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DOE OSTI2023

Scalar Breit interaction for molecular calculations

Variational treatment of the Dirac–Coulomb–Gaunt or Dirac–Coulomb–Breit two-electron interaction at the Dirac–Hartree–Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac–Coulomb–Gaunt and Dirac–Coulomb–Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac–Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin–spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Au n (n = 2–8) show that the scalar Dirac–Coulomb–Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac–Coulomb–Breit Hamiltonian. In conclusion, the scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

New approach to terahertz diagnostics of human psychoemotional state

A new approach to terahertz (THz) diagnostics of the human psychoemotional state is proposed, based on the analysis of the THz contribution to the total signal while simultaneously recording the IR and THz emissions from the human body (hereinafter referred to as the IR – THz image). The developed image-processing algorithm allows extraction of the informative contribution determined by the THz radiation from the total signal perceived by the recording system. Simultaneous registration of the IR – THz images of the human face and the psychophysiological indicators are carried out in situations of physical stress (short-term intense physical exercise – squats functional test), electrical stimulation, and information stress (cognitive load – simple arithmetic mental calculations). The obtained data are compared with those of similar measurements at rest. It is shown that using cluster analysis of IR – THz images it is possible to divide the test subjects into classes according to the type of reaction of the circulatory system under stressful conditions. (paper)

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2020

Effect of elastic anisotropy on thermally induced distortions of a laser beam in single cubic syngony crystals with radial cooling. Part I

We have studied thermally induced distortions of a beam in single cubic syngony crystals of all symmetry groups with an anisotropic elastic stiffness tensor. The arithmetic mean and the difference between the thermally induced phase incursions of eigenpolarisations, as well as the angle of incidence of these polarisations, are calculated for a long rod and a thin disk with radial cooling under uniform volume pumping of the active element. The position of the specific crystal orientations unrelated to its symmetry elements is investigated. The effective values of the thermo-optical constant Q in two specific orientations, as well as the thermo-optical constant P in an arbitrary orientation, are found. (invited paper)

36 MATERIALS SCIENCE↗

DOE OSTI2014

A holomorphic version of the Tate-Iwasawa method for unramified L-functions. I

Using the Tate-Iwasawa method the problem of meromorphic continuation and of the existence of a functional equation can be solved for the zeta and L-functions of one-dimensional arithmetical schemes. A new version of this method is put forward, which looks at the case of curves over a finite field and of unramified L-functions. The proof is based on a reduction of the problem to a Cousin problem on the Riemann sphere which is related to the curve under consideration. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Periodic analysis of solar activity and its link with the Arctic oscillation phenomenon

Based on spectrum analysis, we provide the arithmetic expressions of the quasi 11 yr cycle, 110 yr century cycle of relative sunspot numbers, and quasi 22 yr cycle of solar magnetic field polarity. Based on a comparative analysis of the monthly average geopotential height, geopotential height anomaly, and temperature anomaly of the northern hemisphere at locations with an air pressure of 500 HPa during the positive and negative phases of AO (Arctic Oscillation), one can see that the abnormal warming period in the Arctic region corresponds to the negative phase of AO, while the anomalous cold period corresponds to its positive phase. This shows that the abnormal change in the Arctic region is an important factor in determining the anomalies of AO. In accordance with the analysis performed using the successive filtering method, one can see that the AO phenomenon occurring in January shows a clear quasi 88 yr century cycle and quasi 22 yr decadal cycle, which are closely related to solar activities. The results of our comparative analysis show that there is a close inverse relationship between the solar activities (especially the solar magnetic field index changes) and the changes in the 22 yr cycle of the AO occurring in January, and that the two trends are basically opposite of each other. That is to say, in most cases after the solar magnetic index MI rises from the lowest value, the solar magnetic field turns from north to south, and the high-energy particle flow entering the Earth's magnetosphere increases to heat the polar atmosphere, thus causing the AO to drop from the highest value; after the solar magnetic index MI drops from the highest value, the solar magnetic field turns from south to north, and the solar high-energy particle flow passes through the top of the Earth's magnetosphere rather than entering it to heat the polar atmosphere. Thus the polar temperature drops, causing the AO to rise from the lowest value. In summary, the variance contribution rate of the changes in the quasi 110 yr century cycle and quasi 22 yr decadal cycle for the AO reaches 62.9%, indicating that solar activity is an important driving factor of the AO.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

A comparison of the velocity parameters of SiO V = 1, J = 1 − 0, and J = 2 − 1 maser emission in semiregular variables

