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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Effects of cosine tapering window on quantum phase estimation

Here, we provide a modification to the quantum phase estimation algorithm (QPEA) [Abrams and Lloyd, Phys. Rev. Lett. 83, 5162 (1999); Cleve et al., Proc. R. Soc. A 454, 339 (1998); Nielsen and Chuang, Quantum computation and quantum information, 2002.] inspired by classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Fixed lines in four fermion models in two dimensions

Motivated by conjectures about near-horizon dynamics in quantum gravity, we search for lines of perturbatively accessible fixed points emanating from models of N free fermions. Through two loops we find a new class of models, apart from the well-known Abelian Thirring models. Further study is needed to see whether these can lead to true conformal manifolds, or perhaps a new class of large- N fixed points. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2020

Materials Data on Li9V6(P8O29)2 by Materials Project

Li9V6(P8O29)2 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are nine inequivalent Li sites. In the first Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share corners with four PO4 tetrahedra and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.89–2.24 Å. In the second Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.88–2.32 Å. In the third Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with three VO6 octahedra and corners with four PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 64–68°. There are a spread of Li–O bond distances ranging from 1.86–2.27 Å. In the fourth Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.92–2.22 Å. In the fifth Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.89–2.21 Å. In the sixth Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.89–2.21 Å. In the seventh Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.89–2.27 Å. In the eighth Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.94–2.22 Å. In the ninth Li site, Li is bonded to four O atoms to form distorted LiO4 tetrahedra that share corners with two LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.94–2.30 Å. There are six inequivalent V sites. In the first V site, V is bonded to six O atoms to form VO6 octahedra that share corners with six PO4 tetrahedra and edges with two LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.87–1.99 Å. In the second V site, V is bonded to six O atoms to form VO6 octahedra that share a cornercorner with one LiO4 tetrahedra, corners with six PO4 tetrahedra, and an edgeedge with one LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.91–1.99 Å. In the third V site, V is bonded to six O atoms to form VO6 octahedra that share a cornercorner with one LiO4 tetrahedra and corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.86–1.99 Å. In the fourth V site, V is bonded to six O atoms to form VO6 octahedra that share corners with six PO4 tetrahedra and an edgeedge with one LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.83–2.02 Å. In the fifth V site, V is bonded to six O atoms to form VO6 octahedra that share corners with six PO4 tetrahedra and edges with two LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.86–2.01 Å. In the sixth V site, V is bonded to six O atoms to form VO6 octahedra that share a cornercorner with one LiO4 tetrahedra, corners with six PO4 tetrahedra, and edges with two LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.82–1.96 Å. There are sixteen inequivalent P sites. In the first P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 41–44°. There are a spread of P–O bond distances ranging from 1.47–1.61 Å. In the second P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–45°. There are a spread of P–O bond distances ranging from 1.48–1.61 Å. In the third P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–44°. There are a spread of P–O bond distances ranging from 1.49–1.62 Å. In the fourth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and corners with four LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 36–37°. There are a spread of P–O bond distances ranging from 1.51–1.58 Å. In the fifth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 28–33°. There are a spread of P–O bond distances ranging from 1.49–1.61 Å. In the sixth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with three LiO4 tetrahedra. The