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Results for “Mathematical physics methods”

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 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Searching for metastable particles using graph computing

The reconstruction of charged particle trajectories at the Large Hadron Collider and future colliders relies on energy depositions in sensors placed at distances ranging from a centimeter to a meter from the colliding beams. We propose a method of detecting charged particles that decay invisibly after traversing a short distance of about 25 cm inside the experimental apparatus. One of the decay products may constitute the dark matter known to be 84% of all matter at galactic and cosmological distance scales. Our method uses graph computing to cluster spacepoints recorded by two-dimensional silicon pixel sensors into mathematically-defined patterns. The algorithm may be implemented on silicon-based integrated circuits using field-programmable gate array technology to augment or replace traditional computing platforms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Reference solutions for linear radiation transport: the Hohlraum and Lattice Benchmarks

Radiation transport describes the propagation of energetic particles through space as they interact with a surrounding material medium. In a kinetic description, radiation transport is modeled by a radiation transport equation (RTE) that prescribes the density of the radiation in position-momentum phase space. The purpose of this dataset is to provide highly resolved solutions to two benchmark problems. These two benchmarks do not possess exact solutions; moreover, the construction of a manufactured solution may require a non-physical source that is not desirable, especially if it spoils the physical nature of the solution. Thus the goal of this computational study is to provide a highly resolved reference solution for testing newer, more cost efficient methods that are currently being developed in the research community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Understanding Technical and Psychosocial Barriers to Realizing FAIR Data Process

The present study investigates barriers and facilitators to the implementation of Findable, Accessible, Interoperable, and Reusable (FAIR) data processes within the Physical Sciences Division of the Computational Sciences Directorate (PCSD). Employing a dual-method approach consisting of surveys and focus group discussions, the study aims to illuminate the complex interplay between technical and psychosocial factors that influence FAIR data adoption.

42 ENGINEERING↗
DOE OSTI2023

Direct Monte Carlo Simulations of Chemical Equilibrium Composition of Molecular Fluid Mixtures Under Shock Conditions

A new Monte Carlo simulation method is implemented which holds the number and kind of atoms constant rather than the number and kind of molecules for a molecular fluid mixture. Chemical reactions are allowed as a correlated move of atoms such as an interchange of atoms between molecules. Equilibrium chemical composition is determined as an average over the simulation along with equation of state quantities. Results are presented for N 2 + O 2 → 2NO at 30GPa and 3000K. The equilibrium composition is shown to be sensitive to the potentials between unlike species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Cyber physical attack detection

A cyber-security threat detection system and method stores physical data measurements from a cyber-physical system and extracts synchronized measurement vectors synchronized to one or more timing pulses. The system and method synthesizes data integrity attacks in response to the physical data measurements and applies alternating parametrized linear and non-linear operations in response to the synthesized data integrity attacks. The synthesis renders optimized model parameters used to detect multiple cyber-attacks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials’ behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

homogenization↗
DOE OSTI2023

JetNet: A Python package for accessing open datasets and benchmarking machine learning methods in high energy physics

JetNet is a Python package that aims to increase accessibility and reproducibility for machinelearning (ML) research in high energy physics (HEP), primarily related to particle jets. Basedon the popular PyTorch ML framework, it provides easy-to-access and standardized interfacesfor multiple heterogeneous HEP datasets and implementations of evaluation metrics, lossfunctions, and more general utilities relevant to HEP.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Quantum Monte Carlo and Fewer-Body Approaches to Scattering, Reactions, and Related Properties of Nuclei

The overall goals of this project were to advance understanding of reactions and scattering states in light nuclei, as well as related properties of bound states, and to facilitate application of that understanding to astrophysics and cosmology. These goals were pursued mainly using quantum Monte Carlo methods to compute nuclear properties using protons and neutrons as the basic degrees of freedom.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantum Spectral Methods for Differential Equations

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ϵ with complexity poly(log(1/ϵ)), no such algorithm was previously known for differential equations with time-dependent coefficients. In this work, we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd, log(1/ϵ)).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Reduced-order autodifferentiable ensemble Kalman filters

This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an EnKF to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structure, ROAD-EnKFs achieve higher accuracy at lower computational cost compared to existing methods. If such structure is not expressed in the latent state dynamics, ROAD-EnKFs achieve similar accuracy at lower cost, making them a promising approach for surrogate state reconstruction and forecasting.

