Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

In vivo visualization of abdominal malignancies with acoustic radiation force elastography.

The utility of acoustic radiation force impulse (ARFI) imaging for real-time visualization of abdominal malignancies was investigated. Nine patients presenting with suspicious masses in the liver (n = 7) or kidney (n = 2) underwent combined sonography/ARFI imaging. Images were acquired of a total of 12 tumors in the nine patients. In all cases, boundary definition in ARFI images was improved or equivalent to boundary definition in B-mode images. Displacement contrast in ARFI images was superior to echo contrast in B-mode images for each tumor. The mean contrast for suspected hepatocellular carcinomas (HCCs) in B-mode images was 2.9 dB (range: 1.5-4.2) versus 7.5 dB (range: 3.1-11.9) in ARFI images, with all HCCs appearing more compliant than regional cirrhotic liver parenchyma. The mean contrast for metastases in B-mode images was 3.1 dB (range: 1.2-5.2) versus 9.3 dB (range: 5.7-13.9) in ARFI images, with all masses appearing less compliant than regional non-cirrhotic liver parenchyma. ARFI image contrast (10.4 dB) was superior to B-mode contrast (0.9 dB) for a renal mass. To our knowledge, we present the first in vivo images of abdominal malignancies in humans acquired with the ARFI method or any other technique of imaging tissue elasticity.

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.