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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

DaMoScope and its internet graphics for the visual control of adjusting mathematical models describing experimental data

The experience of using the dynamic atlas of the experimental data and mathematical models of their description in the problems of adjusting parametric models of observable values depending on kinematic variables is presented. The functional possibilities of an image of a large number of experimental data and the models describing them are shown by examples of data and models of observable values determined by the amplitudes of elastic scattering of hadrons. The Internet implementation of an interactive tool DaMoScope and its interface with the experimental data and codes of adjusted parametric models with the parameters of the best description of data are schematically shown. The DaMoScope codes are freely available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Mathematical model for burden distribution in blast furnace

Burden distribution in a blast furnace is vital to its smooth running. However, it is difficult to directly measure the burden distribution for an operating blast furnace. Therefore, mathematical models have been applied to guide the charging process to achieve the desired burden distribution. The accuracies of such models depend on the prediction of falling curve, stockline profile formation, and burden descent mode. Here, a new stockline profile formation model is proposed in which new equations have been developed for the inner and outer repose angle by considering the influence of the burden flow's vertical and horizontal velocity at the apex of the stockline profile. Furthermore, validation of this new stockline profile formation model is provided through comparison between calculated results and experimental data for stockline profile. A stepped burden descending strategy, in which the burden would descend through a specified distance after each ring charging process, is proposed corresponding to the successive charging process. The influence of the burden descending strategy on the falling point, the final burden profile and radial depth ratio of ore to coke is also analysed. Our results show that the burden descending strategy greatly affects the final burden distribution, especially in the peripheral region.

42 ENGINEERING↗
DOE OSTI2021

Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling

Understanding CRISPR-Cas systems—the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks—is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical ‘rich-get-richer’ mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Mathematical model of a personalized neoantigen cancer vaccine and the human immune system

Cancer vaccines are an important component of the cancer immunotherapy toolkit enhancing immune response to malignant cells by activating CD4 + and CD8 + T cells. Multiple successful clinical applications of cancer vaccines have shown good safety and efficacy. Despite the notable progress, significant challenges remain in obtaining consistent immune responses across heterogeneous patient populations, as well as various cancers. We present a mechanistic mathematical model describing key interactions of a personalized neoantigen cancer vaccine with an individual patient’s immune system. Specifically, the model considers the vaccine concentration of tumor-specific antigen peptides and adjuvant, the patient’s major histocompatibility complexes I and II copy numbers, tumor size, T cells, and antigen presenting cells. We parametrized the model using patient-specific data from a clinical study in which individualized cancer vaccines were used to treat six melanoma patients. Model simulations predicted both immune responses, represented by T cell counts, to the vaccine as well as clinical outcome (determined as change of tumor size). This model, although complex, can be used to describe, simulate, and predict the behavior of the human immune system to a personalized cancer vaccine.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Mathematical modeling of plus-strand RNA virus replication to identify broad-spectrum antiviral treatment strategies

Plus-strand RNA viruses are the largest group of viruses. Many are human pathogens that inflict a socio-economic burden. Interestingly, plus-strand RNA viruses share remarkable similarities in their replication. A hallmark of plus-strand RNA viruses is the remodeling of intracellular membranes to establish replication organelles (so-called “replication factories”), which provide a protected environment for the replicase complex, consisting of the viral genome and proteins necessary for viral RNA synthesis. In the current study, we investigate pan-viral similarities and virus-specific differences in the life cycle of this highly relevant group of viruses. We first measured the kinetics of viral RNA, viral protein, and infectious virus particle production of hepatitis C virus (HCV), dengue virus (DENV), and coxsackievirus B3 (CVB3) in the immuno-compromised Huh7 cell line and thus without perturbations by an intrinsic immune response. Based on these measurements, we developed a detailed mathematical model of the replication of HCV, DENV, and CVB3 and showed that only small virus-specific changes in the model were necessary to describe the in vitro dynamics of the different viruses. Our model correctly predicted virus-specific mechanisms such as host cell translation shut off and different kinetics of replication organelles. Further, our model suggests that the ability to suppress or shut down host cell mRNA translation may be a key factor for in vitro replication efficiency, which may determine acute self-limited or chronic infection. We further analyzed potential broad-spectrum antiviral treatment options in silico and found that targeting viral RNA translation, such as polyprotein cleavage and viral RNA synthesis, may be the most promising drug targets for all plus-strand RNA viruses. Moreover, we found that targeting only the formation of replicase complexes did not stop the in vitro viral replication early in infection, while inhibiting intracellular trafficking processes may even lead to amplified viral growth.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Mechanistic within-host mathematical model of inhalational anthrax

