Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Arithmetic”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multipole interaction in spectral line broadening by plasmas

A long-standing ambiguity in spectral line broadening theory related to the electric field divergence in the quadrupole term of the screened Coulomb radiator-plasma interaction is examined. This is accomplished with multipole expansions from a Taylor series as well as a partial wave analysis of the screened Coulomb interaction. Here, it is explicitly shown that the two approaches agree up to the octupole term for an effective radiator size small compared to the plasma screening length. Furthermore, the ambigous corrections are confirmed appearing naturally in both methods. For higher multipoles the agreement is demonstrated numerically with a computer program using exact arithmetic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Exposure of the Heart in Breast Cancer Radiation Therapy: A Systematic Review of Heart Doses Published During 2003 to 2013

Purpose: Breast cancer radiation therapy cures many women, but where the heart is exposed, it can cause heart disease. We report a systematic review of heart doses from breast cancer radiation therapy that were published during 2003 to 2013. Methods and Materials: Eligible studies were those reporting whole-heart dose (ie, dose averaged over the whole heart). Analyses considered the arithmetic mean of the whole-heart doses for the CT plans for each regimen in each study. We termed this “mean heart dose.” Results: In left-sided breast cancer, mean heart dose averaged over all 398 regimens reported in 149 studies from 28 countries was 5.4 Gy (range, <0.1-28.6 Gy). In regimens that did not include the internal mammary chain (IMC), average mean heart dose was 4.2 Gy and varied with the target tissues irradiated. The lowest average mean heart doses were from tangential radiation therapy with either breathing control (1.3 Gy; range, 0.4-2.5 Gy) or treatment in the lateral decubitus position (1.2 Gy; range, 0.8-1.7 Gy), or from proton radiation therapy (0.5 Gy; range, 0.1-0.8 Gy). For intensity modulated radiation therapy mean heart dose was 5.6 Gy (range, <0.1-23.0 Gy). Where the IMC was irradiated, average mean heart dose was around 8 Gy and varied little according to which other targets were irradiated. Proton radiation therapy delivered the lowest average mean heart dose (2.6 Gy, range, 1.0-6.0 Gy), and tangential radiation therapy with a separate IMC field the highest (9.2 Gy, range, 1.9-21.0 Gy). In right-sided breast cancer, the average mean heart dose was 3.3 Gy based on 45 regimens in 23 studies. Conclusions: Recent estimates of typical heart doses from left breast cancer radiation therapy vary widely between studies, even for apparently similar regimens. Maneuvers to reduce heart dose in left tangential radiation therapy were successful. Proton radiation therapy delivered the lowest doses. Inclusion of the IMC doubled typical heart dose.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

Obtaining identical results with double precision global accuracy on different numbers of processors in parallel particle Monte Carlo simulations

We describe and compare different approaches for achieving numerical reproducibility in photon Monte Carlo simulations. Reproducibility is desirable for code verification, testing, and debugging. Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed. This is a numerical problem because double precision arithmetic is not associative. Parallel Monte Carlo, both domain replicated and decomposed simulations, will run their particles in a different order during different runs of the same simulation because the non-reproducibility of communication between processors. In addition, runs of the same simulation using different domain decompositions will also result in particles being simulated in a different order. In [1], a way of eliminating non-associative accumulations using integer tallies was described. This approach successfully achieves reproducibility at the cost of lost accuracy by rounding double precision numbers to fewer significant digits. This integer approach, and other extended and reduced precision reproducibility techniques, are described and compared in this work. Increased precision alone is not enough to ensure reproducibility of photon Monte Carlo simulations. Non-arbitrary precision approaches require a varying degree of rounding to achieve reproducibility. For the problems investigated in this work double precision global accuracy was achievable by using 100 bits of precision or greater on all unordered sums which where subsequently rounded to double precision at the end of every time-step.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Accelerating solidification process simulation for large-sized system of liquid metal atoms using GPU with CUDA

