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DOE OSTI2017

Effect of Delayed Energy Release on Power Normalization in Reactor Depletion Calculations

Reactor depletion calculations typically assume that the thermal power of the reactor is directly proportional to the instantaneous fission rate within the core. However, approximately 7% of the sensible energy released per fission comes from the radioactive decay of fission products, which occurs alter the fission event. Thus, the assumed direct relationship between reactor power and fission rate implies that all fission products have reached secular equilibrium within the core. In situations where fission product concentrations have not reached equilibrium (e.g., shortly after reactor startup or a change in reactor power during operation), the delayed energy release due to fission product decay creates a nonlinear relationship between reactor power and fission rate. This non-linear relationship, in turn, affects the neutron flux levels and fuel consumption rate required to maintain the desired thermal power output for the reactor. For example, during initial startup of a commercial light water reactor the apparent energy release per fission is ∼7{sup %} lower than the typical value of ∼200 MeV/fission due to the potential energy stored in radioactive fission products. As a consequence, the flux level (and, therefore, uranium consumption rate) in the reactor must be correspondingly higher to preserve the desired reactor power. As the reactor operates and fission product inventories increase, the decay heat produced by the reactor will rise, producing a corresponding increase in the apparent energy release per fission. The characteristic time-dependent behavior of energy release due to the decay of fission products (i.e., decay heat) following reactor startup, shutdown, or changes in reactor power is well-known and widely-used in reactor safety analyses. However, to our knowledge, the effects of time-dependent decay heating rates on reactor depletion calculations have not been thoroughly investigated. In this paper, we present a simple methodology for explicitly accounting for delayed energy release due to the decay of fission products in reactor depletion calculations. In the proposed method, the balance equations for fission product decay energy are incorporated into the depletion coefficient matrix, using a strategy similar to that described by Isotalo in 2016. The modified system of differential equations can be solved via a matrix exponential approximation (or other suitable numerical method) to yield solutions for both nuclide densities and decay energy emission densities as a function of time. Numerical results from the method are presented for simplified (one-group point (0-D) and 1-D) representations of a commercial pressurized water reactor (PWR), in order to estimate the effect of delayed energy release on fuel consumption and flux level immediately following reactor startup.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2014

Linear optical response of finite systems using multishift linear system solvers

We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

A fast non-Fourier method for Landau-fluid operators

An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of “delocalization kernels” [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost and memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUT++ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUT++ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUT++ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Global calculation of two-neutrino double- β decay within the finite amplitude method in nuclear density functional theory

Two-neutrino double-beta (2νββ) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine 2νββ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. Here we work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to 2νββ half-lives themselves, to evaluate the 2νββ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Relativistic four-component calculations of indirect nuclear spin-spin couplings with efficient evaluation of the exchange-correlation response kernel

In this work, we report on the development and implementation of a new scheme for efficient calculation of indirect nuclear spin-spin couplings in the framework of four-component matrix Dirac-Kohn-Sham approach termed matrix Dirac-Kohn-Sham restricted magnetic balance resolution of identity for J and K, which takes advantage of the previous restricted magnetic balance formalism and the density fitting approach for the rapid evaluation of density functional theory exchange-correlation response kernels. The new approach is aimed to speedup the bottleneck in the solution of the coupled perturbed equations: evaluation of the matrix elements of the kernel of the exchange-correlation potential. The performance of the new scheme has been tested on a representative set of indirect nuclear spin-spin couplings. The obtained results have been compared with the corresponding results of the reference method with traditional evaluation of the exchange-correlation kernel, i.e., without employing the fitted electron densities. Overall good agreement between both methods was observed, though the new approach tends to give values by about 4%-5% higher than the reference method. On the average, the solution of the coupled perturbed equations with the new scheme is about 8.5 times faster compared to the reference method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