We have determined and compared the SiO maser velocity parameters of semiregular variables in the v = 1, J = 1 − 0 (J10{sup 1}) and the v = 1, J = 2 − 1 (J21) transitions. Fourteen sources in the Mopra SiO Maser Catalogue are classified as semiregular variables of types SR, SRa, SRb, or SRc. (L2 Puppis, an SRa star with an unusual SiO maser spectrum, has been analyzed individually.) We have previously presented the overall and phase dependent velocity parameters of SiO masers associated with long period variables (LPVs) of well-established periods and maxima. A comparison of the velocity centroid (VC) difference, VC21–VC10, shows mixed results for the variable types. Some differences are negative and some positive. The SRc difference is negative, large, and relatively stable. The SRb difference has the widest distribution. The velocity ranges (VRs) of the maser emission have been compared using arithmetic averages, Gaussian fits to the distributions, and Weibull fits to the distributions. For LPVs, SRs, SRas, and SRcs the VR10 is one to a few km s{sup −1} greater than the VR21. SRcs have the largest VRs by a factor of two or three indicating the greater range over which the conditions necessary for masers to originate exist in these supergiant stars. SRbs are the only classification of semiregular variable in which the VR21 exceeds the VR10. The larger VR21 compared to VR10 for SRbs appears in all comparisons. The difference in the SRb SiO maser velocity parameters may be due to a difference in the oscillation mechanism of the star. The suggested overtone oscillations of SRbs may affect the circumstellar cloud dynamics. Little theoretical work has specifically addressed the masers in semiregular variables. Qualitative comparisons of the data with the existing models of the SiO masers in LPVs are made.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

GRay: A MASSIVELY PARALLEL GPU-BASED CODE FOR RAY TRACING IN RELATIVISTIC SPACETIMES

We introduce GRay, a massively parallel integrator designed to trace the trajectories of billions of photons in a curved spacetime. This graphics-processing-unit (GPU)-based integrator employs the stream processing paradigm, is implemented in CUDA C/C++, and runs on nVidia graphics cards. The peak performance of GRay using single-precision floating-point arithmetic on a single GPU exceeds 300 GFLOP (or 1 ns per photon per time step). For a realistic problem, where the peak performance cannot be reached, GRay is two orders of magnitude faster than existing central-processing-unit-based ray-tracing codes. This performance enhancement allows more effective searches of large parameter spaces when comparing theoretical predictions of images, spectra, and light curves from the vicinities of compact objects to observations. GRay can also perform on-the-fly ray tracing within general relativistic magnetohydrodynamic algorithms that simulate accretion flows around compact objects. Making use of this algorithm, we calculate the properties of the shadows of Kerr black holes and the photon rings that surround them. We also provide accurate fitting formulae of their dependencies on black hole spin and observer inclination, which can be used to interpret upcoming observations of the black holes at the center of the Milky Way, as well as M87, with the Event Horizon Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Fast jet tagging with MLP-Mixers on FPGAs

We explore the innovative use of MLP-Mixer models for real-time jet tagging and establish their feasibility on resource-constrained hardware like FPGAs. MLP-Mixers excel in processing sequences of jet constituents, achieving state-of-the-art performance on datasets mimicking Large Hadron Collider conditions. By using advanced optimization techniques such as High-Granularity Quantization and Distributed Arithmetic, we achieve unprecedented efficiency. These models match or surpass the accuracy of previous architectures, reduce hardware resource usage by up to 97%, double the throughput, and half the latency. Additionally, non-permutation-invariant architectures enable smart feature prioritization and efficient FPGA deployment, setting a new benchmark for machine learning in real-time data processing at particle colliders.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

On Classification of Modular Categories by Rank: Table A.1

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an application, we determine all possible fusion rules for all rank=5 modular categories and describe the corresponding monoidal equivalence classes.

Bruillard, Paul↗

DOE OSTI2023

Latent bone modelling for estimation of plutonium concentration in skeleton of former nuclear workers

Abstract The skeleton is a major plutonium retention site in the human body. Estimation of the total plutonium activity in the skeleton is a challenging problem. For most tissue donors at the United States Transuranium and Uranium Registries, a limited number of bone samples is available. The skeleton activity is calculated using plutonium activity concentration (Cskel) and skeleton weight. In this study, latent bone modelling was used to estimate Cskel from the limited number of analysed bone samples. Data from 13 non-osteoporotic whole-body donors were used to develop latent bone model (LBM) to estimate Cskel for seven cases with four to eight analysed bone samples. LBM predictions were compared to Cskel estimated using an arithmetic mean in terms of accuracy and precision. For the studied cases, LBM offered a significant reduction of uncertainty of Cskel estimate.

