A corrected quadrature formula and applications

A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives

Analysis of the contributions of three-body potentials in the equation of state of 4He

The effect of three-body interatomic contributions in the equation of state of 4He are investigated. A recent two-body potential together with the Cohen and Murrell (Chem. Phys. Lett. 260, 371 (1996)) three-body potential are applied to describe bulk helium. The triple-dipole dispersion and exchange energies are evaluated subjected only to statistical uncertainties. An extension of the diffusion Monte Carlo method is applied in order to compute very small energies differences. The results show how the three-body contributions affects the ground-state energy, the equilibrium, melting and freezing densities.Comment: 18 pages, 3 figures, 4 table

A corrected quadrature formula and applications

A straightforward three-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives

Solid He-4 and the diffusion Monte Carlo method: a study of their properties

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPFUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIRO - FAPERJCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQProperties of helium atoms in the solid phase are investigated using the multiweight diffusion Monte Carlo method. Two different importance function transformations are used in two series of independent calculations. The kinetic energy is estimated for both the solid and liquid phases of He-4. We estimate the melting and freezing densities, among other properties of interest. Our estimates are compared with experimental values. We discuss why walkers biased by two distinctly different guiding functions do not lead to noticeable changes in the reported results. Criticisms concerning the bias introduced into our estimates by population control and system size effects are considered.964110FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPFUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIRO - FAPERJCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPFUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIRO - FAPERJCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQSem informaçãoSem informaçãoSem informaçãoThe authors acknowledge financial support from the Brazilian agencies Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ), and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). Part of the computations were performed at the Centro Nacional de Processamento de Alto Desempenho em São Paulo (CENAPAD-SP), a high-performance computing facility at Universidade Estadual de Campinas

High-accuracy high-mass ratio simulations for binary neutron stars and their comparison to existing waveform models

The subsequent observing runs of the advanced gravitational-wave detector network will likely provide us with various gravitational-wave observations of binary neutron star systems. For an accurate interpretation of these detections, we need reliable gravitational-wave models. To test and to point out how existing models could be improved, we perform a set of high-resolution numerical-relativity simulations for four different physical setups with mass ratios $q$ = $1.25$, $1.50$, $1.75$, $2.00$, and total gravitational mass $M = 2.7M_\odot$ . Each configuration is simulated with five different resolutions to allow a proper error assessment. Overall, we find approximately 2nd order converging results for the dominant $(2,2)$, but also subdominant $(2,1)$, $(3,3)$, $(4,4)$ modes, while, generally, the convergence order reduces slightly for an increasing mass ratio. Our simulations allow us to validate waveform models, where we find generally good agreement between state-of-the-art models and our data, and to prove that scaling relations for higher modes currently employed for binary black hole waveform modeling also apply for the tidal contribution. Finally, we also test if the current NRTidal model to describe tidal effects is a valid description for high-mass ratio systems. We hope that our simulation results can be used to further improve and test waveform models in preparation for the next observing runs

Elliptica: a new pseudo-spectral code for the construction of initial data

Numerical studies of the dynamics of gravitational systems, e.g., black hole-neutron star systems, require physical and constraint-satisfying initial data. In this article, we present the newly developed pseudo-spectral code Elliptica, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, Elliptica deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of Elliptica and the initial data construction algorithm for a black hole-neutron star binary system. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude $\sim 0.8$

Shubnikov - de haas effect in tilted magnetic fields in wide quantum well

Bilayer two-dimensional electron system in double quantum wells demonstrated oscillations of the symmetric–antisymmetric energy gap in the presence of the in-plane magnetic field [1] which has been attributed to Aharonov-Bohm interference effect between cyclotron orbits in different layers [2]. The charge distribution in a wide single quantum well is more subtle than the one in the double quantum well. Here the Coulomb repulsion of the electrons in the well leads to a soft barrier inside the well, which in turn results in a bilayer electron system. Applying of the in-plane magnetic field can also lead to the charge redistribution inside of the well and distortion of the circular Fermi contour. In the present work we have measured and calculated Shubnikov – de Haas effect in wide wells in the tilted magnetic field. The samples used in this paper have a well with of w=45 nm with a density ns = 9.1x1011 cm-2, see sketch of profile in figure (a) with symmetric (S) and anti-symmetric (AS) wave functions.Foundation for Science and Technology (FCT

Visualization of wave function of quantum dot at fermi-edge singularity regime

We consider electron tunneling spectroscopy through an InAs quantum dot in a magnetic field applied perpendicular to the tunneling direction. We examine in details the anisotropic behavior of the amplitude and shape of the resonant peaks of I-V curves and concluded that (i) magnetotunneling spectroscopy at FES regime allows establishing position of resonant level in QD with high accuracy. (ii) The distinguishable shape of FES peak allows extracting the amplitude with much better accuracy. (iii) FES exponent dependence on magnetic field gives additional information about potential distribution outside QD.Foundation for Science and Technology (FCT