Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.

A Measurement of the Proton Structure Function g2p at Low Q2

Experiments at Jefferson Lab have been conducted to extract the nucleon spin-dependent structure functions over a wide kinematic range. Higher moments of these quantities provide tests of QCD sum rules and predictions of chiral perturbation theory ($\chi$PT). While precise measurements of $g_{1}^n$, $g_{2}^n$, and $g_1^p$ have been extensively performed, the data of $g_2^p$ remain scarce. Discrepancies were found between existing data related to $g_2$ and theoretical predictions. Results on the proton at large $Q^2$ show a significant deviation from the Burkhardt-Cottingham sum rule, while results for the neutron generally follow this sum rule. The next-to-leading order $\chi$PT calculations exhibit discrepancy with data on the longitudinal-transverse polarizability $\delta_{LT}^n$. Further measurements of the proton spin structure function $g_2^p$ are desired to understand these discrepancies.

Experiment E08-027 (g2p) was conducted at Jefferson Lab in experimental Hall A in 2012. Inclusive measurements were performed with polarized electron beam and a polarized ammonia target to obtain the proton spin-dependent structure function $g_2^p$ at low Q$^2$ region (0.02$<$Q$^2$$<$0.2 GeV$^2$) for the first time. The results can be used to test the Burkhardt-Cottingham sum rule, and also allow us to extract the longitudinal-transverse spin polarizability of the proton, which will provide a benchmark test of $\chi$PT calculations. This thesis will present and discuss the very preliminary results of the transverse asymmetry and the spin-dependent structure functions $g_1^p$ and $g_2^p$ from the data analysis of the g2p experiment .

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Machine Learning-based Techniques to Address Spectral Distortions in Photon Counting X-ray Computed Tomography

Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables full spectrum CT in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical eects in the detector and are very noisy due to photon starvation. In this work, we proposed two methods based on machine learning to address the spectral distortion issue and to improve the material decomposition. This rst approach is to model distortions using an articial neural network (ANN) and compensate for the distortion in a statistical reconstruction. The second approach is to directly correct for the distortion in the projections. Both technique can be done as a calibration process where the neural network can be trained using 3D printed phantoms data to learn the distortion model or the correction model of the spectral distortion. This replaces the need for synchrotron measurements required in conventional technique to derive the distortion model parametrically which could be costly and time consuming. The results demonstrate experimental feasibility and potential advantages of ANN-based distortion modeling and correction for more accurate K-edge imaging with a PCXD. Given the computational eciency with which the ANN can be applied to projection data, the proposed scheme can be readily integrated into existing CT reconstruction pipelines.

Spectral sensitivity, spatial resolution and temporal resolution and their implications for conspecific signalling in cleaner shrimp.

Cleaner shrimp (Decapoda) regularly interact with conspecifics and client reef fish, both of which appear colourful and finely patterned to human observers. However, whether cleaner shrimp can perceive the colour patterns of conspecifics and clients is unknown, because cleaner shrimp visual capabilities are unstudied. We quantified spectral sensitivity and temporal resolution using electroretinography (ERG), and spatial resolution using both morphological (inter-ommatidial angle) and behavioural (optomotor) methods in three cleaner shrimp species: Lysmata amboinensis, Ancylomenes pedersoni and Urocaridella antonbruunii. In all three species, we found strong evidence for only a single spectral sensitivity peak of (mean ± s.e.m.) 518 ± 5, 518 ± 2 and 533 ± 3 nm, respectively. Temporal resolution in dark-adapted eyes was 39 ± 1.3, 36 ± 0.6 and 34 ± 1.3 Hz. Spatial resolution was 9.9 ± 0.3, 8.3 ± 0.1 and 11 ± 0.5 deg, respectively, which is low compared with other compound eyes of similar size. Assuming monochromacy, we present approximations of cleaner shrimp perception of both conspecifics and clients, and show that cleaner shrimp visual capabilities are sufficient to detect the outlines of large stimuli, but not to detect the colour patterns of conspecifics or clients, even over short distances. Thus, conspecific viewers have probably not played a role in the evolution of cleaner shrimp appearance; rather, further studies should investigate whether cleaner shrimp colour patterns have evolved to be viewed by client reef fish, many of which possess tri- and tetra-chromatic colour vision and relatively high spatial acuity.