We present a mathematical model of the dynamics of Bacillus anthracis bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using in vivo data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time t, assuming that the number of inhaled spores has a Poisson distribution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

Our two key accomplishments in the first three years were towards the development of, (1) a mathematically rigorous and at the same time computationally flexible framework for parallelization of Kinetic Monte Carlo methods, and its implementation on GPUs, and (2) spatial multilevel coarse-graining methods for Monte Carlo sampling and molecular simulation. A common underlying theme in both these lines of our work is the development of numerical methods which are at the same time both computationally efficient and reliable, the latter in the sense that they provide controlled-error approximations for coarse observables of the simulated molecular systems. Finally, our key accomplishment in the last year of the grant is that we started developing (3) pathwise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of nonequilibrium extended (high-dimensional) systems. We discuss these three research directions in some detail below, along with the related publications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

NetMOD Version 2.0 Mathematical Framework

NetMOD ( Net work M onitoring for O ptimal D etection) is a Java-based software package for conducting simulation of seismic, hydroacoustic and infrasonic networks. Network simulations have long been used to study network resilience to station outages and to determine where additional stations are needed to reduce monitoring thresholds. NetMOD makes use of geophysical models to determine the source characteristics, signal attenuation along the path between the source and station, and the performance and noise properties of the station. These geophysical models are combined to simulate the relative amplitudes of signal and noise that are observed at each of the stations. From these signal-to-noise ratios (SNR), the probabilities of signal detection at each station and event detection across the network of stations can be computed given a detection threshold. The purpose of this document is to clearly and comprehensively present the mathematical framework used by NetMOD, the software package developed by Sandia National Laboratories to assess the monitoring capability of ground-based sensor networks. Many of the NetMOD equations used for simulations are inherited from the NetSim network capability assessment package developed in the late 1980s by SAIC (Sereno et al., 1990).

58 GEOSCIENCES↗
DOE OSTI2016

Tractable Experiment Design via Mathematical Surrogates

This presentation summarizes the development and implementation of quantitative design criteria motivated by targeted inference objectives for identifying new, potentially expensive computational or physical experiments. The first application is concerned with estimating features of quantities of interest arising from complex computational models, such as quantiles or failure probabilities. A sequential strategy is proposed for iterative refinement of the importance distributions used to efficiently sample the uncertain inputs to the computational model. In the second application, effective use of mathematical surrogates is investigated to help alleviate the analytical and numerical intractability often associated with Bayesian experiment design. This approach allows for the incorporation of prior information into the design process without the need for gross simplification of the design criterion. Illustrative examples of both design problems will be presented as an argument for the relevance of these research problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

RELAP-7 Progress Report: A Mathematical Model for 1-D Compressible, Single-Phase Flow Through a Branching Junction

In the literature, the abundance of pipe network junction models, as well as inclusion of dissipative losses between connected pipes with loss coefficients, has been treated using the incompressible flow assumption of constant density. This approach is fundamentally, physically wrong for compressible flow with density change. This report introduces a mathematical modeling approach for general junctions in piping network systems for which the transient flows are compressible and single-phase. The junction could be as simple as a 1-pipe input and 1-pipe output with differing pipe cross-sectional areas for which a dissipative loss is necessary, or it could include an active component, between an inlet pipe and an outlet pipe, such as a pump or turbine. In this report, discussion will be limited to the former. A more general branching junction connecting an arbitrary number of pipes with transient, 1-D compressible single-phase flows is also presented. These models will be developed in a manner consistent with the use of a general equation of state like, for example, the recent Spline-Based Table Look-up method [1] for incorporating the IAPWS-95 formulation [2] to give accurate and efficient calculations for properties for water and steam with RELAP-7 [3].

