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DOE OSTI2017

The Random Ray Method for neutral particle transport

A new approach to solving partial differential equations (PDEs) based on the method of characteristics (MOC) is presented. The Random Ray Method (TRRM) uses a stochastic rather than deterministic discretization of characteristic tracks to integrate the phase space of a problem. TRRM is potentially applicable in a number of transport simulation fields where long characteristic methods are used, such as neutron transport and gamma ray transport in reactor physics as well as radiative transfer in astrophysics. In this study, TRRM is developed and then tested on a series of exemplar reactor physics benchmark problems. The results show extreme improvements in memory efficiency compared to deterministic MOC methods, while also reducing algorithmic complexity, allowing for a sparser computational grid to be used while maintaining accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Advances in the computation of the Sjöstrand, Rossi, and Feynman distributions

This study illustrates recent computational advances in the application of the Sjöstrand (area), Rossi, and Feynman methods to estimate the effective multiplication factor of a subcritical system driven by an external neutron source. The methodologies introduced in this study have been validated with the experimental results from the KUKA facility of Japan by Monte Carlo (MCNP6 and MCNPX) and deterministic (ERANOS, VARIANT, and PARTISN) codes. When the assembly is driven by a pulsed neutron source generated by a particle accelerator and delayed neutrons are at equilibrium, the Sjöstrand method becomes extremely fast if the integral of the reaction rate from a single pulse is split into two parts. These two integrals distinguish between the neutron counts during and after the pulse period. To conclude, when the facility is driven by a spontaneous fission neutron source, the timestamps of the detector neutron counts can be obtained up to the nanosecond precision using MCNP6, which allows obtaining the Rossi and Feynman distributions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Rapid sampling of stochastic displacements in Brownian dynamics simulations

Here, we present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4×10 6 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. Finally, a high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Variance reduction techniques for Monte Carlo neutron noise simulations

The small fluctuations of the neutron flux caused by small perturbations of the macroscopic cross-sections take the name of neutron noise. Advanced Monte Carlo methods have been recently proposed in order to solve the neutron noise equations in the frequency domain, which allows establishing reference solutions to validate faster but approximate deterministic solvers. Due to the presence of particles carrying two statistical weights (for the real and imaginary components of the noise field), both of which may be positive or negative, Monte-Carlo simulations of neutron noise pose distinct challenges in terms of variance reduction. In this work we investigate two variance-reduction techniques, namely branchless collisions and weight cancellation, and probe their effectiveness for a benchmark con- figuration concerning the noise field induced by a pin with oscillating cross sections in a fuel assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

Although current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build-up to detonation, a new paradigm is put forth for modelling sub-grid, reaction-induced fluctuations (i.e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin-type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i.e. deterministic) and diffusion (i.e. stochastic) coefficients. Furthermore, the particle values are propagated and averaged to calculate the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave-like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no-go estimation (e.g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i.e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Hence, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub-grid stochastic behaviour of shocked heterogeneous solid explosives.

42 ENGINEERING↗

DOE OSTI2022

Particle Swarm Optimisation for group structure optimization for radiotherapy shielding

Neutron transport simulations are ubiquitous in nuclear engineering because they allow one to model experimental systems and render a model platform for easy perturbation of experimental designs. In addition, simulations allow one to gain experimental insight without actually having to go through the trouble of building a physical experiment. Neutron transport simulations can be stochastic or deterministic based. Stochastic neutron transport simulations are typically simulated using the Monte Carlo method and yield very accurate solutions but are computationally expensive, while deterministic methods are typically faster but can be less accurate. Here we focus on optimizing the accuracy of deterministic neutron transport simulations for radiotherapy simulations. Deterministic neutron transport requires discretization of angle, energy, and space to appropriately analyze the system one is trying to model. Discretization of energy is challenging because of the highly variable neutron flux at certain neutron energies. Improper discretization of energy in the transport model can lead to erroneous results and therefore inaccurate interpretations of the solution. In this study, we evaluate Particle Swarm Optimization (PSO) as a mechanism for selecting optimal group structures for radiotherapy shielding. We tested the particle swarm optimization algorithm on radiotherapy shielding problems using Los Alamos National Laboratory's (LANL) main deterministic transport code PARTISN. Results show that the optimized energy group structures generated from the optimization algorithm outperformed LANL's standard energy group structures, and therefore demonstrate utility in using PSO to expedite computation times due to the increased accuracy obtained with a smaller but optimized group structure. (authors)

43 PARTICLE ACCELERATORS↗

DOE OSTI2016

Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem

In this paper, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Finally, marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms.