corner-sharing octahedral tilt angles are 45°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the seventh P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–42°. There are a spread of P–O bond distances ranging from 1.50–1.62 Å. In the eighth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with three LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 43–44°. There are a spread of P–O bond distances ranging from 1.50–1.61 Å. In the ninth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–44°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the tenth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–41°. There are a spread of P–O bond distances ranging from 1.50–1.61 Å. In the eleventh P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 40–45°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the twelfth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 30–36°. There are a spread of P–O bond distances ranging from 1.49–1.62 Å. In the thirteenth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 25–33°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the fourteenth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 36–45°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the fifteenth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 36–45°. There are a spread of P–O bond distances ranging from 1.47–1.62 Å. In the sixteenth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with three LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 41–48°. There are a spread of P–O bond distances ranging from 1.51–1.62 Å. There are fifty-eight inequivalent O sites. In the first O site, O is bonded in a bent 120 degrees geometry to one Li and one P atom. In the second O site, O is bonded in a distorted trigonal planar geometry to one Li, one V, and one P atom. In the third O site, O is bonded in a bent 120 degrees geometry to one Li and one P atom. In the fourth O site, O is bonded in a bent 150 degrees geometry to one V and one P atom. In the fifth O site, O is bonded in a distorted trigonal planar geometry to one Li, one V, and one P atom. In the sixth O site, O is bonded in a 3-coordinate geometry to one Li, one V, and one P atom. In the seventh O site, O is bonded in a bent 150 degrees geometry to one V and one P atom. In the eighth O site, O is bonded in a trigonal planar geometry to two Li and one P atom. In the ninth O site, O is bonded in a distorted trigonal planar geometry to one Li, one V, and one P atom. In the tenth O site, O is bonded in a bent 150 degrees geometry to one V and one P atom. In the eleventh O site, O is bonded in a bent 150 degrees geometry to one V and one P atom. In the twelfth O site, O is bonded in a 3-coordinate geometry to one Li, one V, and one P atom. In the thirteenth O site, O is bonded in a linear geometry to one Li and one P atom. In the fourteenth O site, O is bonded in a single-bond geometry to one P atom. In the fifteenth O site, O is bonded in a 3-coordinate geometry to one Li, one V, and one P atom. In the sixteenth O site, O is bonded in a distorted trigonal planar geometry to one Li, one V, and one P atom. In the seventeenth O site, O is bonded in a distorted trigonal non-coplanar geometry to one Li, one V, and one P atom. In the eighteenth O site, O is bonded in a distorted trigonal planar geometry to one Li, one V, and one P atom. In the nineteenth O site, O is bonded in a bent 120 degrees geometry to two P atoms. In the twentieth O site, O is bonded in a trigonal planar geometry to two Li and one P atom. In the twenty-first O site, O is bonded in a bent 120 degrees geometry to one Li and one P atom. In the twenty-second O site, O is bonded in a trigonal planar geometry to one Li, one V, and one P atom. In the twenty-third O site, O is bonded in a 3-coordinate geometry to one Li, one V, and one P atom. In the twenty-fourth O site, O is bonded in a distorted trigonal planar geometry to one Li, one V, and one P atom. In the twenty-fifth O site, O is bonded in a bent 150 degrees geometry to one V and one P atom. In the twenty-sixth O site, O is bonded in a bent 150 degrees geometry to one V and one P atom. In the twenty-seventh O site, O is bonded in a distorted bent 120 degrees geometry to two P atoms. In the twenty-eighth O site, O is bonded in a bent 120 degrees geometry to one Li and one P atom. In the twenty-ninth O site, O is bonded in a bent 120 degrees geometry to one Li and one P atom. In the thir