Molecular dynamics simulation is a powerful tool to simulate and analyze complex physical processes and phenomena at atomic characteristic for predicting the natural time-evolution of a system of atoms. Precise simulation of physical processes has strong requirements both in the simulation size and computing timescale. Therefore, finding available computing resources is crucial to accelerate computation. However, a tremendous computational resource (GPGPU) are recently being utilized for general purpose computing due to its high performance of floating-point arithmetic operation, wide memory bandwidth and enhanced programmability. As for the most time-consuming component in MD simulation calculation during the case of studying liquid metal solidification processes, this paper presents a fine-grained spatial decomposition method to accelerate the computation of update of neighbor lists and interaction force calculation by take advantage of modern graphics processors units (GPU), enlarging the scale of the simulation system to a simulation system involving 10 000 000 atoms. In addition, a number of evaluations and tests, ranging from executions on different precision enabled-CUDA versions, over various types of GPU (NVIDIA 480GTX, 580GTX and M2050) to CPU clusters with different number of CPU cores are discussed. The experimental results demonstrate that GPU-based calculations are typically 9∼11 times faster than the corresponding sequential execution and approximately 1.5∼2 times faster than 16 CPU cores clusters implementations. On the basis of the simulated results, the comparisons between the theoretical results and the experimental ones are executed, and the good agreement between the two and more complete and larger cluster structures in the actual macroscopic materials are observed. Moreover, different nucleation and evolution mechanism of nano-clusters and nano-crystals formed in the processes of metal solidification is observed with large-sized system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Exploiting data representation for fault tolerance

Incorrect computer hardware behavior may corrupt intermediate computations in numerical algorithms, possibly resulting in incorrect answers. Prior work models misbehaving hardware by randomly flipping bits in memory. We start by accepting this premise, and present an analytic model for the error introduced by a bit flip in an IEEE 754 floating-point number. We then relate this finding to the linear algebra concepts of normalization and matrix equilibration. In particular, we present a case study illustrating that normalizing both vector inputs of a dot product minimizes the probability of a single bit flip causing a large error in the dot product's result. Moreover, the absolute error is either less than one or very large, which allows detection of large errors. Then, we apply this to the GMRES iterative solver. We count all possible errors that can be introduced through faults in arithmetic in the computationally intensive orthogonalization phase of GMRES, and show that when the matrix is equilibrated, the absolute error is bounded above by one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On the classification of weakly integral modular categories

In this paper we classify all modular categories of dimension 4m, where m is an odd square-free integer, and all rank 6 and rank 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7. In particular, our results imply that all integral modular categories of rank at most 7 are pointed (that is, every simple object has dimension 1). All the non-integral (but weakly integral) modular categories of ranks 6 and 7 have dimension 4m, with m an odd square free integer, so their classification is an application of our main result. The classification of rank 7 integral modular categories is facilitated by an analysis of the two group actions on modular categories: the Galois group of the field generated by the entries of the S-matrix and the group of invertible isomorphism classes of objects. We derive some valuable arithmetic consequences from these actions.

modular categories↗
DOE OSTI2018

Computational framework for modeling membrane processes without process and solution property simplifications

Accurately modeling membrane processes is critical to evaluating novel process configurations, designing scalable membrane systems, informing process cost estimates, and directing future research. Most membrane process models trade accuracy for computational efficiency by employing simplified approximations of the process (i.e. no salt flux, no pressure drop) and solution properties (i.e. ideal solution, and constant density, viscosity, and diffusivity). Our report introduces a detailed one-dimensional finite difference model for evaluating membrane processes that avoids these common simplifications. We apply this model to quantify the error introduced by these simplifications for case studies of reverse osmosis, osmotically assisted reverse osmosis, forward osmosis, and pressure retarded osmosis. While the magnitude of error introduced by these simplifications is reliant on the case study parameters and specifications, we find that existing model formulations can underestimate or overestimate average water flux by nearly 50% for some membrane processes operating under standard conditions. Lastly we investigate the error introduced by simplified inlet-outlet models that do not solve the governing system of differential equations, and we assess the accuracy of novel inlet-outlet formulations that use a log and geometric mean, instead of the typical arithmetic mean, to represent non-linear water flux profiles.

42 ENGINEERING↗
DOE OSTI2022

Characterization of multi-material 316L-Hastelloy X fabricated via laser powder-bed fusion

The aim of this work is to provide firsthand knowledge of 316 L stainless steel (316 L) and Hastelloy X (HX) multi-material processing via laser powder bed fusion (PBF). Specifically, microstructure of the interface is studied using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). Surface metrology is performed to characterize the resulting surface roughness at the interface followed by tensile and flexural testing of multi-material samples to characterize the mechanical properties of the interfaces. Results showed that use of proper process parameters for each individual material led to formation of a compositional gradient at the interface that stretched for 240 μm (10–12 layers) with no evidence of cracking or porosity. The interface exhibited higher surface roughness compared to 316 L or HX as measured by arithmetic mean height, Sa, and maximum valley depth, Sv, parameters. During tensile testing, samples failed in the 316 L region away from the interface, with comparable yield strength, ultimate strength, and ductility. Finally, it was concluded that the “naturally” formed interface created a compositional gradient which was defect free due to similar values of coefficient of thermal expansion, input energy density, and different Marangoni numbers of the materials.

