Search NASA⌕ Search

SEARCH · Search NASA

Results for “Real Numbers”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Simulation of shot noise effects in the EIC strong hadron cooling accelerator using real number of electrons

In the electron ion collider design, in order to achieve the peak luminosity 10 34 /cm 2 /s with a reasonable lifetime, an efficient coherent electron cooling scheme was proposed to reduce the hadron beam emittance growth. Such a cooling scheme requires a good electron beam quality with a small energy spread. However, the shot noise in the electron beam through the accelerator might be amplified due to the microbunching instability and degrades the electron beam quality in the modulator section of the strong hadron cooling channel and correspondingly cooling rate. In this study, we report on self-consistent simulations of these effects using a real number of electrons to capture the details of shot noise and analysis of the shot noise growth through the accelerator.

Qiang, Ji↗
DOE OSTI2020

Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form

We propose a one-parameter family of low-dissipation centred numerical schemes for solving hyperbolic equations in conservative or non-conservative form, using finite volume or discontinuous Galerkin finite element methods. The new schemes spring out from the multi-dimensional FORCE method and are determined by a single parameter α ≥ 1. Given an increasing sequence of real numbers 1 ≤ α 1 < α 2 < . . . < α K , there corresponds a sequence of numerical schemes with stability restriction associated to a decreasing sequence of Courant numbers 1 > c 1 > c 2 > . . . > c K > 0 and a decreasing sequence of corresponding numerical viscosity functions d 1 > d 2 > . . . > d K . For a given Courant number c k ≤ 1 there is a real number α k > 0 and a corresponding stable scheme with minimal numerical viscosity d k . The proposed schemes suit very well the family of high-order discontinuous Galerkin finite element methods and the recently proposed class of ADER-TR schemes, whose orders of accuracy define decreasing sequences of Courant numbers, as the order of accuracy increases. The centred methods of this paper are stable in 2D and 3D in the frame of simultaneous updating formulae, unlike other centred methods, such as 1D FORCE, which are not. Furthermore, the schemes are highly accurate for slowly-moving waves, which is precisely the kind of waves that traditional centred methods smear disastrously. Additional features of the proposed schemes include ease of implementation and applicability to any hyperbolic system either in conservative or non-conservative form. Here, the proposed schemes are analysed and computationally assessed through a suite of test problems for a linear model system, for the Euler equations in one and two space dimensions, and for the Baer-Nunziato equations for compressible two-phase flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes

Here, this paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton’s method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function α cos(1000x) (polynomial degree ≈ 1433) takes 6 iterations to converge to machine precision when α = 0.9, and the number of iterations only increases to 18 iterations when α = 1 – 10 -9 with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product state structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method’s efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Continuous and discrete modeling of HIV-1 decline on therapy

Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. Here, one of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Degrees of rate control and AutoDiff-driven direct sensitivity analysis in heterogeneous catalysis

Despite the wide application and benefits of the degree of rate control (DRC) analysis, several details remain argued, particularly about the conservation of DRCs at transient (TR) and steady-state (SS) conditions, especially for complex reaction networks. This work argues that previous proofs about the conservation properties of DRCs have been incomplete, and we provide new mathematical proofs at TR and SS conditions. In addition, we use both analytical (automatic differentiation) and numerical (finite difference) approaches to compute DRCs for the case study of ethane hydrogenolysis (EH) over Pt(111). This work confirms that at both TR and SS conditions, the sum of all DRCs, i.e., sum of the degrees of kinetic (DKRC) and thermodynamic rate control (DTRC), is conserved at zero. At SS conditions, the sum of DKRC is conserved at 1 while the sum of DTRC is conserved at −1. In corroboration of previous works, we show that the DTRC for any adsorbate at SS is equal to the product of the species coverage and a constant. In contrast, at TR conditions, the individual sums of both DTRC and DKRC are not conserved and can be any real number, with potential implications for the novel field of dynamic catalysis. Finally, we show that the conventional finite difference (FD) approach, only useful at SS, is prone to inaccuracy and very sensitive to the value of the differential change applied. The optimal differential value also varies significantly with system and rate definition. Consequently, we describe and illustrate in this work the application of the automatic differentiation (AD) approach for the more accurate determination of DRCs at both TR and SS conditions.