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li4V3P8O29 by Materials Project

Li4V3P8O29 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.91–2.33 Å. In the second Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.35 Å. In the third Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.99–2.19 Å. In the fourth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.88–2.32 Å. In the fifth Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.89–2.27 Å. In the sixth Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.89–2.24 Å. In the seventh Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 tetrahedra that share a cornercorner with one LiO4 tetrahedra, corners with four PO4 tetrahedra, and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.91–2.21 Å. In the eighth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.97–2.29 Å. There are six inequivalent V+4.67+ sites. In the first V+4.67+ site, V+4.67+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.86–1.94 Å. In the second V+4.67+ site, V+4.67+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra and edges with two LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.88–1.99 Å. In the third V+4.67+ site, V+4.67+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.88–1.90 Å. In the fourth V+4.67+ site, V+4.67+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra and an edgeedge with one LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.84–1.99 Å. In the fifth V+4.67+ site, V+4.67+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra and an edgeedge with one LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.89–2.02 Å. In the sixth V+4.67+ site, V+4.67+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.84–1.98 Å. There are sixteen inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–41°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 40–46°. There are a spread of P–O bond distances ranging from 1.48–1.61 Å. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–43°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the fourth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 30–37°. There are a spread of P–O bond distances ranging from 1.49–1.63 Å. In the fifth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 29–35°. There are a spread of P–O bond distances ranging from 1.49–1.61 Å. In the sixth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 40–43°. There are a spread of P–O bond distances ranging from 1.48–1.62 Å. In the seventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 41–42°. There are a spread of P–O bond distances ranging from 1.50–1.62 Å. In the eighth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–46°. There are a spread of P–O bond distances ranging from 1.50–1.61 Å. In the ninth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–40°. There are a spread of P–O bond distances ranging from 1.47–1.62 Å. In the tenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–40°. There are a spread of P–O bond distances ranging from 1.50–1.61 Å. In the eleventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–41°. There are a spread of P–O bond distances ranging from 1.50–1.62 Å. In the twelfth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 30–35°. There are a spread of P–O bond distances ranging from 1.49–1.60 Å. In the thirteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 27–36°. There are a spread of P–O bond distances ranging from 1.49–1.61 Å. In the fourteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–43°. There are a spread of P–O bond distances ranging from 1.48–1.60 Å. In the fifteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–44°. There are a spread of P–O bond distances ranging from 1.48–1.63 Å. In the sixteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 42–47°. There are a spread of P–O bond distances ranging from 1.51–1.62 Å. There are fifty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 120 degrees geometry to one Li1+ and one P5+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V+4.67+, and one P5+ atom. In the third O2- site, O2- is bonded in a single-bond geometry to one P5+ atom. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the fifth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the sixth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the seventh O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the eighth O2- site, O2- is bonded in a trigonal planar geometry to two Li1+ and one P5+ atom. In the ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V+4.67+, and one P5+ atom. In the tenth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the eleventh O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the twelfth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V+4.67+, and one P5+ atom. In the thirteenth O2- site, O2- is bonded in a single-bond geometry to one P5+ atom. In the fourteenth O2- site, O2- is bonded in a single-bond geometry to one P5+ atom. In the fifteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V+4.67+, and one P5+ atom. In the sixteenth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the seventeenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+, one V+4.67+, and one P5+ atom. In the eighteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V+4.67+, and one P5+ atom. In the nineteenth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two P5+ atoms. In the twentieth O2- site, O2- is bonded in a trigonal planar geometry to two Li1+ and one P5+ atom. In the twenty-first O2- site, O2- is bonded in a bent 120 degrees geometry to one Li1+ and one P5+ atom. In the twenty-second O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the twenty-third O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V+4.67+, and one P5+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V+4.67+, and one P5+ atom. In the twenty-fifth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the twenty-sixth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the twenty-seventh O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two P5+ atoms. In the twenty-eighth O2- site, O2- is bonded in a bent 120 degrees geometry to one Li1+ and one P5+ atom. In the twenty-ninth O2- site, O2- is bonded in a bent 120 degrees geometry to one Li1+ and one P5+ atom. In the thirtieth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the thirty-first O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the thirty-second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V+4.67+, and one P5+ atom. In the thirty-third O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V+4.67+, and one P5+ atom. In the thirty-fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one V+4.67+ and one P5+ atom. In the thir

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li6V3P8O29 by Materials Project