42 ENGINEERING↗

DOE OSTI2017

Design Analysis of SNS Target StationBiological Shielding Monoligh with Proton Power Uprate

This report documents the analysis of the dose rate in the experiment area outside the Spallation Neutron Source (SNS) target station shielding monolith with proton beam energy of 1.3 GeV. The analysis implemented a coupled three dimensional (3D)/two dimensional (2D) approach that used both the Monte Carlo N-Particle Extended (MCNPX) 3D Monte Carlo code and the Discrete Ordinates Transport (DORT) two dimensional deterministic code. The analysis with proton beam energy of 1.3 GeV showed that the dose rate in continuously occupied areas on the lateral surface outside the SNS target station shielding monolith is less than 0.25 mrem/h, which complies with the SNS facility design objective. However, the methods and codes used in this analysis are out of date and unsupported, and the 2D approximation of the target shielding monolith does not accurately represent the geometry. We recommend that this analysis is updated with modern codes and libraries such as ADVANTG or SHIFT. These codes have demonstrated very high efficiency in performing full 3D radiation shielding analyses of similar and even more difficult problems.

42 ENGINEERING↗

DOE OSTI2018

Improving the real-time probabilistic channel flood forecasting by incorporating the uncertainty of inflow using the particle filter

An accurate and reliable real-time flood forecast is crucial for mitigating flood disasters. The errors associated with the inflow boundary forcing data are considered as an important source of uncertainties in hydraulic model. In this paper, a real-time probabilistic channel flood forecasting model is developed with a novel function to incorporate the uncertainty of the forcing inflow. This new approach couples a hydraulic model with the particle filter (PF) data assimilation algorithm, a sequential Bayesian Monte Carlo method. The stage observations at hydrological stations are assimilated at each time step to update the model states in order to improve the next time step’s forecasting. This new approach is tested against a real flood event occurred in the upper Yangtze River. As compared with the open loop simulations, the evaluations of model performance with several deterministic and probabilistic metrics indicate that the accuracy of the ensemble mean prediction and the reliability of the uncertainty quantification are improved pronouncedly as a result of the PF assimilation. Further assessment of the prediction results at different lead times shows that the improvement of model performance deteriorates with the increase of the lead time due to the gradual diminishing of the updating effect for the initial conditions. Based on the analyses of the number of particles and the assimilation frequency, we find that the optimal number of particles can be determined by balancing the model performance and the computation cost, while a high assimilation frequency is preferred to incorporate the emerging observations to update the model states to match the real conditions.

Channel flood forecasting, probabilistic forecast,↗

DOE OSTI2026

CADIS and FW-CADIS Variance Reduction in Gamma Transport for Predicting Prompt Forensics Signatures

The goal of prompt nuclear forensics is to determine the characteristics of a nuclear detonation based on the signatures available almost immediately after the explosion. An important characteristic is the reaction time history (RTH), a measure of the device’s rate of neutron multiplication. The RTH can be estimated by observation of the gamma radiation emitted from the detonation, which can be detected directly or observed indirectly as Teller light. Gamma transport simulations used to predict these radiation fields are often modeled stochastically using the Monte Carlo N-Particle (MCNP) code, which can be a computationally demanding task due to the number of particle histories needed to achieve statistical convergence. In an attempt to improve the efficiency of these calculations, we evaluate two variance reduction techniques: Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS). These methods use a deterministically calculated adjoint flux to create weight windows and source biasing that guide MCNP sampling. We study the utility of CADIS and FW-CADIS for their use in MCNP gamma transport for nuclear forensics prediction simulations. Furthermore, the results demonstrate that both CADIS and FW-CADIS improve the accuracy for forensics-focused simulations, with CADIS being most beneficial in direct detection and FW-CADIS being ideal for computing a global Teller light source.