Mathematics↗
DOE OSTI2021

XCP- Computational Summer Workshop: Equation of State Overview [Slides]

An overview of Equation of State (EOS) theory, some relevant physics, experiments, computational methods, and the SESAME database will be presented. The goal will be to describe what types of data and modeling are required to make an EOS that typically spans up to ~10 9 GPa in pressure and 10 9 K in temperature.

42 ENGINEERING↗
DOE OSTI2021

Modeling the Nonlinear Rheology of Polymer Additive Manufacturing

This report summarizes molecular and continuum simulation studies focused on developing physics - based predictive models for the evolution of polymer molecular order during the nonlinear processing flows of additive manufacturing. Our molecular simulations of polymer elongation flows identified novel mechanisms of fluid dissipation for various polymer architectures that might be harnessed to enhance material processability. In order to predict the complex thermal and flow history of polymer realistic additive manufacturing processes, we have developed and deployed a high - performance mesh - free hydrodynamics module in Sandia's LAMMPS software. This module called RHEO – short for Reproducing Hydrodynamics and Elastic Objects – hybridizes an updated - Lagrange reproducing - kernel method for complex fluids with a bonded particle method (BPM) to capture solidification and solid objects in multiphase flows. In combination, our two methods allow rapid, multiscale characterization of the hydrodynamics and molecular evolution of polymers in realistic processing geometries.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier–Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a two-dimensional synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a centre plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. Furthermore, the results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression

Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer's disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follows a reaction-diffusion type equation. However, the precise mathematical model and parameters that characterize the progression of misfolded protein across the brain remain incompletely understood. Here, we use deep learning and artificial intelligence to discover a mathematical model for the progression of Alzheimer's disease using longitudinal tau positron emission tomography from the Alzheimer's Disease Neuroimaging Initiative database. Specifically, we integrate physics informed neural networks (PINNs) and symbolic regression to discover a reaction-diffusion type partial differential equation for tau protein misfolding and spreading. First, we demonstrate the potential of our model and parameter discovery on synthetic data. Then, we apply our method to discover the best model and parameters to explain tau imaging data from 46 individuals who are likely to develop Alzheimer's disease and 30 healthy controls. Our symbolic regression discovers different misfolding models f(c) for two groups, with a faster misfolding for the Alzheimer's group, f(c) = 0.23c 3 – 1.34c 2 + 1.11c, than for the healthy control group, f(c) = –c 3 + 0.62c 2 + 0.39c. Our results suggest that PINNs, supplemented by symbolic regression, can discover a reaction-diffusion type model to explain misfolded tau protein concentrations in Alzheimer's disease. Furthermore, we expect our study to be the starting point for a more holistic analysis to provide image-based technologies for early diagnosis, and ideally early treatment of neurodegeneration in Alzheimer's disease and possibly other misfolding-protein based neurodegenerative disorders.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Probabilistic Evaluation of Geomechanical Risks in CO2 Storage: An Exploration of Caprock Integrity Metrics Using a Multilaminate Model

The probabilistic uncertainty assessment of geomechanical risk—specifically, caprock failure—attributable to CO2 injection, as presented in a simplified hypothetical geological model, was the focus of this study. Our approach amalgamates the implementation of a multilaminate model, the creation of a response surface model in conjunction with the Box–Behnken sampling design, the execution of associated numerical modeling experiments, and the utilization of Monte Carlo simulations. Probability distributions to encapsulate the inherent variability (elastic and mechanical properties of the caprock and reservoir) and uncertainty in prediction estimates (vertical displacement, total strain, and F value) were employed. Our findings reveal that the Young modulus of the caprock is a key factor controlling equivalent total strain but is insufficient as a stand-alone indicator of caprock integrity. It is confirmed that the caprock can accommodate significant deformation without failure, if it possesses a low Young’s modulus and high mechanical strength properties, such as the friction angle and uniaxial compressive strength. Similarly, vertical displacement was found to be an unreliable indicator for caprock integrity, as caprock failure can occur across a broad spectrum of vertical displacements, particularly when both the Young modulus and mechanical strength properties have wide ranges. This study introduces the F value as the most dependable indicator for caprock failure, although it is a theoretical attribute (the shortest distance between the Mohr circle and the nearest failure envelope used to measure the sensitivity to failure) and not physically measurable in the field. Deviatoric stress levels were found to vary based on stress regimes, with the maximum levels observed under extensive and compressive stress regimes. In conjunction with the use of the response surface method, this study demonstrates the efficacy of the multilaminate framework and the Mohr–Coulomb constitutive model in providing a simplified, yet effective, probabilistic model of the mechanical behavior of caprock failure, reducing mathematical and computational complexities.

Energy & Fuels↗