Li6V3P8O29 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twelve inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.95–2.24 Å. In the second Li1+ site, Li1+ is bonded in a distorted see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.94–2.09 Å. In the third Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 2.00–2.19 Å. In the fourth Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 tetrahedra that share corners with four PO4 tetrahedra and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 1.97–2.25 Å. In the fifth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.91–2.28 Å. In the sixth Li1+ site, Li1+ is bonded to four O2- atoms to form distorted LiO4 tetrahedra that share corners with four PO4 tetrahedra and an edgeedge with one VO6 octahedra. There are a spread of Li–O bond distances ranging from 2.01–2.21 Å. In the seventh Li1+ site, Li1+ is bonded in a distorted see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 2.00–2.09 Å. In the eighth Li1+ site, Li1+ is bonded to four O2- atoms to form LiO4 tetrahedra that share corners with three VO6 octahedra and corners with four PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 67–69°. There are a spread of Li–O bond distances ranging from 1.86–2.31 Å. In the ninth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 2.00–2.24 Å. In the tenth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.99–2.20 Å. In the eleventh Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.98–2.59 Å. In the twelfth Li1+ site, Li1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Li–O bond distances ranging from 1.93–2.83 Å. There are six inequivalent V4+ sites. In the first V4+ site, V4+ is bonded to six O2- atoms to form VO6 octahedra that share a cornercorner with one LiO4 tetrahedra, corners with six PO4 tetrahedra, and edges with two LiO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.87–2.01 Å. In the second V4+ site, V4+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.89–2.01 Å. In the third V4+ site, V4+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.86–2.01 Å. In the fourth V4+ site, V4+ is bonded to six O2- atoms to form VO6 octahedra that share a cornercorner with one LiO4 tetrahedra and corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.89–2.02 Å. In the fifth V4+ site, V4+ is bonded to six O2- atoms to form VO6 octahedra that share a cornercorner with one LiO4 tetrahedra and corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.85–2.04 Å. In the sixth V4+ site, V4+ is bonded to six O2- atoms to form VO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of V–O bond distances ranging from 1.90–2.06 Å. There are sixteen inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 35–41°. There are a spread of P–O bond distances ranging from 1.50–1.60 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedral tilt angles are 39°. There are a spread of P–O bond distances ranging from 1.52–1.61 Å. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 41–46°. There are a spread of P–O bond distances ranging from 1.51–1.62 Å. In the fourth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 32–35°. There are a spread of P–O bond distances ranging from 1.49–1.59 Å. In the fifth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra. The corner-sharing octahedra tilt angles range from 36–38°. There are a spread of P–O bond distances ranging from 1.50–1.60 Å. In the sixth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–43°. There are a spread of P–O bond distances ranging from 1.51–1.63 Å. In the seventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–47°. There are a spread of P–O bond distances ranging from 1.52–1.61 Å. In the eighth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 40–41°. There are a spread of P–O bond distances ranging from 1.52–1.62 Å. In the ninth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 46–48°. There are a spread of P–O bond distances ranging from 1.49–1.61 Å. In the tenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 37–40°. There are a spread of P–O bond distances ranging from 1.50–1.60 Å. In the eleventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one LiO4 tetrahedra, and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 45–49°. There are a spread of P–O bond distances ranging from 1.49–1.62 Å. In the twelfth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 30–36°. There are a spread of P–O bond distances ranging from 1.48–1.59 Å. In the thirteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with three VO6 octahedra and a cornercorner with one LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 31–37°. There are a spread of P–O bond distances ranging from 1.50–1.60 Å. In the fourteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 41–48°. There are a spread of P–O bond distances ranging from 1.50–1.62 Å. In the fifteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 37–46°. There are a spread of P–O bond distances ranging from 1.52–1.61 Å. In the sixteenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with two VO6 octahedra, a cornercorner with one PO4 tetrahedra, and corners with two LiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 46–48°. There are a spread of P–O bond distances ranging from 1.51–1.62 Å. There are fifty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to two Li1+ and one P5+ atom. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the third O2- site, O2- is bonded in a 3-coordinate geometry to two Li1+ and one P5+ atom. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the fifth O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the sixth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V4+, and one P5+ atom. In the seventh O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the eighth O2- site, O2- is bonded in a distorted trigonal planar geometry to two Li1+ and one P5+ atom. In the ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V4+, and one P5+ atom. In the tenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+, one V4+, and one P5+ atom. In the eleventh O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the twelfth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+, one V4+, and one P5+ atom. In the thirteenth O2- site, O2- is bonded in a single-bond geometry to one P5+ atom. In the fourteenth O2- site, O2- is bonded in a single-bond geometry to one P5+ atom. In the fifteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V4+, and one P5+ atom. In the sixteenth O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the seventeenth O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+, one V4+, and one P5+ atom. In the eighteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V4+, and one P5+ atom. In the nineteenth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two P5+ atoms. In the twentieth O2- site, O2- is bonded in a 3-coordinate geometry to three Li1+ and one P5+ atom. In the twenty-first O2- site, O2- is bonded in a 3-coordinate geometry to two Li1+ and one P5+ atom. In the twenty-second O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the twenty-third O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+, one V4+, and one P5+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V4+, and one P5+ atom. In the twenty-fifth O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the twenty-sixth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V4+, and one P5+ atom. In the twenty-seventh O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two P5+ atoms. In the twenty-eighth O2- site, O2- is bonded in a 4-coordinate geometry to three Li1+ and one P5+ atom. In the twenty-ninth O2- site, O2- is bonded in a 3-coordinate geometry to three Li1+ and one P5+ atom. In the thirtieth O2- site, O2- is bonded in a distorted trigonal planar geometry to one Li1+, one V4+, and one P5+ atom. In the thirty-first O2- site, O2- is bonded in a bent 150 degrees geometry to one V4+ and one P5+ atom. In the thir

