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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Fast inference of Boosted Decision Trees in FPGAs for particle physics

We describe the implementation of Boosted Decision Trees in the hls4ml library, which allows the translation of a trained model into FPGA firmware through an automated conversion process. Thanks to its fully on-chip implementation, hls4ml performs inference of Boosted Decision Tree models with extremely low latency. With a typical latency less than 100 ns, this solution is suitable for FPGA-based real-time processing, such as in the Level-1 Trigger system of a collider experiment. These developments open up prospects for physicists to deploy BDTs in FPGAs for identifying the origin of jets, better reconstructing the energies of muons, and enabling better selection of rare signal processes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Benchmarking Monte Carlo codes for the modelling of low-energy neutron production target reactions

The increasing adoption of accelerator-based neutron sources (ABNS) for applications including neutron capture therapy (NCT) research has highlighted the need for accurate simulation tools. Precise modelling of the neutron production target is crucial to ensure that simulated predictions of neutron beam characteristics used for subsequent beam shaping assembly design are reliable. This work presents a comprehensive benchmarking of four widely-used Monte Carlo codes - Geant4, PHITS, FLUKA (CERN), and MCNP - for modelling low-energy neutron production target reactions. Using their recommended physics models and cross-section libraries, we evaluate each code’s performance in simulating four beam-target reactions: 7 Li(p,n) 7 Be, 9 Be(p,n) 9 B, 9 Be(d,n) 10 B, and C(d,n)N. Predictions of neutron yield, angular distributions, and energy spectra are compared against available thick target experimental data. Results show varying levels of agreement between the codes depending on the reaction type, energy range, and beam characteristics. Geant4, MCNP and PHITS are the overall best performing codes for the simulation of total neutron yield and yield in the forward direction across most reactions. Across energies where experimental benchmarks exist, inter-code discrepancies in total and forward-directed yield are typically 10 to 30%, with larger deviations at near-threshold incident ion energies. PHITS provides the best overall reproduction of experimental spectra, particularly for the 9 Be(p,n) 9 B reaction. Additionally, PHITS demonstrates superior computational performance for most reactions. These findings provide valuable guidance for ABNS design, highlighting the strengths and limitations of each code for the simulation of low-energy neutron production reactions.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Multigroup Examination of Nickel-Reflected HEU System

Critical configurations of HEU-MET-FAST-003 (HMF-003) from the International Criticality Safety Benchmark Evaluation Project Handbook were modeled for addition into the Verified, Archived Library of Inputs and Data maintained at Oak Ridge National Laboratory. HMF-003 contains models of a highly enriched uranium sphere with a spherical metal reflector of natural uranium, tungsten carbide, or nickel. For these simple models, good agreement is expected between the k eff calculated with continuous-energy (CE) and multigroup (MG) transport. However, using the CSAS5 sequence of the SCALE 6.2.4 package, the 8 in. thick nickel reflector model resulted in a difference of around 1.2 % Δ k . Results presented a clear indication of poor performance for the SCALE 252-group based on ENDF/B-VII.1 cross section library for this model. The bias was investigated over a range of nickel thickness and then compared with other MG libraries available in SCALE 6.2.4. As the nickel thickness increases, the MG k eff deviates from the CE result, confirming a performance issue with the MG calculation. Additionally, the reactions were compared between the two libraries to help determine the cause of k eff bias. Finally, additional MG libraries within SCALE 6.3 and based on ENDF/B-VII.1 and ENDF/B-VIII were reviewed. The 302-group and 1597-group result in significant improvements compared with the 252-group library. Nickel cross sections were modified from ENDF/B-VII.1 to ENDF/B-VIII. For the ENDF/B-VIII library, the deviation between the CE libraries and MG libraries is less pronounced than for ENDF/VII.1, except for the 1597-group. This examination clearly indicates the importance of validating calculations with applicable benchmark experiments and caution when using MG libraries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Particle track classification using quantum associative memory