VMAT QA: Measurement-guided 4D dose reconstruction on a patient

Purpose: To develop and validate a volume-modulated arc therapy (VMAT) quality assurance (QA) tool that takes as input a time-resolved, low-density ({approx}10 mm) cylindrical surface dose map from a commercial helical diode array, and outputs a high density, volumetric, time-resolved dose matrix on an arbitrary patient dataset. This first validation study is limited to a homogeneous 'patient.'Methods: A VMAT treatment is delivered to a diode array phantom (ARCCHECK, Sun Nuclear Corp., Melbourne, FL). 3DVH software (Sun Nuclear) derives the high-density volumetric dose using measurement-guided dose reconstruction (MGDR). MGDR cylindrical phantom results are then used to perturb the three-dimensional (3D) treatment planning dose on the patient dataset, producing a semiempirical volumetric dose grid. Four-dimensional (4D) dose reconstruction on the patient is also possible by morphing individual sub-beam doses instead of the composite. For conventional (3D) dose comparison two methods were developed, using the four plans (Multi-Target, C-shape, Mock Prostate, and Head and Neck), including their structures and objectives, from the AAPM TG-119 report. First, 3DVH and treatment planning system (TPS) cumulative point doses were compared to ion chamber in a cube water-equivalent phantom ('patient'). The shape of the phantom is different from the ARCCHECK and furthermore the targets were placed asymmetrically. Second, coronal and sagittal absolute film dose distributions in the cube were compared with 3DVH and TPS. For time-resolved (4D) comparisons, three tests were performed. First, volumetric dose differences were calculated between the 3D MGDR and cumulative time-resolved patient (4D MGDR) dose at the end of delivery, where they ideally should be identical. Second, time-resolved (10 Hz sampling rate) ion chamber doses were compared to cumulative point dose vs time curves from 4D MGDR. Finally, accelerator output was varied to assess the linearity of the 4D MGDR with global fluence change. Results: Across four TG-119 plans, the average PTV point dose difference in the cube between 3DVH and ion chamber is 0.1 {+-} 1.0%. Average film vs TPS {gamma}-analysis passing rates are 83.0%, 91.1%, and 98.4% for 1%/2 mm, 2%/2 mm, and 3%/3 mm threshold combinations, respectively, while average film vs 3DVH {gamma}-analysis passing rates are 88.6%, 96.1%, and 99.5% for the same respective criteria. 4D MGDR was also sufficiently accurate. First, for 99.5% voxels in each case, the doses from 3D and 4D MGDR at the end of delivery agree within 0.5%local dose-error/1 mm distance. Moreover, all failing voxels are confined to the edge of the cylindrical reconstruction volume. Second, dose vs time curves track between the ion chamber and 4D MGDR within 1%. Finally, 4D MGDR dose changes linearly with the accelerator output: the difference between cumulative ion chamber and MGDR dose changed by no more than 1% (randomly) with the output variation range of 10%. Conclusions: Even for a well-commissioned TPS, comparison metrics show better agreement on average to MGDR than to TPS on the arbitrary-shaped measurable 'patient.' The method requires no more accelerator time than standard QA, while producing more clinically relevant information. Validation in a heterogeneous thoracic phantom is under way, as is the ultimate application of 4D MGDR to virtual motion studies.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

High temperature phonon dispersion in graphene using classical molecular dynamics

Phonon dispersion and phonon density of states of graphene are calculated using classical molecular dynamics simulations. In this method, the dynamical matrix is constructed based on linear response theory by computing the displacement of atoms during the simulations. The computed phonon dispersions show excellent agreement with experiments. The simulations are done in both NVT and NPT ensembles at 300 K and found that the LO/TO modes are getting hardened at the Γ point. The NPT ensemble simulations capture the anharmonicity of the crystal accurately and the hardening of LO/TO modes is more pronounced. We also found that at 300 K the C-C bond length reduces below the equilibrium value and the ZA bending mode frequency becomes imaginary close to Γ along K-Γ direction, which indicates instability of the flat 2D graphene sheets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Spin dynamics simulation of electron spin relaxation in Ni{sup 2+}(aq)

The ability to quantitatively predict and analyze the rate of electron spin relaxation of open-shell systems is important for electron paramagnetic resonance and paramagnetic nuclear magnetic resonance spectroscopies. We present a combined molecular dynamics (MD), quantum chemistry (QC), and spin dynamics simulation method for calculating such spin relaxation rates. The method is based on the sampling of a MD trajectory by QC calculations, to produce instantaneous parameters of the spin Hamiltonian used, in turn, to numerically solve the Liouville-von Neumann equation for the time evolution of the spin density matrix. We demonstrate the approach by simulating the relaxation of electron spin in an aqueous solution of Ni{sup 2+} ion. The spin-lattice (T{sub 1}) and spin-spin (T{sub 2}) relaxation rates are extracted directly from the simulations of the time dependence of the longitudinal and transverse magnetization, respectively. Good agreement with the available, indirectly obtained experimental data is obtained by our method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

