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DOE OSTI2022

ARPIST: Provably accurate and stable numerical integration over spherical triangles

Numerical integration on spherical triangles, including the computation of their areas, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and stable integration of functions on spherical triangles. ARPIST is based on an easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency. More importantly, ARPIST overcomes potential instabilities in computing the Jacobian of the transformation, even for poorly shaped triangles that may occur at poles in regular longitude-latitude meshes, by avoiding potential catastrophic rounding errors. We compare our proposed technique with L’Huilier’s Theorem for computing the area of spherical triangles, and also compare it with the recently developed LSQST method (Beckmann et al., 2014) and a radial-basis-function-based technique (Reeger and Fornberg, 2016) for integration of smooth functions on spherical triangulations. In conclusion, our results show that ARPIST enables better or comparable accuracy over previous methods while being easier to implement, significantly faster, and more tolerant of poor element shapes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Spherical time-encoded radiation imaging simulations

Radiation source localization is important for nuclear nonproliferation and can be obtained using time-encoded imaging systems with unsegmented detectors. A scintillation crystal can be used with a moving coded-aperture mask to vary the detected count rate produced from radiation sources in the far field. The modulation of observed counts over time can be used to reconstruct an image with the known coded-aperture mask pattern. Current time-encoded imaging systems incorporate cylindrical coded-aperture masks and have limits to their fully coded imaging field-of-view. This work focuses on expanding the field-of-view to 4π by using a novel spherical coded-aperture mask. A regular icosahedron is used to approximate a spherical mask. This icosahedron consists of 20 equilateral triangles; the faces of which are each subdivided into four equilateral triangle-shaped voxels which are then projected onto a spherical surface, creating an 80-voxel coded-aperture mask. Furthermore, these polygonal voxels can be made from high-Z materials for gamma-ray modulation and/or low-Z materials for neutron modulation. In this work, we present Monte Carlo N-Particle (MCNP) simulations and simple models programmed in Mathematica to explore image reconstruction capabilities of this 80-voxel coded-aperture mask.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Shape-Selective Mesoscale Nanoarchitectures: Preparation and Photocatalytic Performance

We create ordered arrays of shape-selective gold-titania composite nanomaterials at the mesoscale (100 µm to 5 mm) by a combination of both bottom-up and top-down approaches for exquisite control of the size, shape, and arrangement of nanomaterials. Lithographic techniques along with wet chemical synthetic methods were combined to create these composite nanomaterials. The photocatalytic activity of these TiO 2, TiO 2 -Au and SiO 2 -TiO 2 -Au nano-composite mesoscale materials was monitored by the photodegradation of a model analyte, methyl orange, under UV and visible (Vis) illumination. Bare TiO 2 - and SiO 2 -TiO 2 -coated pillar arrays showed significant activity toward methyl orange in UV light with degradation rates on the order of 10 −4 –10 −3 min −1 . The photocatalytic activity of these arrays was also found to depend on the nanoparticle shape, in which particles with more edges and corners were found to be more reactive than spherical particles (i.e., the photocatalytic activity decreased as follows: diamonds > squares > triangles > spheres). SiO 2 -TiO 2 -Au nano-composite pillar arrays were tested in both UV and Vis light and showed increased activity in Vis light but decreased activity in UV light as compared to the bare semiconductor arrays. Additionally, the Au nanorod-functionalized nanoarrays exhibit a strong shape-dependence in their photocatalytic activity toward methyl orange degradation in Vis light.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Deformation and Collectivity in Doubly Magic 208 Pb

Lead-208 is the heaviest known doubly magic nucleus and its structure is therefore of special interest. Despite this magicity, which acts to provide a strong restorative force toward sphericity, it is known to exhibit both strong octupole correlations and some of the strongest quadrupole collectivity observed in doubly magic systems. In this Letter, we employ state-of-the-art experimental equipment to conclusively demonstrate, through four Coulomb-excitation measurements, the presence of a large, negative, spectroscopic quadrupole moment for both the vibrational octupole 3$^{−}_{1}$ and quadrupole 2$^{+}_{1}$ state, indicative of a preference for prolate deformation of the states. The observed quadrupole moment is discussed in the context of the expected splitting of the 3 − ⊗3 − two-phonon states, due to the coupling of the quadrupole and octupole motion. These results are compared with theoretical values from three different methods, which are unable to reproduce both the sign and magnitude of this deformation. Thus, in spite of its well-studied nature, 208 Pb remains a puzzle for our understanding of nuclear structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