Pattern recognition algorithms are commonly employed to simplify the challenging and necessary step of track reconstruction in sub-atomic physics experiments. Aiding in the discrimination of relevant interactions, pattern recognition seeks to accelerate track reconstruction by isolating signals of interest. In high collision rate experiments, such algorithms can be particularly crucial for determining whether to retain or discard information from a given interaction even before the data is transferred to tape. As data rates, detector resolution, noise, and inefficiencies increase, pattern recognition becomes more computationally challenging, motivating the development of higher efficiency algorithms and techniques. Quantum associative memory is an approach that seeks to exploits quantum mechanical phenomena to gain advantage in learning capacity, or the number of patterns that can be stored and accurately recalled. Here, we study quantum associative memory based on quantum annealing and apply it to the particle track classification. We focus on discrimination models based on Ising formulations of quantum associative memory model (QAMM) recall and quantum content-addressable memory (QCAM) recall. We characterize classification performance of these approaches as a function detector resolution, pattern library size, and detector inefficiencies, using the D-Wave 2000Q processor as a testbed. Discrimination criteria is set using both solution-state energy and classification labels embedded in solution states. We find that energy-based QAMM classification performs well in regimes of small pattern density and low detector inefficiency. In contrast, state-based QCAM achieves reasonably high accuracy recall for large pattern density and the greatest recall accuracy robustness to a variety of detector noise sources.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Stochastically estimated covariance matrices for independent and cumulative fission yields in the ENDF/B-VIII.0 and JEFF-3.3 evaluations

A Monte-Carlo method for the generation of correlation and covariance matrices for independent and cumulative fission yields has been developed. The method uses a constrained Monte-Carlo resampling structure in order to vary evaluated fission yield libraries in a way that meets basic conservation principles. This results in the generation of correlation/covariance matrices with limited model bias and uncertainty; the matrices are primarily reflective of the evaluated fission yield uncertainties and correlations that arise from the evaluation process. This method has been applied to generate correlation and covariance matrices for all of the fissioning systems of the ENDF/B-VIII.0 and JEFF-3.3 evaluations, marking the first time such matrices have been generated for all of these systems. These covariance matrices have been published online for immediate public use. These correlation and covariance matrices can be used to improve uncertainty estimation in calculations of reactor antineutrino emission rates, decay heat problems, and nuclear forensics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A fast Monte Carlo cell-by-cell simulation for radiobiological effects in targeted radionuclide therapy using pre-calculated single-particle track standard DNA damage data

Introduction: We developed a new method that drastically speeds up radiobiological Monte Carlo radiation-track-structure (MC-RTS) calculations on a cell-by-cell basis. Methods: The technique is based on random sampling and superposition of single-particle track (SPT) standard DNA damage (SDD) files from a “pre-calculated” data library, constructed using the RTS code TOPAS-nBio, with “time stamps” manually added to incorporate dose-rate effects. This time-stamped SDD file can then be input into MEDRAS, a mechanistic kinetic model that calculates various radiation-induced biological endpoints, such as DNA double-strand breaks (DSBs), misrepairs and chromosomal aberrations, and cell death. As a benchmark validation of the approach, we calculated the predicted energy-dependent DSB yield and the ratio of direct-to-total DNA damage, both of which agreed with published in vitro experimental data. We subsequently applied the method to perform a superfast cell-by-cell simulation of an experimental in vitro system consisting of neuroendocrine tumor cells uniformly incubated with 177 Lu. Results and discussion: The results for residual DSBs, both at 24 and 48 h post-irradiation, are in line with the published literature values. Our work serves as a proof-of-concept demonstration of the feasibility of a cost-effective “in silico clonogenic cell survival assay” for the computational design and development of radiopharmaceuticals and novel radiotherapy treatments more generally.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the equivalent Dancoff factor cell method performing slowing down calculations on the fly for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for pin-cell, unit-cell, and fuel assembly problems with various resonance self-shielding conditions based on very high temperature reactor, high temperature test reactor, and Empire benchmark cores, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also showed that the methodology worked well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Building an Efficient Cluster Cosmology Software Package for Modeling Cluster Counts and Lensing

We introduce a software suite developed for galaxy cluster cosmological analysis with the Dark Energy Survey Data. Cosmological analyses based on galaxy cluster number counts and weak-lensing measurements need efficient software infrastructure to explore an increasingly large parameter space, and account for various cosmological and astrophysical effects. Our software package is designed to model the cluster observables in a wide-field optical survey, including galaxy cluster counts, their averaged weak-lensing masses, or the cluster's averaged weak-lensing radial signals. To ensure maximum efficiency, this software package is developed in C++ in the CosmoSIS software framework, making use of the CUBA integration library. We also implement a testing and validation scheme to ensure the quality of the package. We demonstrate the effectiveness of this development by applying the software to the Dark Energy Survey Year 1 galaxy cluster cosmological data sets, and acquired cosmological constraints that are consistent with the fiducial Dark Energy Survey analysis.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the on-the-fly slowing down method for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Among various on-the-fly slowing down methods, the equivalent Dancoff factor cell method was employed. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for the very high temperature reactor (VHTR), high temperature test reactor (HTTR), and Empire benchmark problems with various resonance self-shielding conditions, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also show that the methodology works well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