SU-E-T-341: DVH-Based Comparison of True 3D Measurements to a Delta4 System

Purpose: Delta4 dosimetric software can be used to calculate DVH-based metrics for patient-specific quality assurance from measurements made by a Delta4 QA device. This study investigates the effectiveness of a novel transform method that transposes measurements made with a full-density 3D dosimeter onto patient anatomy, enabling the calculation of DVHs. This allows for DVH comparisons from the transformed dose distribution, which are based on true 3D measurements, to those from the Delta4 system, which are based on semi-3D measurements and interpolation. Methods: A double-arc VMAT treatment for a head-and-neck case was delivered to a 1kg PRESAGE 3D dosimeter inserted into a polyurethane head phantom. The dosimeter was readout using an in-house optical-CT scanner to gather full-density 3D dosimetric data. The transform method is achieved by multiplication of the measured doses with a “transformation matrix” which accounts for heterogeneities and differences in geometry between the patient and the phantom. The transformation matrix is a voxel-by-voxel division of the patient planned dose by the phantom planned dose, both calculated in the treatment planning system (Eclipse). The transformed distribution was then overlaid on the patient CT data, enabling the calculation of DVHs. The same VMAT treatment was delivered to the Delta4 phantom and DVH data was calculated using its associated software. Results: The transformed dose distribution showed good agreement with calculated patient values, determined by similarity in dose profiles between the two distributions and a 3D gamma index passing rate of 94.87% for 3%/3mm criteria. For every structure contained within the dosimeter volume, the transformed DVHs demonstrated better agreement than the Delta4 DVHs, when compared to the values calculated in the treatment planning system. Conclusion: The coupled technique of full-density 3D dose measurements and the presented transform method enables clinical patient-specific quality assurance data that is more accurate than the semi-3D Delta4 system. This work was supported by NIH R01CA100835.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Multi-level coupled cluster theory

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and present proof of principle applications. The formalism is an essential tool in order to obtain size-intensive complexity in the calculation of local molecular properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Interaction picture density matrix quantum Monte Carlo

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Detecting superconductivity out of equilibrium

Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above Tc. This poses the question of how to reliably identify the emergence of long-range order, in particular superconductivity, out of equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved angle-resolved photoemission spectroscopy experiments to probe for the formation of a condensate in the two-particle channel.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Performance of wave function and Green's function methods for non-equilibrium many-body dynamics

Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime. Published by the American Physical Society 2025

Reeves, Cian C. (ORCID:0009000642581845)↗

DOE OSTI2015

RADIATIVE TRANSFER MODELING OF THE ENIGMATIC SCATTERING POLARIZATION IN THE SOLAR Na i D{sub 1} LINE

The modeling of the peculiar scattering polarization signals observed in some diagnostically important solar resonance lines requires the consideration of the detailed spectral structure of the incident radiation field as well as the possibility of ground level polarization, along with the atom's hyperfine structure and quantum interference between hyperfine F-levels pertaining either to the same fine structure J-level, or to different J-levels of the same term. Here we present a theoretical and numerical approach suitable for solving this complex non-LTE radiative transfer problem. This approach is based on the density-matrix metalevel theory (where each level is viewed as a continuous distribution of sublevels) and on accurate formal solvers of the transfer equations and efficient iterative methods. We show an application to the D-lines of Na i, with emphasis on the enigmatic D{sub 1} line, pointing out the observable signatures of the various physical mechanisms considered. We demonstrate that the linear polarization observed in the core of the D{sub 1} line may be explained by the effect that one gets when the detailed spectral structure of the anisotropic radiation responsible for the optical pumping is taken into account. This physical ingredient is capable of introducing significant scattering polarization in the core of the Na i D{sub 1} line without the need for ground-level polarization.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1983

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

NASA NTRS1984

Ultrasonic wave propagation in two-phase media - Spherical inclusions

Fu, L. S.↗

DOE OSTI2018

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10 -5 , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.

97 MATHEMATICS AND COMPUTING↗