CADIS↗

DOE OSTI2018

BAM: bias assignment method to generate mock catalogues

Combining the statistics of dark matter tracers from a high-resolution cosmological N-body simulation and the dark matter density field calculated from down-sampled initial conditions using efficient structure formation solvers, we extract the halo-bias relation on a mesh of a 3$h^{-1}$ Mpc cell side resolution as a function of properties of the dark matter density field (e.g. local density, cosmic web type), automatically including stochastic, deterministic, local and non-local components. We use this information to sample the halo density field, accounting for ignored dependencies through an iterative process. By construction, our approach reaches ~1% accuracy in the majority of the k-range up to the Nyquist frequency without systematic deviations for power spectra (about $k ~ 1h$ Mpc -1 ) using either particle mesh or Lagrangian perturbation theory based solvers. When using phase-space mapping to compensate the low resolution of the approximate gravity solvers, our method reproduces the bispectra of the reference within 10% precision studying configurations tracing the quasi-non-linear regime. BAM has the potential to become a standard technique to produce mock halo and galaxy catalogues for future galaxy surveys and cosmological studies being highly accurate, efficient and parameter free.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

Bailo, Rafael (ORCID:0000000180183799)↗

DOE OSTI2021

Assessment of model parameters in MFiX particle-in-cell approach

The limitations in numerical treatment of solids-phase in conventional methods like Discrete Element Model and Two-Fluid Model have facilitated the development of alternative techniques such as Particle-In-Cell (PIC). However, a number of parameters are involved in PIC due to its empiricism. In this work, global sensitivity analysis of PIC model parameters is performed under three distinct operating regimes common in chemical engineering applications, viz. settling bed, bubbling fluidized bed and circulating fluidized bed. Simulations were performed using the PIC method in Multiphase Flow with Interphase eXchanges (MFiX) developed by National Energy Technology Laboratory (NETL). A non-intrusive uncertainty quantification (UQ) based approach is applied using Nodeworks to first construct an adequate surrogate model and then identify the most influential parameters in each case. This knowledge will aid in developing an effective design of experiments and determine optimal parameters through techniques such as deterministic or statistical calibration.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Comparison of Generation of Higher-Order Neutron Scattering Cross Sections

The generation of high-order neutron scattering cross sections consistent with high-fidelity simulations remains an area of active research. Popular options include generating cross sections from continuous energy Monte Carlo calculations or generating cross sections from a deterministic neutron transport calculation with high-fidelity tabulated cross sections. Both options present challenges. Monte Carlo simulations can naturally process continuous energy cross section data and allow for the general description of anisotropic neutron scattering given a scattering law. However, Monte Carlo simulations are inherently related to particle weighting and it has been suggested that this may be unacceptable for generating high-order neutron scattering cross sections. Deterministic neutron transport calculations can easily calculate high-order moments of the flux to appropriately calculate higher-order neutron scattering cross sections but are generally limited by discretization of space, energy, and angle. In this work, the trade-offs between generation of high-order neutron scattering cross sections via Monte Carlo and deterministic neutron transport methods are investigated. The methods implemented in the Monte Carlo computer program Serpent and the deterministic fast reactor neutron cross section generator MC2-3 are compared. Cross sections resulting from these methods are used in Rattlesnake, a deterministic neutron transport code developed by Idaho National Laboratory (INL), and results are compared to a reference continuous energy Monte Carlo calculation. Whereas previous work investigating the effects of anisotropic neutron scattering has focused on light water reactor (LWR) simulations, this work focuses on high-order neutron scattering cross sections as they relate to fast reactor simulations. To investigate the consequences of the Serpent and MC2-3 methodologies, a test problem is developed. The test problem is a one-dimensional geometry with fast reactor materials designed to demonstrate deep penetration and exacerbate the effects of high-order neutron scattering. Based on the results of the deep penetration test problem, it is concluded that P3 neutron scattering cross sections are sufficient to describe anisotropic scattering in fast reactor materials. Any neutron scattering of order higher than P3 offers negligible change in the eigenvalue of the test problem. Additionally, it is determined that the methodology as implemented in Serpent is applicable for generating high-order neutron scattering cross sections through at least P3 in fast reactor materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Automated label flows for excited states of correlation functions in lattice gauge theory

Extracting excited states from lattice gauge theory correlation functions can be achieved through $χ^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. Further, as an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Lastly, potential applications and caveats to the usage of LD are included as a summary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Cost-optimized Automated Variance Reduction for Highly Angle-dependent Radiation Transport Analyses [Dissertation]

Monte Carlo variance-reduction techniques that directly bias particle direction have historically received limited attention despite being useful for many radiation transport applications such as those in which radiation travels through large regions with a low probability of colliding. One such technique is known as DXTRAN (short for deterministic transport) in the MCNP Monte Carlo radiation transport code. Until now, effectively applying DXTRAN in calculations is largely based on empirical observations of computational performance. Optimal DXTRAN parameters are identified through manual iteration. This work develops new mathematical descriptions of the DXTRAN variance-reduction process and demonstrates a new automated variance-reduction method that applies these mathematical formulations to determine the optimal application of DXTRAN in a given problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