`SkyPy`: A package for modelling the Universe

SkyPy is an open-source Python package for simulating the astrophysical sky. It comprises a library of physical and empirical models across a range of observables and a command-line script to run end-to-end simulations. The library provides functions that sample realisations of sources and their associated properties from probability distributions. Simulation pipelines are constructed from these models using a YAML-based configuration syntax, while task scheduling and data dependencies are handled internally and the modular design allows users to interface with external software. SkyPy is developed and maintained by a diverse community of domain experts with a focus on software sustainability and interoperability. By fostering development, it provides a framework for correlated simulations of a range of cosmological probes including galaxy populations, large scale structure, the cosmic microwave background, supernovae and gravitational waves. Version 0.4 implements functions that model various properties of galaxies including luminosity functions, redshift distributions and optical photometry from spectral energy distribution templates. Future releases will provide additional modules, for example, to simulate populations of dark matter halos and model the galaxy-halo connection, making use of existing software packages from the astrophysics community where appropriate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Performance of the Initial Implementation of the Shift Monte Carlo Code in SCALE 6.3

The Shift Monte Carlo code will be introduced in SCALE 6.3 as an alternative to the KENO V.a, KENO-VI, and Monaco codes. Calculations were performed to establish the performance of Shift for criticality safety analyses within the criticality safety analyses sequence (CSAS) based on models in the Verified, Archived Library of Inputs and Data (VALID). This test suite contains over 600 critical experiment models covering a broad range of fissile materials and neutron energy spectra. The comparisons presented include calculated k eff values and runtime performance for serial calculations and a selection of parallel calculations. Comparisons are presented for multigroup (MG) and continuous-energy (CE) calculations for KENO V.a and KENO-VI models. Results generated with a beta version of SCALE 6.3 indicate excellent agreement in k eff values between KENO and Shift. The largest differences in the average k eff value calculated for the 15 categories of KENO V.a models are 0.00020 ± 0.00011 Δ k for MG calculations and 0.00011 ± 0.00005 Δ k for CE calculations. Similar comparisons in three categories using KENO-VI result in the largest differences for MG calculations: as 0.00004 ± 0.00003 Δ k , and -0.00002 ± 0.00003 Δ k for CE. The preliminary results also indicate that Shift is faster than KENO on a per particle basis, especially for fast spectrum systems. The uncertainty per history is also higher, however, so the Monte Carlo figure of merit is higher for KENO for thermal and intermediate spectrum systems. As expected, Shift generally has better speedup than KENO for parallel calculations, regardless of neutron energy spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Memory forensic analysis of a programmable logic controller in industrial control systems

In industrial control systems (ICS), programmable logic controllers (PLCs) are used to automate physical processes such as nuclear plants and power grid stations, and are often subject to cyber attacks. As in conventional IT domain, the memory analysis of the PLCs can help answer important forensic questions about the attack, such as the presence of malicious firmware, injection of modified control logic (the program running on the PLC), and manipulation of I/O devices (e.g., sensors and actuators). Unlike conventional IT domain, PLCs have heterogeneous hardware architecture, proprietary firmware and control software, making it challenging to employ a unified framework for their memory forensics. For merely extracting artifacts of forensic importance, reverse-engineering the firmware is a tedious task, and the effort needs to be repeated for every PLC model. As a community, a step-wise approach to tackle this challenge is to analyze the memory of specific PLCs, and subsequently find a generic framework applicable to all PLCs. Our work is a step forward in this direction. By following a methodology that focuses on the functional layer of PLCs instead of reverse engineering the firmware, we analyze the digital forensic artifacts available in a common PLC, Allen-Bradley ControlLogix 1756-L61. Before diving into the memory dump, we analyze the PLC control software to create a list of important artifacts that are sure to exist in the PLC memory dump. The approach employs a setup where PLC control software RSLogix-5000 is connected to the PLC, and the memory dump can be obtained as and when needed. We create test cases that sequentially highlight each category of artifacts, followed by an examination of the resultant impact on memory. After attaining the listed artifacts, we employ conventional string and known data searches to extract interesting information present in this PLC's memory. The memory analysis profile, presented as a Python library and shared with the community, can help a forensic investigator to readily extract forensic artifacts from the same model's controller. The adopted approach may help researchers in creating memory profile of other PLCs, and ultimately formulating a generic PLC memory analysis framework.