316L stainless Steel↗
DOE OSTI2016

Sequence polymorphism in an insect RNA virus field population: A snapshot from a single point in space and time reveals stochastic differences among and within individual hosts

Population structure of Homalodisca coagulata Virus-1 (HoCV-1) among and within field-collected insects sampled from a single point in space and time was examined. Polymorphism in complete consensus sequences among single-insect isolates was dominated by synonymous substitutions. The mutant spectrum of the C2 helicase region within each single-insect isolate was unique and dominated by nonsynonymous singletons. Bootstrapping was used to correct the within-isolate nonsynonymous:synonymous arithmetic ratio (N:S) for RT-PCR error, yielding an N:S value ~one log-unit greater than that of consensus sequences. Probability of all possible single-base substitutions for the C2 region predicted N:S values within 95% confidence limits of the corrected within-isolate N:S when the only constraint imposed was viral polymerase error bias for transitions over transversions. These results indicate that bottlenecks coupled with strong negative/purifying selection drive consensus sequences toward neutral sequence space, and that most polymorphism within single-insect isolates is composed of newly-minted mutations sampled prior to selection. -- Highlights: •Sampling protocol minimized differential selection/history among isolates. •Polymorphism among consensus sequences dominated by negative/purifying selection. •Within-isolate N:S ratio corrected for RT-PCR error by bootstrapping. •Within-isolate mutant spectrum dominated by new mutations yet to undergo selection.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network

In this work, time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix–matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree–Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Advanced Polymer Characterization: Modular Operations for Spectral Alignment by Iterative Compression (MOSAIC)

Matrix-assisted laser desorption/ionization (MALDI) mass spectrometry encodes structural information across diverse homo- and copolymer ensembles, yet decrypting these spectra requires a systematic analytical approach. We introduce Modular Operations for Spectral Alignment by Iterative Compression (MOSAIC)─a general cipher algorithm that applies modular arithmetic to filter monomer-derived mass contributions and cluster MALDI peaks by nonconstitutional repeating units (non-CRUs). MOSAIC performs sequential modular operations using monomer mass differences as base units to compress complex spectral data, revealing end-group distributions and comonomer incorporation. As a demonstration, we applied MOSAIC to five copolymers formed by two different polymerization mechanisms. Furthermore, the resulting remainder–mass plots clearly resolve polymer homologs with distinct non-CRUs into visually apparent clusters, enabling intuitive assignment of mass spectral features.

Wang, Hanlin M. [University of Illinois at Urbana−↗
DOE OSTI2024

Quantum-parallel vectorized data encodings and computations on trapped-ion and transmon QPUs

Compact data representations in quantum systems are crucial for the development of quantum algorithms for data analysis. In this study, we present two innovative data encoding techniques, known as QCrank and QBArt, which exhibit significant quantum parallelism via uniformly controlled rotation gates. The QCrank method encodes a series of real-valued data as rotations on data qubits, resulting in increased storage capacity. On the other hand, QBArt directly incorporates a binary representation of the data within the computational basis, requiring fewer quantum measurements and enabling well-established arithmetic operations on binary data. We showcase various applications of the proposed encoding methods for various data types. Notably, we demonstrate quantum algorithms for tasks such as DNA pattern matching, Hamming weight computation, complex value conjugation, and the retrieval of a binary image with 384 pixels, all executed on the Quantinuum trapped-ion QPU. Furthermore, we employ several cloud-accessible QPUs, including those from IBMQ and IonQ, to conduct supplementary benchmarking experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

HDBind: encoding of molecular structure with hyperdimensional binary representations

Traditional methods for identifying “hit” molecules from a large collection of potential drug-like candidates rely on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have a significant limitation in that they require exceptional computing capabilities for even relatively small collections of molecules. Increasingly large and complex state-of-the-art deep learning approaches have gained popularity with the promise to improve the productivity of drug design, notorious for its numerous failures. However, as deep learning models increase in their size and complexity, their acceleration at the hardware level becomes more challenging. Hyperdimensional Computing (HDC) has recently gained attention in the computer hardware community due to its algorithmic simplicity relative to deep learning approaches. The HDC learning paradigm, which represents data with high-dimension binary vectors, allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas (computer vision, bioinformatics, mass spectrometery, remote sensing, edge devices, etc.). To the best of our knowledge, our work is the first to consider HDC for the task of fast and efficient screening of modern drug-like compound libraries. We also propose the first HDC graph-based encoding methods for molecular data, demonstrating consistent and substantial improvement over previous work. We compare our approaches to alternative approaches on the well-studied MoleculeNet dataset and the recently proposed LIT-PCBA dataset derived from high quality PubChem assays. We demonstrate our methods on multiple target hardware platforms, including Graphics Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs), showing at least an order of magnitude improvement in energy efficiency versus even our smallest neural network baseline model with a single hidden layer. Our work thus motivates further investigation into molecular representation learning to develop ultra-efficient pre-screening tools. We make our code publicly available at https://github.com/LLNL/hdbind.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Synthetic-domain computing and neural networks using lithium niobate integrated nonlinear phononics