Automatic differentiation↗
DOE OSTI2024

Infinite quantum signal processing

Quantum signal processing (QSP) represents a real scalar polynomial of degree d using a product of unitary matrices of size 2 × 2 , parameterized by ( d + 1 ) real numbers called the phase factors. This innovative representation of polynomials has a wide range of applications in quantum computation. When the polynomial of interest is obtained by truncating an infinite polynomial series, a natural question is whether the phase factors have a well defined limit as the degree d → ∞ . While the phase factors are generally not unique, we find that there exists a consistent choice of parameterization so that the limit is well defined in the ℓ 1 space. This generalization of QSP, called the infinite quantum signal processing, can be used to represent a large class of non-polynomial functions. Our analysis reveals a surprising connection between the regularity of the target function and the decay properties of the phase factors. Our analysis also inspires a very simple and efficient algorithm to approximately compute the phase factors in the ℓ 1 space. The algorithm uses only double precision arithmetic operations, and provably converges when the ℓ 1 norm of the Chebyshev coefficients of the target function is upper bounded by a constant that is independent of d . This is also the first numerically stable algorithm for finding phase factors with provable performance guarantees in the limit d → ∞ .

Dong, Yulong [Department of Mathematics, Universit↗
DOE OSTI2020

Twisted bulk-boundary correspondence of fragile topology

A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Science & Technology - Other Topics↗
DOE OSTI2020

Formulation of Three-Phase State Estimation Problem Using a Virtual Reference

State Estimation (SE) is the backbone of modern Energy Management System (EMS) due its capability of processing real time measurements and provide reliable information to system operators. Since its introduction to power systems in the 70’s, SE has been widely used in transmission networks. Distribution grids on the other hand lack sufficient number of real time measurements, and for that reason SE has not been widely implemented on these systems. The recent increase in the number of renewable energy sources connected to the grid at lower voltage levels, the advent of Distribution Automation (DA) and Smart Grids necessitate closer monitoring of distribution networks and thus forcing utilities to upgrade their operations and deploy Advanced Distribution Management Sytems (ADMS). Therefore, Distribution System State Estimation (DSE) is paramount to provide real time monitoring of active distribution grids. This papers investigates the formulation of the three-phase distribution state estimation where in the most general case, none of the system buses may have balanced three phase voltages. In such a case, the choice and definition of the slack bus need to be revisited. Most of the existing work arbitrarily assign the root bus of the distribution feeder as the balanced three-phase reference which may not be realistic for today’s active distribution systems. This paper addresses this shortcoming of the existing SE formulations by introducing a virtual reference bus. Here, the proposed approach is effectively validated by simulations carried out on distribution test systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Low-frequency Raman signature of Ag-intercalated few-layer MoS 2

Density functional theory based calculations and experimental analysis on a limited number of real samples are performed to study how the presence of silver intercalated in the van der Waals gap of few-layer MoS 2 affects the low-frequency Raman active modes of this material. Silver is found to predominantly affect the breathing-like and shear-like vibrational modes of MoS 2 . These modes correspond to quasi-rigid movements of each individual layer with a restoring force (and, in turn, frequency) that is determined by modulations in the weak interlayer interactions. Noticeable red-shifts with increasing Ag concentration are found for all low-frequency modes. This finding indicates the potential for low-frequency vibrations as useful gauges for practical determination of silver concentration using low-frequency Raman spectroscopy. Finally, this work also describes a semi-classical linear chain model that allows to extrapolate results to a large number of layers. Further, first-principles calculations show how Raman spectroscopy can be used to characterize the quality of the two-dimensional interface between MoS 2 and a silver substrate.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Controlled precision QUBO-based algorithm to compute eigenvectors of symmetric matrices

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvector/eigenvalue pair to essentially any arbitrary precision, and with minor modifications, can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Tau-Jet Matching and Tag-and-Probe Tau Tagging Efficiencies for HH→bbτ+τ− Searches Using Run 3 CMS Scouting Data

We are studying tau-jet matching efficiency and tau tagging efficiency for the search for Higgs boson pair production in the HH→bbτ+τ− decay channel using Run 3 CMS scouting data. Collision events in the CMS detector produce many particle candidates, so jets are clustered using the anti-kT algorithm to identify possible tau signatures. In Monte Carlo simulation, tau-jet matching efficiency can be measured by comparing generated taus to reconstructed jets. In actual collision data, however, generated taus are not available, so we use a tag-and-probe method with Z→τ+τ− candidate events. In this method, one tau candidate is used as the tag and the other as the probe. The invariant mass of the tau-pair candidates is plotted and fitted with signal and background functions to estimate the number of real tau events and determine the tagging efficiency. By comparing efficiencies in data and Monte Carlo simulation, this work helps evaluate the performance of scouting-based tau reconstruction and tau tagging for future HH→bbτ+τ− searches.