Rais, Muhammad Haris↗
DOE OSTI2024

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗
DOE OSTI2020

Covariance Testing at BNL [Slides]

This presentation discusses testing implemented in FUDGE & ADVANCE in regard to proper ENDF formatting: STAN, STANEF, CHECKR, FUDGE, NJOY, convert to BOXR format, plotting, endfcovreport.py which is an overview of ENDF library’s covariance contents, and covariance Matrix class implements that are the core of all GNDS covariance. Several checks are performed, including symmetric, real, positive definite, condition # of Eigenvalues, and too big uncertainties. The presentation states that it can fix too big and/or small uncertainties and that it can plot matrices. It states that further testing is recommended by CSEWG but has not yet been implemented and suggests methods such as documentation which needs a human to execute, completeness which is partially complete, and reasonableness which has not been started. The presentation concludes by elaborating on reasonableness and states that only cross section is documented, that similar limits on CP reactions cross sections are needed, that maximum limits are needed too which is tricky since ENDF assumes Normal PDFs, and that there may be other observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Reduced-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Abstract – Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗
DOE OSTI2024

Advanced Cross Section Library Generation using Reduced Order Models

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗
DOE OSTI2020

Procedure for Creating, Reviewing, and Submitting Input Files into the Benchmark Library

Los Alamos National Laboratory (LANL) has a number of criticality benchmark input files, modeled for use with MCNP, developed and maintained by various organizations including the Nuclear Criticality Safety (NCS) Division, XCP-3, and XCP-5. The purpose of this procedure is to standardize input file creation, review, and maintenance. This procedure incorporates existing practices used by IRSN as documented in the original report and the translation from French in addition to practices used by the LANL NCS Division as documented in. The report relates to input files used for the validation of the continuous energy Monte Carlo code MCNP6 but is general enough to be extended to other codes. This report describes the procedure on how to prepare and use benchmarks (taken mainly from the ICSBEP Handbook) for the validation of calculation routes. In particular, this report describes the procedure to follow in the creation of the input files and their integration in the experimental validation databases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Atomic Mixing of Initially Separated Mixtures

We consider the atomic mixing of two materials, initially separated in space, at fixed temperature– pressure conditions [T, p], and zero mass-mean velocity. Each material is composed of a specified set of atomic species whose density corresponds to the specieswise real Equation of State (EOS) $\tilde{&#961}$ i [T, p]. Because there are no spatial gradients in the mean [T, p] state, the only mechanism for mixing is a specieswise nonequilibrium thermal velocity distribution. The recipe for nonequilibrium species mass fluxes is taken directly from Hirschfelder, Curtiss, and Bird, who express the diffusion velocities in terms of gradients in the molar concentrations and pairwise coefficients of diffusion. EOS data from the SESAME library is used for all species. Data for the specieswise self diffusion coefficients is adopted from the Orbital Free Molecular Dynamics (OFMD) simulations of Ticknor et al.; the so-called Darken approximation is used to express the mutual diffusion coefficients of a mixture in the manner used by White et al. A one-dimensional spatial domain is used; with the left half occupied by one multispecies material and the right half occupied by the other, and with zero–gradient boundary conditions at the ends of the domain. Hence the total mass in the domain is a constant. At time t = 0 the materials are separated. Accordingly, spatial gradients at the separation point are infinite and the species fluxes are also infinite. As t → $\textbf{∞}$ the spatial gradients approach zero and a uniform set of species concentrations is obtained; at this point the system is said to be at “thermodynamic equilibrium.” Analytic solution of the problem is not possible in general due to the nonlinear concentration dependence of the species fluxes. Hence we utilize the numerical solution apparatus in Mathematica for obtaining accurate time-dependent solutions for the mixing of various initial species masses for conditions of interest in laser-driven Inertial Confinement Fusion. Concentration profiles and the speed of propagation of the mixing fronts are discussed in light of the nonlinearity of the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