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DOE OSTI2022

Electron scattering on A = 3 nuclei from quantum Monte Carlo based approaches

We perform first-principle calculations of electron-nucleus scattering on 3 He and 3 H using the Green's function Monte Carlo method and two approaches based on the factorization of the final hadronic state: the spectral-function formalism and the short-time approximation. These three methods are benchmarked among each other and compared to the experimental data for the longitudinal and transverse electromagnetic response functions of 3 He, and the inclusive cross sections of both 3 He and 3 H. Since these three approaches are based on the same description of nuclear dynamics of the initial target state, comparing their results enables a precise quantification of the uncertainties inherent to factorization schemes. At sufficiently large values of the momentum transfer, we find an excellent agreement of the Green's function Monte Carlo calculation with experimental data and with both the spectral-function formalism and the short-time approximation. Here, we also analyze the relevance of relativistic effects, whose inclusion becomes crucial to explain data at high momentum and energy transfer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Electron scattering on ${\mathbf{A=3}}$ nuclei from quantum Monte Carlo based approaches

We perform first-principle calculations of electron-nucleus scattering on $^3$He and $^3$H using the Green's function Monte Carlo method and two approaches based on the factorization of the final hadronic state: the spectral-function formalism and the short-time approximation. These three methods are benchmarked among each other and compared to the experimental data for the longitudinal and transverse electromagnetic response functions of $^3$He, and the inclusive cross sections of both $^3$He and $^3$H. Since these three approaches are based on the same description of nuclear dynamics of the initial target state, comparing their results enables a precise quantification of the uncertainties inherent to factorization schemes. At sufficiently large values of the momentum transfer, we find an excellent agreement of the Green's function Monte Carlo calculation with experimental data and with both the spectral-function formalism and the short-time approximation. We also analyze the relevance of relativistic effects, whose inclusion becomes crucial to explain data at high momentum and energy transfer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Fractional occupation numbers and self-interaction correction-scaling methods with the Fermi-Löwdin orbital self-interaction correction approach

In this work, we present a new assessment of the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) approach with an emphasis on its performance for predicting energies as a function of fractional occupation numbers (FONs) for various multielectron systems. Our approach is implemented in the massively parallelized NWChem quantum chemistry software package and has been benchmarked on the prediction of total energies, atomization energies, and ionization potentials of small molecules and relatively large aromatic systems. Within our study, we also derive an alternate expression for the FLO-SIC energy gradient expressed in terms of gradients of the Fermi-orbital eigenvalues and revisit how the FLO-SIC methodology can be seen as a constrained unitary transformation of the canonical Kohn–Sham orbitals. Finally, we conclude with calculations of energies as a function of FONs using various SIC-scaling methods to test the limits of the FLO-SIC formalism on a variety of multielectron systems. We find that these relatively simple scaling methods do improve the prediction of total energies of atomic systems as well as enhance the accuracy of energies as a function of FONs for other multielectron chemical species.

fractional occupation number↗

DOE OSTI2022

AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. Here, the same goes for ansätze on a quantum computer. We develop a unitary coupled cluster method based on the antisymmetrized geminal power (AGP)—a state formally equivalent to the number-projected Bardeen–Cooper–Schrieffer wavefunction. We demonstrate our method for the single-band Fermi–Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than O(√M) in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Estimation of uncertainties for subcritical benchmark measurements - 14387