36 MATERIALS SCIENCE↗
DOE OSTI2023

Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks

The angular momentum of gas feeding a black hole (BH) may be misaligned with respect to the BH spin, resulting in a tilted accretion disk. Rotation of the BH drags the surrounding spacetime, manifesting as Lense–Thirring torques that lead to disk precession and warping. We study these processes by simulating a thin (H/r = 0.02), highly tilted ($\tau$ = 65°) accretion disk around a rapidly rotating (a = 0.9375) BH at extremely high resolutions, which we performed using the general-relativistic magnetohydrodynamic code H-AMR. The disk becomes significantly warped and continuously tears into two individually precessing subdisks. We find that mass accretion rates far exceed the standard α-viscosity expectations. We identify two novel dissipation mechanisms specific to warped disks that are the main drivers of accretion, distinct from the local turbulent stresses that are usually thought to drive accretion. In particular, we identify extreme scale height oscillations that occur twice an orbit throughout our disk. When the scale height compresses, "nozzle" shocks form, dissipating orbital energy and driving accretion. Separate from this phenomenon, there is also extreme dissipation at the location of the tear. This leads to the formation of low-angular momentum "streamers" that rain down onto the inner subdisk, shocking it. The addition of low-angular momentum gas to the inner subdisk causes it to rapidly accrete, even when it is transiently aligned with the BH spin and thus unwarped. These mechanisms, if general, significantly modify the standard accretion paradigm. Additionally, they may drive structural changes on much shorter timescales than expected in α-disks, potentially explaining some of the extreme variability observed in active galactic nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1969

Validity of approximations used in mesonic atom calculations.

The Deser-Goldberger-Baumann-Thirring (DGBT) formula [a = 1/4B(ΔE 1S /|E 1S |)] and other various approximations commonly used to extract meson-nucleus scattering lengths from energy-level measurements on mesonic atoms are studied by means of a model calculation and are shown to be inadequate for most of the π − -mesonic atoms commonly considered. A simple empirical formula is obtained in place of the DGBT formula for the π − -mesonic atoms of the light nuclei. The DGBT formula is also examined for the case of the K − −He 4 atom and is found to be a good approximation.

Ryoichi Seki↗
NASA NTRS1972

Vertical motions inferred from satellite radiometry

Medium resolution radiometer measurements on Nimbus 2 and 3 and relatively high resolution measurements on Nimbus 4 have been made in 6.4 to 6.9 and 20 to 23 microns water vapor absorption regions where the weighed means in the observed radiation occur in the troposphere near the 400 and 600 mbar levels, respectively. An example of the imagery obtained from the Nimbus 4 temperature-humidity infrared radiometer (THIR) is shown. This example demonstrates clearly that there is a distinct pattern difference between the 6.7 microns observations coming from the midtroposphere and the more common 11.5 microns atmospheric window observations showing the emitted radiation associated with opaque surfaces such as the ground or optically thick clouds.

Salomonson, V. V.↗
NASA NTRS1972

Meteorological applications of the Nimbus 4 temperature-humidity infrared radiometer, 6.7 micron channel data.

Midtropospheric circulation features under essentially clear sky conditions have been noted in the data of the 6.7-micron channel of the Nimbus 4 temperature-humidity infrared radiometer (THIR), while at the same time these features were undetected by the 11.5-micron channel of the same instrument. The characteristic response of the 6.7-micron channel to atmospheric water vapor emission is primarily from the 250-mb (10.5 km) to 500-mb (5.5 km) levels with a peak contribution at 350 mb (8 km). Dry and moist patterns seen in the 6.7-micron data on Feb. 21, 1971, have been integrated into a 400-mb moisture analysis over the United States. This analysis provided more detailed and timely information than was conventionally available about the advection of dry air aloft prior to development of the Mississippi Tornado of February 1971.