Analogue computing uses the physical behaviours of devices to provide energy-efficient arithmetic operations. However, scaling up analogue computing platforms by simply increasing the number of devices leads to challenges such as device-to-device variation. Here, in this study, we report scalable analogue computing and neural networks in the synthetic frequency domain using an integrated nonlinear phononic platform on lithium niobate. This synthetic-domain computing is robust to device variations, as vectors and matrices are concurrently encoded at different frequencies within a single device, achieving a high throughput per area. Leveraging inherent nonlinearities, our device-aware neural network can perform a four-class classification task with an accuracy of 98.2%. The nonlinear phononic computing hardware also maintains consistent performance over a wide operational temperature range (characterized up to 192 °C). Our synthetic-domain computing combines single-device parallelism, inherent nonlinearity and environmental stability, and could be of use in edge computing applications in which power efficiency and environmental resilience are crucial.

Ji, Jun [Virginia Polytechnic Inst. and State Univ↗
DOE OSTI2017

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of our linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Photolysis of CH{sub 3}CHO at 248 nm: Evidence of triple fragmentation from primary quantum yield of CH{sub 3} and HCO radicals and H atoms

Radical quantum yields have been measured following the 248 nm photolysis of acetaldehyde, CH{sub 3}CHO. HCO radical and H atom yields have been quantified by time resolved continuous wave Cavity Ring Down Spectroscopy in the near infrared following their conversion to HO{sub 2} radicals by reaction with O{sub 2}. The CH{sub 3} radical yield has been determined using the same technique following their conversion into CH{sub 3}O{sub 2}. Absolute yields have been deduced for HCO radicals and H atoms through fitting of time resolved HO{sub 2} profiles, obtained under various O{sub 2} concentrations, to a complex model, while the CH{sub 3} yield has been determined relative to the CH{sub 3} yield from 248 nm photolysis of CH{sub 3}I. Time resolved HO{sub 2} profiles under very low O{sub 2} concentrations suggest that another unknown HO{sub 2} forming reaction path exists in this reaction system besides the conversion of HCO radicals and H atoms by reaction with O{sub 2}. HO{sub 2} profiles can be well reproduced under a large range of experimental conditions with the following quantum yields: CH{sub 3}CHO + hν{sub 248nm} → CH{sub 3}CHO{sup *}, CH{sub 3}CHO{sup *} → CH{sub 3} + HCO ϕ{sub 1a} = 0.125 ± 0.03, CH{sub 3}CHO{sup *} → CH{sub 3} + H + CO ϕ{sub 1e} = 0.205 ± 0.04, CH{sub 3}CHO{sup *}→{sup o{sub 2}}CH{sub 3}CO + HO{sub 2} ϕ{sub 1f} = 0.07 ± 0.01. The CH{sub 3}O{sub 2} quantum yield has been determined in separate experiments as ϕ{sub CH{sub 3}} = 0.33 ± 0.03 and is in excellent agreement with the CH{sub 3} yields derived from the HO{sub 2} measurements considering that the triple fragmentation (R1e) is an important reaction path in the 248 nm photolysis of CH{sub 3}CHO. From arithmetic considerations taking into account the HO{sub 2} and CH{sub 3} measurements we deduce a remaining quantum yield for the molecular pathway: CH{sub 3}CHO{sup *} → CH{sub 4} + CO ϕ{sub 1b} = 0.6. All experiments can be consistently explained with absence of the formerly considered pathway: CH{sub 3}CHO{sup *} → CH{sub 3}CO + H ϕ{sub 1c} = 0.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The multifacet graphically contracted function method. I. Formulation and implementation

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N{sup 2}n{sup 4}) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N{sub 2} dissociation, cubic H{sub 8} dissociation, the symmetric dissociation of H{sub 2}O, and the insertion of Be into H{sub 2}. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