quarks and are performed directly at the physical values of the quark masses and in volumes of linear extent larger than $6\,\mathrm{fm}$. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain $a_e^\mathrm{LO-HVP}=189.3(2.6)(5.6)\times 10^{-14}$, $a_\mu^\mathrm{LO-HVP}=711.1(7.5)(17.4)\times 10^{-10}$ and $a_\tau^\mathrm{LO-HVP}=341.0(0.8)(3.2)\times 10^{-8}$, where the first error is statistical and the second is systematic.Comment: 17 pages, 8 figures (in 13 PDF files), RevTeX 4.1. Minor changes to results and to text. References updated. Matches version published in Physical Review Letter

Pfaffian pairing wave functions in electronic structure quantum Monte Carlo

We investigate the accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-pfaffian pairing wave functions. We show that a small number of pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.Comment: 4 pages, 2 figures, 2 tables, submitted to PR