Allison, L. J.↗
NASA NTRS1972

Study to determine cloud motion from meteorological satellite data

Processing techniques were tested for deducing cloud motion vectors from overlapped portions of pairs of pictures made from meteorological satellites. This was accomplished by programming and testing techniques for estimating pattern motion by means of cross correlation analysis with emphasis placed upon identifying and reducing errors resulting from various factors. Techniques were then selected and incorporated into a cloud motion determination program which included a routine which would select and prepare sample array pairs from the preprocessed test data. The program was then subjected to limited testing with data samples selected from the Nimbus 4 THIR data provided by the 11.5 micron channel.

Clark, B. B.↗
NASA NTRS1973

Analysis of the relativistic orbiting gyroscope experiment

A gyroscope experiment designed to measure both the geodetic and the Lense-Thirring precessions to an accuracy of 0.01 arc-second per year appears economically and technically feasible. It is estimated that an accuracy of about one part in 10 to the 11th power in an Eotvos experiment would be required to detect a situation in which the weak interaction contributed to the inertial masses but not the gravitational masses of nuclei; a correspondingly higher accuracy in the experiment is required to detect the situation where the weak interaction contributed to the gravitational masses some fraction between zero and one of its contribution to the inertial masses.

Coulter, A. C.↗
NASA NTRS1974

Tropical cyclone rainfall as measured by the Nimbus 5 electrically scanning microwave radiometer

A selected group of 1973 North Pacific Ocean tropical cyclones was studied by using data from the Nimbus 5 Electrically Scanning Microwave Radiometer (ESMR), the Temperature-Humidity Infrared Radiometer (THIR), NOAA-2 and USAF DMSP imageries. From the unique combination of infrared, visible, and microwave data, it was possible during various stages of storm development to differentiate between dense cirrus outflow and rain areas, to identify centers of circulation and areas of low-level moisture, and by the use of a theoretical model to estimate semi-quantitatively areas of light, moderate, and heavy rainfall rates.

Allison, L. J.↗
NASA NTRS1975

Relativity mission with two counter-orbiting polar satellites

In 1918, J. Lense and H. Thirring calculated that a moon in orbit around a massive rotating planet would experience a nodal dragging effect due to general relativity. We describe an experiment to measure this effect with two counter-orbiting drag-free satellites in polar earth orbit. For a 2 1/2 year experiment, the measurement accuracy should approach 1%. In addition to precision tracking data from existing ground stations, satellite-to-satellite Doppler ranging data are taken at points of passing near the poles. New geophysical information on both earth harmonics and tidal effects is inherent in the polar ranging data.

Van Patten, R. A.↗
NASA NTRS1975

The Nimbus 6 data catalog. Volume 1: 12 June 1975 through 31 August 1975. Data orbits 1 through 1082

Subsections 1.2 through 1.10 of this catalog summarize the operational highlights of the individual experiments, present preliminary experiment results, and call attention to known data anamolies. Section 2 lists the on-off times for each experiment and provides a method for determining the geographical coverage of each experiment. Section 3 shows selected HIRS, SCAMS and ESMR images, and Section 4 presents THIR montages. Section 5 presents corrections to The Nimbus 6 User's Guide.

Source record↗
NASA NTRS1976

A possible experiment with two counter-orbiting drag-free satellites to obtain a new test of Einstein's general theory of relativity and improved measurements in geodesy

In 1918, Lense and Thirring calculated that a moon in orbit around a massive rotating planet would experience a nodal dragging effect due to general relativity. We describe an experiment to measure this effect by means of two counter-orbiting drag-free satellites in polar orbit about the earth. For a 2-1/2 year experiment, the measurement should approach an accuracy of 1%. An independent measurement of the geodetic precession of the orbit plane due to the motion about the sun may also be possible to about 10% accuracy. In addition to precision tracking data from existing ground stations, satellite-to-satellite Doppler data are taken at points of passing near the poles to yield an accurate measurement of the separation distance between the two satellites. New geophysical information on both earth harmonics and tidal effects is inherent in this polar ranging data.

Van Patten, R. A.↗
NASA NTRS1981

Implications of photometric and spectroscopic periods of SS433

It is suggested that a comparison of the periodicities inferred from spectroscopic and photometric observations of SS433 may help clarify its structure. The interaction between the orbital and beam motions may produce sideband periods in the photometry. It is found that Lense-Thirring and slaved disk models make differing predictions.

Katz, J. I.↗