42 ENGINEERING↗
DOE OSTI2018

Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design

We developed path-wise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of non-equilibrium extended molecular systems. The combination of these novel methodologies provided the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale stochastic models such as (bio)chemical reaction networks, with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, hybrid micro-macro systems, etc. A particular computational challenge arises in simulations of multi-scale reaction networks and molecular systems. Mathematical techniques were applied to in silico prediction of novel materials with emphasis on the effect of microstructure on model uncertainty quantification (UQ). We outline acceleration methods to make calculations of real chemistry feasible followed by two complementary tasks on structure optimization and microstructure-induced UQ.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) SciDAC Institute

The FASTMath SciDAC Institute addressed two key challenges that application scientists faced at the beginning of SciDAC-3. First, FASTMath helped them continue to improve the quality of their simulations by increasing accuracy and reliability of both their software and algorithms. Second, FASTMath helped them adapt their computations to make effective use of high-end computing facilities acquired by DOE over the past five years. This required the development of new mathematical algorithms that were appropriate for the physics problems being solved, implementations that scaled to million-way parallelism, and software that effectively leveraged both distributed memory and on-node parallelism. The Rensselaer Polytechnic Institute team’s efforts focused on the unstructured mesh technologies developed by FASTMath.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)(Final Technical Report)

Our work on the CM4 grant focused on new mathematical and computational approaches for stochastic methods for mesoscopic systems. Our work included continuum SPDEs, molecular coarse-grained models, and hybrid particle-continuum approaches. This work was motivated by applications in soft materials, fluidic devices, and interfacial phenomena. Throughout the project we collaborated with several staff researchers, including from Pacific Northwest National Laboratories (PNNL) and Sandia National Laboratory (SNL) as well as other members of the CM4 project. Below we summarize briefly a few specific accomplishments from this work over the funding period. A full list of published papers and software releases supported by the grant are listed at the end.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report)

Nonlocal models provide a much-needed predictive capability for important Sandia mission applications, ranging from fracture mechanics for nuclear components to subsurface flow for nuclear waste disposal, where traditional partial differential equations (PDEs) models fail to capture effects due to long-range forces at the microscale and mesoscale. However, utilization of this capability is seriously compromised by the lack of a rigorous nonlocal interface theory, required for both application and efficient solution of nonlocal models. To unlock the full potential of nonlocal modeling we developed a mathematically rigorous and physically consistent interface theory and demonstrate its scope in mission-relevant exemplar problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

PhILMs: Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems

The landscape of computational science and engineering is continually evolving, with the challenge of high-dimensional regression problems standing as a significant hurdle in numerous scientific endeavors. Addressing this challenge, our research, funded by this award, has led to the development of an innovative computational framework known as Probabilistic Partition of Unity Networks (PPOU-Nets). This initiative represents a collaborative effort to harness the potential of mathematics and physics-informed machine learning in tackling multiscale and multiphysics problems prevalent in high-dimensional spaces. Through this work, we have proposed a novel methodology that seamlessly integrates adaptive dimensionality reduction and a mixture of experts model, thereby facilitating a more efficient and accurate approximation of complex functions. This research effort has not only advanced the state of computational science but also opened new avenues for exploration in quantum computing and beyond. This report outlines the motivation, methodology, key findings, and implications of our work, underscoring our contributions to the broader scientific community and the potential pathways for future research.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Mathematical methods for optimal polynomial recovery of high-dimensional systems from noisy data

The goal of our Early Career Research Project (ECRP) is to establish a modern mathematical foundation that will enable next-generation computational methods for polynomial approximation of high-dimensional systems, having a certain set of constraints, from a limited amount of noisy data. Such a foundation is critical to realizing the future potential of the DOE user facilities, and will ultimately empower scientists to address a fundamental question, namely, “how many realizations of a nonlinear manifold are required to recover the entire high-dimensional solution map, with optimal approximation guarantees and minimal computational cost?” The central theme of this effort aims to conquer this challenge by pioneering the development of extraordinarily innovative theoretical analysis and transformational non-intrusive computational methodologies. Such approaches will enable the reconstruction of the entire high-dimensional solution map, with accuracy comparable to the best approximation, while utilizing an optimal number of samples. During this reporting period we have made significant progress on four thrusts.

97 MATHEMATICS AND COMPUTING↗