Subcritical measurements are used for many applications including nonproliferation, treaty verification, in-situ monitoring for criticality, and reactor subcriticality monitoring. Most analysis methods involve correlated neutron detection, based upon the property that fission events can create multiple neutrons that are born at nearly the same time (on a scale of 10{sup -13} or 10{sup -14} seconds). Many different time-correlated methods have been used since the 1950's and are still widely utilized today. This particular work describes an uncertainty analysis of measured data using the Hage-Cifarelli formalism of the Feynman Variance-to-Mean method. The Feynman Variance-to-Mean method was introduced by Feynman et al. in 1956 and is based upon the differences between the detector count data and the data that would be expected from measurements taken from a Poissonian source. The Hage-Cifarelli formalism relates moments of the Feynman histograms to several parameters of a system: leakage multiplication (M{sub L}), spontaneous fission rate (F{sub S}), (α,n) neutron emission rate (S{sub α}), detector efficiency (ε), and the moments of the number of neutrons emitted per fission (ν). The first part of the uncertainty method described in this work will show how to determine uncertainties of the first (R{sub 1}) and second (R{sub 2}) reduced factorial moments of the Feynman histograms. The second part of the method will describe how to determine the uncertainties in the other parameters given uncertainties in the reduced factorial moments; in particular, this work will focus on determining the uncertainties in M{sub L} and F{sub S}. This work will utilize measured data from a recent benchmark evaluation with a 4.5 kg sphere of α-phase plutonium to validate the uncertainty analysis. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Rapid decline of Lyα emission toward the reionization era

The observed deficit of strongly Lyα emitting galaxies at z > 6.5 is attributed to increasing neutral hydrogen in the intergalactic medium (IGM) and/or to the evolving galaxy properties. To investigate this we have performed very deep near-IR spectroscopy of z ≳ 7 galaxies using MOSFIRE on the Keck-I Telescope. We measure the Lyα fraction at z ∼ 8 using two methods. First, we derived N {sub Lyα}/N {sub tot} directly, using extensive simulations to correct for incompleteness. Second, we used a Bayesian formalism (introduced by Treu et al.) that compares the z > 7 galaxy spectra to models of the Lyα equivalent width (W {sub Lyα}) distribution at z ∼ 6. We explored two simple evolutionary scenarios: pure number evolution where Lyα is blocked in some fraction of galaxies (perhaps due to the IGM being opaque along only some fraction of sightlines) and uniform dimming evolution where Lyα is attenuated in all galaxies by a constant factor (perhaps owing to processes from galaxy evolution or a slowly increasing IGM opacity). The Bayesian formalism places stronger constraints compared with the direct method. Combining our data with that in the literature, we find that at z ∼ 8 the Lyα fraction has dropped by a factor of >3 (84% confidence interval) using both the dimming and number evolution scenarios, compared to the z ∼ 6 values. Furthermore, we find a tentative positive Bayesian evidence favoring the number evolution scenario over dimming evolution, extending trends observed at z ≲ 7 to higher redshift. A comparison of our results with theoretical models implies the IGM volume averaged neutral hydrogen fraction ≳ 0.3, suggesting that we are likely witnessing reionization in progress at z ∼ 8.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Quantum-field-theoretical approach to phase–space techniques: Symmetric Wick theorem and multitime Wigner representation

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. Analogs of Wick’s theorem for the Weyl ordering are verified. Using the Bose–Hubbard chain as an example, we show how these may be applied to constructing a mapping of the system in question to phase space. Regularisation issues and the reordering problem for the Heisenberg operators are addressed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Color instabilities in the quark–gluon plasma

When the quark–gluon plasma (QGP) – a system of deconfined quarks and gluons – is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. Here, we begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh–Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, are analyzed in detail. We pay particular attention to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches – purely classical or quantum – to simulate the temporal evolution of an unstable quark–gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Optimal experimental design: Formulations and computations

Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Theoretical Study of Oxovanadium(IV) Complexation with Formamidoximate: Implications for the Design of Uranyl-Selective Adsorbents

Poly(acrylamidoxime) fibers are the current state of the art adsorbent for mining uranium from seawater. However, the competition between uranyl (UO 2 2+ ) and vanadium ions poses a challenge to mining on the industrial scale. In this work, we employ density functional theory (DFT) and coupled-cluster methods (CCSD(T)) in the restricted formalism to investigate potential binding motifs of the oxovanadium(IV) ion (VO 2+ ) with the formamidoximate ligand. Consistent with experimental EXAFS data, the hydrated six-coordinate complex is predicted to be preferred over the hydrated five-coordinate complex. Here, our investigation of formamidoximate-VO 2+ complexes universally identified the most stable binding motif formed by chelating a tautomerically rearranged imino hydroxylamine via the imino nitrogen and hydroxylamine oxygen. The alternative binding motifs for amidoxime chelation via a non-rearranged tautomer and 2 coordination are found to be ~11 kcal/mol less stable. Ultimately, the difference in the most stable VO 2+ and UO 2 2+ binding conformation has important implications for the design of more selective UO 2 2+ ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A hybrid calorimetry-simulation model of mixing enthalpy for molten salt