Environmental Sciences & Ecology↗

DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Probing the properties of event-by-event distributions in Hanbury-Brown–Twiss radii

Hanbury-Brown–Twiss interferometry is a method which yields effective widths (i.e., “HBT radii”) of homogeneity regions in the fireballs produced in heavy ion collisions. Because the initial conditions of these collisions are stochastically fluctuating, the measured HBT radii also exhibit variation on an event-by-event basis. Yet, HBT measurements have, to date, been performed only on an ensemble-averaged basis, due to inherent limitations of finite particle statistics. Here, we show that experimental measurements to date are best characterized theoretically as weighted averages of the event-by-event HBT radii, and we propose a new method for extracting experimentally both the arithmetic mean and the variance of the event-by-event distribution of HBT radii. We demonstrate the extraction of the mean and variance of this distribution for a particular ensemble of numerically generated events, and offer some ideas to extend and generalize the method to enable measurement of higher moments of the HBT distribution as well.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Stitching an asymmetric texture with T 13 × Z 5 family symmetry

We propose T 13 = Z 13 x Z 3 as the underlying non-Abelian discrete family symmetry of the asymmetric texture presented. Its mod 13 arithmetic distinguishes each Yukawa matrix element of the texture. We construct a model of effective interactions that singles out the asymmetry and equates, without fine-tuning, the products of down-quark and charged-lepton masses at a GUT-like scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Algorithms for numerically stable scattering amplitudes

The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double-precision arithmetic and reaches higher precision than a naive quadruple-precision implementation at smaller computational cost. The method is based on physics-driven modifications to propagators, vertices, and external polarizations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

TomocuPy – efficient GPU-based tomographic reconstruction with asynchronous data processing

Fast 3D data analysis and steering of a tomographic experiment by changing environmental conditions or acquisition parameters require fast, close to real-time, 3D reconstruction of large data volumes. Here a performance-optimized TomocuPy package is presented as a GPU alternative to the commonly used central processing unit (CPU) based TomoPy package for tomographic reconstruction. TomocuPy utilizes modern hardware capabilities to organize a 3D asynchronous reconstruction involving parallel read/write operations with storage drives, CPU–GPU data transfers, and GPU computations. In the asynchronous reconstruction, all the operations are timely overlapped to almost fully hide all data management time. Since most cameras work with less than 16-bit digital output, the memory usage and processing speed are furthermore optimized by using 16-bit floating-point arithmetic. As a result, 3D reconstruction with TomocuPy became 20–30 times faster than its multi-threaded CPU equivalent. Full reconstruction (including read/write operations and methods initialization) of a 2048 3 tomographic volume takes less than 7 s on a single Nvidia Tesla A100 and PCIe 4.0 NVMe SSD, and scales almost linearly increasing the data size. To simplify operation at synchrotron beamlines, TomocuPy provides an easy-to-use command-line interface. Efficacy of the package was demonstrated during a tomographic experiment on gas-hydrate formation in porous samples, where a steering option was implemented as a lens-changing mechanism for zooming to regions of interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Melt Pool characteristics on surface roughness and printability of 316L stainless steel in laser powder bed fusion

Purpose Surface quality and porosity significantly influence the structural and functional properties of the final product. This study aims to establish and explain the underlying relationships among processing parameters, top surface roughness and porosity level in additively manufactured 316L stainless steel. Design/methodology/approach A systematic variation of printing process parameters was conducted to print cubic samples based on laser power, speed and their combinations of energy density. Melt pool morphologies and dimensions, surface roughness quantified by arithmetic mean height (Sa) and porosity levels were characterized via optical confocal microscopy. Findings The study reveals that the laser power required to achieve optimal top surface quality increases with the volumetric energy density (VED) levels. A smooth top surface (Sa < 15 µm) or a rough surface with humps at high VEDs (VED > 133.3 J/mm 3 ) can serve as indicators for fully dense bulk samples, while rough top surfaces resulting from melt pool discontinuity correlate with high porosity levels. Under insufficient VED, melt pool discontinuity dominates the top surface. At high VEDs, surface quality improves with increased power as mitigation of melt pool discontinuity, followed by the deterioration with hump formation. Originality/value This study reveals and summarizes the formation mechanism of dominant features on top surface features and offers a potential method to predict the porosity by observing the top surface features with consideration of processing conditions.

Engineering↗