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DOE OSTI2017

The Thick Level-Set model for dynamic fragmentation

The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies in one dimension demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. In conclusion, additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Billion-atom synchronous parallel kinetic Monte Carlo simulations of critical 3D Ising systems

An extension of the synchronous parallel kinetic Monte Carlo (spkMC) algorithm developed by Martinez et al. [J. Comp. Phys. 227 (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors' time clocks current in a global sense. Boundary conflicts are resolved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of serial calculations, which confirms the statistical validity of our algorithm. We have analyzed the parallel efficiency of spkMC and find that it scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Quantum Fokker-Planck modeling of degenerate electrons

In this work, an implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and electron-electron collision operators are discretized using a discontinuous Galerkin method, and the electron energy distribution is updated by an implicit time integration method. The numerical scheme is designed to satisfy all conservation laws exactly. Numerical tests and comparisons with other modeling approaches are shown to demonstrate the accuracy and conservation properties of the proposed method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d + s)-wave superconductors

The time-dependent Ginzburg-Landau formalism for (d + s)-wave superconductors and their representation using auxiliary fields is investigated. By using the link variable method, we then develop suitable discretization of these equations. Numerical simulations are carried out for a mesoscopic superconductor in a homogeneous perpendicular magnetic field which revealed peculiar vortex states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Development of a Faraday cup fast ion loss detector for keV beam ions

The development and testing of a Faraday cup fast-ion loss detector capable of measuring sub 100 keV particles is documented. Such measurement capabilities play an important role in the assessment of particle confinement of nuclear fusion experiments. The detector is manufactured using thin-film deposition techniques, building upon previous work using discrete foils. This new manufacturing method allows the form factor of the sensor to become that of essentially a microchip. Analysis of the diagnostic response is performed using Monte-Carlo particle simulations. These simulations show peaks in the detector response at 40 and 70 keV. The sensor is then tested in a tunable linear accelerator capable of accelerating protons from 20 to 120 keV. Finally, the detector response was found to be well matched to simulations. Improvements to the design to facilitate robustness are discussed.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Direct measurement of storage and loss behavior in AFM force–distance experiments using the modified Fourier transformation

Force–distance curve experiments are commonly performed in atomic force microscopy (AFM) to obtain the viscoelastic characteristics of materials, such as the storage and loss moduli or compliances. The classic methods used to obtain these characteristics consist of fitting a viscoelastic material model to the experimentally obtained AFM data. Here, we demonstrate a new method that utilizes the modified discrete Fourier transform to approximate the storage and loss behavior of a material directly from the data, without the need for a fit. Additionally, one may still fit a model to the resulting storage and loss behavior if a parameterized description of the material is desired. In contrast to fitting the data to a model chosen a priori, departing from a model-free description of the material's frequency behavior guides the selection of the model, such that the user may choose the one that is most appropriate for the particular material under study. To this end, we also include modified Fourier domain descriptions of commonly used viscoelastic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗

DOE OSTI2023

Numerical discreteness errors in multispecies cosmological N -body simulations

ABSTRACT We present a detailed analysis of numerical discreteness errors in two-species, gravity-only, cosmological simulations using the density power spectrum as a diagnostic probe. In a simple set-up where both species are initialized with the same total matter transfer function, biased growth of power forms on small scales when the solver force resolution is finer than the mean interparticle separation. The artificial bias is more severe when individual density and velocity transfer functions are applied. In particular, significant large-scale offsets in power are measured between simulations with conventional offset grid initial conditions when compared against converged high-resolution results where the force resolution scale is matched to the interparticle separation. These offsets persist even when the cosmology is chosen so that the two particle species have the same mass, indicating that the error is sourced from discreteness in the total matter field as opposed to unequal particle mass. We further investigate two mitigation strategies to address discreteness errors: the frozen potential method and softened interspecies short-range forces. The former evolves particles under the approximately ‘frozen’ total matter potential in linear theory at early times, while the latter filters cross-species gravitational interactions on small scales in low-density regions. By modelling closer to the continuum limit, both mitigation strategies demonstrate considerable reductions in large-scale power spectrum offsets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Precision calculation of above-threshold multiphoton ionization in intense short-wavelength laser fields: The momentum-space approach and time-dependent generalized pseudospectral method

We present an approach in momentum (P) space for the accurate study of multiphoton and above-threshold ionization (ATI) dynamics of atomic systems driven by intense laser fields. In this approach, the electron wave function is calculated by solving the P-space time-dependent Schroedinger equation (TDSE) in a finite P-space volume under a simple zero asymptotic boundary condition. The P-space TDSE is propagated accurately and efficiently by means of the time-dependent generalized pseudospectral method with optimal momentum grid discretization and a split-operator time propagator in the energy representation. The differential ionization probabilities are calculated directly from the continuum-state wave function obtained by projecting the total electron wave function onto the continuum-state subspace using the projection operator constructed by the continuum eigenfunctions of the unperturbed Hamiltonian. As a case study, we apply this approach to the nonperturbative study of the multiphoton and ATI dynamics of a hydrogen atom exposed to intense short-wavelength laser fields. High-resolution photoelectron energy-angular distribution and ATI spectra have been obtained. We find that with the increase of the laser intensity, the photoelectron energy-angular distribution changes from circular to dumbbell shaped and is squeezed along the laser field direction. We also explore the change of the maximum photoelectron energy with laser intensity and strong-field atomic stabilization phenomenon in detail.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