Calorimetric determination of enthalpies of mixing (ΔH mix ) in multicomponent molten salts is often interpreted using empirical models that lack physically meaningful parameters. However, for improving pyrochemical separation of spent nuclear fuel, where lanthanides are major fission products and critical elements, a deeper thermodynamic understanding of the link between excess thermodynamic properties and solvation structure is critically needed. In this work, we implement a hybrid and physics-informed framework, MIVM+Calorimetry+AIMD, which integrates experimentally measured ΔH mix (via high temperature drop calorimetry) with solvation structures from ab initio molecular dynamics (AIMD). This approach is demonstrated using LaCl 3 mixed with eutectic LiCl-KCl (58 mol% – 42 mol%) at 873 K and 1133 K. MIVM-derived parameters enable extrapolation of excess Gibbs energy and La 3+ activity across compositions. In contrast, direct ΔH mix predictions from AIMD and polarizable ion model simulations deviate significantly. By incorporating experimentally benchmarked solvation structures into an interpretable thermodynamic model, the MIVM+Calorimetry+AIMD formalism achieves higher accuracy and generalizable method for studying molten salts, offering a robust path for understanding and optimizing molten salt chemistry relevant to nuclear fuel cycles and separation science.

Goncharov, Vitaliy G. [Washington State Univ., Pul↗

DOE OSTI2016

Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs

We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry–Pérot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. As a result, we show BICs at the center and on the edge of the Brillouin zone protected by symmetry, BICs at generic wave vectors not protected by symmetry, and the annihilation of BICs at low-symmetry wave vectors.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Consistent interaction vertices in arbitrary topological BF theories

Here we extend the previous results from [12] to the computation of all consistent self-interactions for topological BF theories with maximal field spectra in D =5,6,7,8 and present some partial results on possible generalizations on a space-time of arbitrary dimension D. For convenience, the deformation of the solution to the master equation in the context of the BRST-antifield formalism is used as a general method of constructing consistent interacting gauge field theories together with most of the standard hypotheses on quantum field theories on Minkowski space-times.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Control of simulation of a particle accelerator as a spatially distributed system

The work deals with the construction of strategy for finding optimal control of systems for spatially distributed systems on an example of problems in physics beams. The suggested approach is based on use of exact and approximate invariants as a controlling mechanism for control of modelling process of beam lines. The classical problem of optimal control of similar systems as an optimal control problem is formulated in a functional space. This approach is based on algebraic methods Lie and the corresponding matrix formalism that allows you to build not only the formal procedures for finding optimal solutions, but also provide the necessary constructive computational procedures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Fano effect dominance over Coulomb blockade in transport properties of parallel coupled quantum dot system

Theoretical study of the Coulomb blockade effect on transport properties (Transmission Probability and I-V characteristics) for varied configuration of coupled quantum dot system has been studied by using Non Equilibrium Green Function(NEGF) formalism and Equation of Motion(EOM) method in the presence of magnetic flux. The self consistent approach and intra-dot Coulomb interaction is being taken into account. As the key parameters of the coupled quantum dot system such as dot-lead coupling, inter-dot tunneling and magnetic flux threading through the system can be tuned, the effect of asymmetry parameter and magnetic flux on this tuning is being explored in Coulomb blockade regime. The presence of the Coulomb blockade due to on-dot Coulomb interaction decreases the width of transmission peak at energy level ε + U and by adjusting the magnetic flux the swapping effect in the Fano peaks in asymmetric and symmetric parallel configuration sustains despite strong Coulomb blockade effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Hierarchy of forward-backward stochastic Schrödinger equation

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