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Results for “Mathematics and Computing, Engineering”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Software engineering as an engineering discipline

The following topics are discussed in the context of software engineering: early use of the term; the 1968 NATO conference; Barry Boehm's definition; four requirements fo software engineering; and additional criteria for software engineering. Additionally, the four major requirements for software engineering--computer science, mathematics, engineering disciplines, and excellent communication skills--are discussed. The presentation is given in vugraph form.

Berard, Edward V.↗
DOE OSTI2026

Second Order System Study

During my education in mathematics, engineering and physics, I learned transform pairs and their usage mechanics but I never remember seeing the derivations of the solutions to second order ordinary differential equations (ODE) and difference equations. A solution to a question posed in a potential funder meeting put me on a path to solving second order systems using the five principal Fourier based methods: Fourier transform (FT), Z-transform (ZT), discrete time Fourier transform (DTFT), discrete Fourier transform (DFT) and Laplace transform (LT).

42 ENGINEERING↗
DOE OSTI2024

A multiscale anisotropic polymer network model coupled with phase field fracture

The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local-global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double-edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. In conclusion, the results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber-like materials.

42 ENGINEERING↗
NASA NTRS1996

Computer-Based Mathematics Instructions for Engineering Students

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Khan, Mustaq A.↗
DOE OSTI2022

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Light-powered end-to-end neutron detection and imaging with an edge-deployed optical AI chip

Neutron detection is widely used in many applications including nuclear physics, nuclear energy, nuclear technologies and nuclear safeguards. Developing an end-to-end neutron detection and imaging workflow paves way towards fully automated processes for many applications. We implemented an automated workflow for neutron detection experiments which use a solid state image sensor to capture neutron hits as a digital image. We deploy the workflow to an edge-based optical neural network (ONN) to increase the radiation-hardness and lifetime of neutron detection instruments. We present a two-stage neural network framework for detection of neutrons at sub-pixel resolution. The first stage uses a region proposal network to efficiently detect and extract neutron hits from the input camera image. The second stage feeds the extracted hits into a fully connected neural network to predict the sub-pixel hit position. The performance of the two-stage framework is evaluated using the edge-based ONN. The results show that we can achieve above 96% neutron detection accuracy as well as sub-pixel and sub-micron position resolution, while enjoying the advantages of the ONN hardware including radiation-hardness, low energy consumption and high computing speed for integrated edge camera and hardware deployment, when compared with electronic counterparts.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Assessment of the Loss of Vacuum on the Local Metal Temperature in the TEX Experiment Assembly

A four-part assessment using analytical methods and semi-analytical simulation tools finds that the maximum temperature variation in the highly enriched uranium (HEU) Jemima plate assembly is less than ten Kelvin (< 10 K) in an abrupt loss of vacuum scenario. The temperature variation in the metals is likely to be one to four Kelvin (1 K – 4 K) based on the most realistic conditions in the assessment. The four assessment parts include: (1) the peak gas temperature bound for the initial influx of the ambient air; (2) the high-heat transfer limit during the high-speed forced convection period in an insulated HEU plate; (3) the high-heat transfer limit during the high-speed forced convection period with aluminum spacers; and (4) the longer-time thermal equilibration period between the air and metal stack. The four-part assessment serves as conservative upper bound on the temperature variation in the metal stack and remains well below the 40 Kelvin limit where the temperature-induced stresses could lead to permanent, plastic deformation.

42 ENGINEERING↗
NASA NTRS2006

The 'Biologically-Inspired Computing' Column

The field of Biology changed dramatically in 1953, with the determination by Francis Crick and James Dewey Watson of the double helix structure of DNA. This discovery changed Biology for ever, allowing the sequencing of the human genome, and the emergence of a "new Biology" focused on DNA, genes, proteins, data, and search. Computational Biology and Bioinformatics heavily rely on computing to facilitate research into life and development. Simultaneously, an understanding of the biology of living organisms indicates a parallel with computing systems: molecules in living cells interact, grow, and transform according to the "program" dictated by DNA. Moreover, paradigms of Computing are emerging based on modelling and developing computer-based systems exploiting ideas that are observed in nature. This includes building into computer systems self-management and self-governance mechanisms that are inspired by the human body's autonomic nervous system, modelling evolutionary systems analogous to colonies of ants or other insects, and developing highly-efficient and highly-complex distributed systems from large numbers of (often quite simple) largely homogeneous components to reflect the behaviour of flocks of birds, swarms of bees, herds of animals, or schools of fish. This new field of "Biologically-Inspired Computing", often known in other incarnations by other names, such as: Autonomic Computing, Pervasive Computing, Organic Computing, Biomimetics, and Artificial Life, amongst others, is poised at the intersection of Computer Science, Engineering, Mathematics, and the Life Sciences. Successes have been reported in the fields of drug discovery, data communications, computer animation, control and command, exploration systems for space, undersea, and harsh environments, to name but a few, and augur much promise for future progress.

Hinchey, Mike↗
DOE OSTI2020

Better together: Elements of successful scientific software development in a distributed collaborative community

Many scientific disciplines rely on computational methods for data analysis, model generation, and prediction. Implementing these methods is often accomplished by researchers with domain expertise but without formal training in software engineering or computer science. This arrangement has led to underappreciation of sustainability and maintainability of scientific software tools developed in academic environments. Some software tools have avoided this fate, including the scientific library Rosetta. We use this software and its community as a case study to show how modern software development can be accomplished successfully, irrespective of subject area. Rosetta is one of the largest software suites for macromolecular modeling, with 3.1 million lines of code and many state-of-the-art applications. Since the mid 1990s, the software has been developed collaboratively by the RosettaCommons, a community of academics from over 60 institutions worldwide with diverse backgrounds including chemistry, biology, physiology, physics, engineering, mathematics, and computer science. Developing this software suite has provided us with more than two decades of experience in how to effectively develop advanced scientific software in a global community with hundreds of contributors. Here we illustrate the functioning of this development community by addressing technical aspects (like version control, testing, and maintenance), community-building strategies, diversity efforts, software dissemination, and user support. We demonstrate how modern computational research can thrive in a distributed collaborative community. The practices described here are independent of subject area and can be readily adopted by other software development communities

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