Lyapunov-Based Iterative Learning of Regions of Attraction for Autonomous Systems

This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Individually optimized uniform contrast enhancement in CT angiography for the diagnosis of pulmonary thromboembolic disease—A simulation study

Purpose: To improve the diagnostic quality of CT pulmonary angiography (CTPA) by individually optimizing a biphasic contrast injection function to achieve targeted uniform contrast enhancement. To compare the results against a previously reported discrete Fourier transform (DFT) approach. Methods: This simulation study used the CTPA datasets of 27 consecutive patients with pulmonary thromboembolic disease (PE). An optimization approach was developed consisting of (1) computation of the impulse enhancement function (IEF) based on a test bolus scan, and (2) optimization of a biphasic contrast injection function using the IEF in order to achieve targeted uniform enhancement. The injection rates and durations of a biphasic contrast injection function are optimized by minimizing the difference between the resulting contrast enhancement curve and the targeted uniform enhancement curve, while conforming to the clinical constraints of injection rate and total contrast volume. The total contrast volume was limited first to the clinical standard of 65 ml, and then to the same amount used in the DFT approach for comparison. The optimization approach and the DFT approach were compared in terms of the root mean square error (RMSE) and total contrast volume used. Results: When the total contrast volume was limited to 65 ml, the optimization approach produced significantly better contrast enhancement (closer to the targeted uniform contrast enhancement) than the DFT approach (RMSE 17 HU vs 56 HU,p < 0.00001). On average, the optimization approach used 63 ml contrast, while the DFT approach used 50 ml with four patients exceeding 65 ml. When equivalent total contrast volume was used for individual patient, the optimization approach still generated significantly better contrast enhancement (RMSE 44 HU vs 56 HU, p < 0.01). Constraints for the injection function could be easily accommodated into the optimization process when searching for the optimal biphasic injection function. Conclusions: The optimization approach generated individually optimized biphasic injection functions yielding significantly better contrast enhancement compared to the DFT approach. This new approach has the potential to improve the diagnostic quality of CTPA for PE.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2022

Neural Phase Simulation

The Neural Phase Simulation (NPS) is a package of codes for simulating microstructure evolution and accelerated molecular dynamics with deep neural-networks based surrogate models. NPS is designed to offer quantitatively accurate and computationally efficient simulation capabilities by leveraging modern machine-learning techniques. The primary intended use cases of NPS are training neural network surrogate models, though performing simulations on a single node is also supported. The NPS surrogate models can be trained from ground truth simulation methods, which are supposed to be accurate but expensive, such as molecular dynamics, phase field methods, kinetic Monte Carlo and discrete dislocation dynamics.

Zhou, Fei↗

DOE OSTI2018

NCI Pilot 3 - Synthetic Data Generation Report

Two methods have been implemented so far: Independent Marginals (IM) and Bayesian Network (BN). In the IM method, it simply estimates individual discrete probability distribution from the available real data for each variable, and then sample from them.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Initial Demonstration of New Griffin Technologies for Simulating the Running-In Phase of Pebble Bed Reactors

Griffin is a reactor multiphysics modeling application based on MOOSE (Multiphysics Object-Oriented Simulation Environment) and specifically targeting transient modeling of advanced reactors. Griffin has been used recently to model pebble-bed reactors for the Nuclear Regulatory Commission (NRC) Office of Nuclear Regulatory Research and the Advanced Reactor Technology program. This modeling work has focused thus far on the direct calculation of equilibrium cores. This report documents an initial demonstration of a new running-in simulation capability. The new running-in capability is verified using the existing direct equilibrium core calculation capability. A simplified pebble-bed reactor model is then used to demonstrate the running-in simulation capability. This demonstration shows that Griffin is able to simulate years of operation during the running-in phase efficiently with each depletion step taking only several seconds. Two new technologies are also presented in this report which have been developed in Griffin that will be essential for improved accuracy both of the direct equilibrium core computation and the new running-in simulation capability. The first technology is an online cross section generation capability specifically targeted for pebble-bed reactors. This will improve the accuracy of the depletion calculation as the cross sections are generated at the exact core status. This also avoids the difficult step of pre-generating a separate standalone multigroup cross section set. Secondly, a newly implemented discretization for discontinuous finite element method (DFEM) SN transport in cylindrical (RZ) coordinates, which can be solved efficiently using the existing SN sweep solver, is discussed and some results are shown demonstrating the usefulness of the additional accuracy transport provides over a diffusion approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

SCEPTRE 2.7 User's Guide

Sandia’s Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) is a computer code that solves the linear Boltzmann transport equation, particularly targeting coupled photon-electron problems. It uses unstructured finite element meshes in space, multigroup in energy, and discrete ordinates (Sn) or other methods in angle. SCEPTRE uses an xml-based input file to specify the problem. This report documents the options and syntax of that input file.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗

DOE OSTI2026

Lyapunov-Based Iterative Learning of the Region of Attraction for Autonomous Systems

This presentation introduces a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