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Results for “Mathematical Computing”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Trends in computerized structural analysis and synthesis; Proceedings of the Symposium, Washington, D.C., October 30-November 1, 1978

The subjects considered are related to future directions of structural applications and potential of new computing systems, advances and trends in data management and engineering software development, advances in applied mathematics and symbolic computing, computer-aided instruction and interactive computer graphics, nonlinear analysis, dynamic analysis and transient response, structural synthesis, structural analysis and design systems, advanced structural applications, supercomputers, numerical analysis, and trends in software systems. Attention is given to the reliability and optimality of the finite element method, computerized symbolic manipulation in structural mechanics, a standard computer graphics subroutine package, and a drag method as a finite element mesh generation scheme.

Noor, A. K.↗
NASA NTRS1996

The Quest for Pi

This article gives a brief history of the analysis and computation of the mathematical constant Pi=3.14159 ..., including a number of the formulas that have been used to compute Pi through the ages. Recent developments in this area are then discussed in some detail, including the recent computation of Pi to over six billion decimal digits using high-order convergent algorithms, and a newly discovered scheme that permits arbitrary individual hexadecimal digits of Pi to be computed.

Bailey, David H.↗
NASA NTRS1966

Computer simulation program is adaptable to industrial processes

The Reaction kinetics ablation program /REKAP/, developed to simulate ablation of various materials, provides mathematical formulations for computer programs which can simulate certain industrial processes. The programs are based on the use of nonsymmetrical difference equations that are employed to solve complex partial differential equation systems.

Schultz, F. E.↗
DOE OSTI2025

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty [Brochure]

The four priority research directions outlined in this brochure represent a cohesive vision for advancing the science of inverse problems for complex systems under uncertainty. Together, they address the critical challenges of: discovering, exploiting, and preserving physical and problem structure; overcoming model limitations; integrating disparate, multimodal, and/or dynamic data; and tailoring the solution of inverse problems to downstream tasks. While each PRD focuses on a distinct aspect of inverse-problem research, their interconnected nature highlights the importance of a holistic approach that leverages progress across all areas to achieve transformative solutions. This agenda calls for research across mathematics, statistics, and computer science disciplines, which are guided and complemented by rapid advances in artificial intelligence, high-performance computing, and experimental facilities, to unlock new capabilities, maximize scientific impact, and meet the growing demands of inverse problems that arise across applications that are critical to DOE's mission.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Provable bounds for noise-free expectation values computed from noisy samples

Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers. However, today’s quantum computers are noisy, posing challenges to obtaining accurate results. Here, we explore the impact of noise on quantum computing, focusing on the challenges in sampling bit strings from noisy quantum computers and the implications for optimization and machine learning. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the conditional value at risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on real quantum computers involving up to 127 qubits. The results show strong alignment with theoretical predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Viability of Additively Manufactured Electrodes for Lithium-Ion Batteries

As the global economy becomes increasingly electrified, the demand for batteries and energy storage is expected to rise significantly, particularly in the transportation and electricity sectors. Lithium-ion batteries (LIBs) are currently the most advanced and widely used technology in this field. Traditionally, LIBs are manufactured using simple 2D planar geometries to maximize production efficiency and minimize costs. However, this approach limits energy density due to the restricted design flexibility of the electrodes. Additive manufacturing (AM) offers a promising solution to enhance the energy density and efficiency of LIBs by enabling the design of architectures that reduce diffusive losses and allow for a greater amount of active material to be incorporated within the same device footprint, thereby minimizing the use of inactive materials. Different AM techniques come with their own set of limitations, including printing speed, material compatibility, and scale, which must be considered when designing electrodes. Scalable and cost-effective methods are particularly important for electric vehicle batteries, while achieving higher energy densities in microbatteries is crucial for the miniaturization of wearable electronics and medical devices. Here, in this study, we simulate various 3D porous electrode designs for LIBs using graphite and nickel manganese cobalt oxide (NMC) electrodes. These designs are selected to represent structures that could be produced using different AM techniques, such as direct ink writing, fused deposition modeling, and stereolithography. Our results indicate that at higher charging rates and increased areal mass loading, 3D structures can outperform traditional 2D electrodes, although the benefits may diminish with more complex designs that are harder to manufacture. The observed gains in energy density are attributed to improved electrode utilization and reduced diffusive energy losses. This comprehensive analysis of structure–performance relationships will provide valuable insights to guide future research on 3D designs, material selection, and AM techniques for additively manufactured battery electrodes.

25 ENERGY STORAGE↗
DOE OSTI2025

Science & Technology Review December 2025 - Optimizing Future Design

At Lawrence Livermore National Laboratory, we focus on science and technology research to ensure our nation’s security. We also apply that expertise to solve other important national problems in energy, bioscience, and the environment. Science & Technology Review is published eight times a year to communicate, to a broad audience, the Laboratory’s scientific and technological accomplishments in fulfilling its primary missions. The publication’s goal is to help readers understand these accomplishments and appreciate their value to the individual citizen, the nation, and the world.

36 MATERIALS SCIENCE↗
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 NTRS1994

Computational Approaches to Vestibular Research

The Biocomputation Center at NASA Ames Research Center is dedicated to a union between computational, experimental and theoretical approaches to the study of neuroscience and of life sciences in general. The current emphasis is on computer reconstruction and visualization of vestibular macular architecture in three-dimensions (3-D), and on mathematical modeling and computer simulation of neural activity in the functioning system. Our methods are being used to interpret the influence of spaceflight on mammalian vestibular maculas in a model system, that of the adult Sprague-Dawley rat. More than twenty 3-D reconstructions of type I and type II hair cells and their afferents have been completed by digitization of contours traced from serial sections photographed in a transmission electron microscope. This labor-intensive method has now been replace d by a semiautomated method developed in the Biocomputation Center in which conventional photography is eliminated. All viewing, storage and manipulation of original data is done using Silicon Graphics workstations. Recent improvements to the software include a new mesh generation method for connecting contours. This method will permit the investigator to describe any surface, regardless of complexity, including highly branched structures such as are routinely found in neurons. This same mesh can be used for 3-D, finite volume simulation of synapse activation and voltage spread on neuronal surfaces visualized via the reconstruction process. These simulations help the investigator interpret the relationship between neuroarchitecture and physiology, and are of assistance in determining which experiments will best test theoretical interpretations. Data are also used to develop abstract, 3-D models that dynamically display neuronal activity ongoing in the system. Finally, the same data can be used to visualize the neural tissue in a virtual environment. Our exhibit will depict capabilities of our computational approaches and some of our findings from their application. For example, our research has demonstrated that maculas of adult mammals retain the property of synaptic plasticity. Ribbon synapses increase numerically and undergo changes in type and distribution (p<0.0001) in type II hair cells after exposure to microgravity for as few as nine days. The finding of macular synaptic plasticity is pertinent to the clinic, and may help explain some. balance disorders in humans. The software used in our investigations will be demonstrated for those interested in applying it in their own research.

Ross, Muriel D.↗
DOE OSTI2025

Idaho National Laboratory CY 2024 National Emission Standards for Hazardous Air Pollutants Analysis, Methodology, and Results for Radionuclides

This report documents the methodology and results for calculating the effective dose equivalent (EDE) to the maximally exposed individual (MEI) from atmospheric radionuclide emissions from Idaho National Laboratory (INL) sources in Calendar Year (CY) 2024. The calculations were performed in accordance with requirements in Code of Federal Regulations (CFR), Title 40, “Protection of the Environment,” Part 61, “National Emission Standards for Hazardous Air Pollutants (NESHAPs),” Subpart H, “National Emission Standards for Emissions of Radionuclides Other than Radon from Department of Energy Facilities” (40 CFR 61, Subpart H). UDFs were calculated using the computer model CAP88-PC for unit (1 Ci/yr) emission rates at INL Site facilities and INL in-town (Idaho Falls) facilities and stored in Microsoft Access databases. The UDFs—in this case, mrem/Ci—were then combined with radionuclide-specific release (emission) rates for each facility-specific source to compute doses at predetermined public receptor locations, including the MEI locations. This report contains the dose results and a description of the methodology and tools used to compute the doses.

07 - ISOTOPES AND RADIATION SOURCES↗
DOE OSTI2026

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Correction, improvement and model verification of CARE 3, version 3

An independent verification of the CARE 3 mathematical model and computer code was conducted and reported in NASA Contractor Report 166096, Review and Verification of CARE 3 Mathematical Model and Code: Interim Report. The study uncovered some implementation errors that were corrected and are reported in this document. The corrected CARE 3 program is called version 4. Thus the document, correction. improvement, and model verification of CARE 3, version 3 was written in April 1984. It is being published now as it has been determined to contain a more accurate representation of CARE 3 than the preceding document of April 1983. This edition supercedes NASA-CR-166122 entitled, 'Correction and Improvement of CARE 3,' version 3, April 1983.

Rose, D. M.↗
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 OSTI2024

Perfectly Matched Layers and Characteristic Boundaries in Lattice Boltzmann: Accuracy vs Cost

Artificial boundary conditions (BCs) play a ubiquitous role in numerical simulations of transport phenomena in several diverse fields, such as fluid dynamics, electromagnetism, acoustics, geophysics, and many more. They are essential for accurately capturing the behavior of physical systems whenever the simulation domain is truncated for computational efficiency purposes. Ideally, an artificial BC would allow relevant information to enter or leave the computational domain without introducing artifacts or unphysical effects. Boundary conditions designed to control spurious wave reflections are referred to as nonreflective boundary conditions (NRBCs). Another approach is given by the perfectly matched layers (PMLs), in which the computational domain is extended with multiple dampening layers, where outgoing waves are absorbed exponentially in time. Here, in this work, the definition of PML is revised in the context of the lattice Boltzmann method. The impact of adopting different types of BCs at the edge of the dampening zone is evaluated and compared, in terms of both accuracy and computational costs. It is shown that for sufficiently large buffer zones, PMLs allow stable and accurate simulations even when using a simple zeroth-order extrapolation BC. Moreover, employing PMLs in combination with NRBCs potentially offers significant gains in accuracy at a modest computational overhead, provided the parameters of the BC are properly tuned to match the properties of the underlying fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Simulating plasma wave propagation on a superconducting quantum chip

Quantum computers may one day enable the efficient simulation of strongly coupled plasmas that lie beyond the reach of classical computation in regimes where quantum effects are important and the scale separation is large. Here, in this article, we take a first step toward efficient simulation of quantum plasmas by demonstrating linear plasma wave propagation on a superconducting quantum chip. Using high-fidelity and highly expressive device-native gates, combined with an error-mitigation technique, we simulate the scattering of laser pulses from inhomogeneous plasmas. Our approach is made feasible by the identification of a suitable local spin model whose excitations mimic plasma waves, and whose circuit implementation requires a lower gate count than other proposed approaches that would require a future fault-tolerant quantum computer. This work opens avenues to study more complicated phenomena that cannot be simulated efficiently on classical computers, such as nonlinear quantum dynamics when strongly coupled plasmas are driven out of equilibrium.

general physics↗