Bellot, Annella [North Central Coll.; Fermilab]↗
DOE OSTI2026

Tau-Jet Matching and Tag-and-Probe Tau Tagging Efficiencies for HH→bbτ+τ− Searches Using Run 3 CMS Scouting Data

We are studying tau-jet matching efficiency and tau tagging efficiency for the search for Higgs boson pair production in the HH→bbτ+τ− decay channel using Run 3 CMS scouting data. Collision events in the CMS detector produce many particle candidates, so jets are clustered using the anti-kT algorithm to identify possible tau signatures. In Monte Carlo simulation, tau-jet matching efficiency can be measured by comparing generated taus to reconstructed jets. In actual collision data, however, generated taus are not available, so we use a tag-and-probe method with Z→τ+τ− candidate events. In this method, one tau candidate is used as the tag and the other as the probe. The invariant mass of the tau-pair candidates is plotted and fitted with signal and background functions to estimate the number of real tau events and determine the tagging efficiency. By comparing efficiencies in data and Monte Carlo simulation, this work helps evaluate the performance of scouting-based tau reconstruction and tau tagging for future HH→bbτ+τ− searches.

Bellot, Annella [North Central Coll.; Fermilab]↗
DOE OSTI2020

Selective adsorption removal of carbonyl molecular foulants from real fast pyrolysis bio-oils

A novel sorbent-based separation process has been developed to selectively remove target molecules from the real fast pyrolysis (FP) pine bio-oils. Specifically, zeolitic molecular sieves and functionalized polymeric resins were found to effectively reduce carbonyl content and carboxylic acid number of a real pine fast pyrolysis bio-oils, therefore enhance bio-oil stability and preserve down-stream catalyst. Our results provide the first-time evidence on the potential effectiveness of sorption technology strategy for dealing with real FP bio-oils, reducing the carbonyl-rich FP oils from 7.5 mmolg-1 down to 4 mmolg-1 at 40 ?, which has potential to enable bio-oil stabilization and enhance operation stability for down-stream upgrading/hydrotreating processes.

Church, Aimee L.↗
DOE OSTI2020

How Low Can You Go? Using Synthetic 3D Imagery to Drastically Reduce Real-World Training Data for Object Detection

Deep convolutional neural networks (DCNNs) currently provide state-of-the-art performance on image classification and object detection tasks, and there are many global security mission areas where such models could be extremely useful. Crucially, the success of these models is driven in large part by the widespread availability of high-quality open source data sets such as Image Net, Common Objects in Context (COCO), and KITTI, which contain millions of images with thousands of unique labels. However, global security relevant objects-of-interest can be difficult to obtain: relevant events are low frequency and high consequence; the content of relevant images is sensitive; and adversaries and proliferators seek to obscure their activities. For these cases where exemplar data is hard to come-by, even fine-tuning an existing model with available data can be effectively impossible. Recent work demonstrated that models can be trained using a combination of real-world and synthetic images generated from 3D representations; that such models can exceed the performance of models trained using real-world data alone; and that the generated images need not be perfectly realistic (Tremblay, et al., 2018). However, this approach still required hundreds to thousands of real-world images for training and fine tuning, which for sparse, global security-relevant datasets can be an unrealistic hurdle. In this research, we validate the performance and behavior of DCNN models as we drive the number of real-world images used for training object detection tasks down to a minimal set. We perform multiple experiments to identify the best approach to train DCNNs from an extremely small set of real-world images. In doing so, we: Develop state-of-the-art, parameterized 3D models based on real-world images and sample from their parameters to increase the variance in synthetic image training data; Use machine learning explainability techniques to highlight and correct through targeted training the biases that result from training using completely synthetic images; and Validate our results by comparing the performance of the models trained on synthetic data to one another, and to a control model created by fine-tuning an existing ImageNet-trained model with a limited number (hundreds) of real-world images.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantifying the Influence of Size, Shape, and Density of Microplastics on Their Transport Modes: A Modeling Approach

Microplastics (MPs) pose significant risks to marine ecosystems and human health, necessitating accurate predictions of their distributions in aquatic environments for effective risk mitigation. However, understanding MP transport dynamics is challenging because of the inadequate representation of MP characteristics such as size, shape, and density in numerical models. Further, the accuracy of the MP vertical profiles in existing models has not been thoroughly validated. Thus, we developed an MP transport model within the Finite Volume Community Ocean Model framework (FVCOM-MP) by integrating MP characteristics. We validated FVCOM-MP against experimental and analytical data, focusing on various MP transport modes and transitions. FVCOM-MP successfully replicates MP profiles in different transport modes, including the bedload, surface-load, suspended-load, and mixed-load modes. Additionally, we introduce phase diagrams for classifying MP transport modes based on particle characteristics, enhancing our understanding of MP dynamics in aquatic systems. The transport modes for a number of real-world MP particles, including fishing line, plastic bag/bottle fragments, synthetic fibers, tire wear particles, polyvinyl chloride and expanded polystyrene pellets, were analyzed with these phase diagrams.

Microplastic transport, Settling velocity, Rising ↗
DOE OSTI2026

Roadmap for Solar Photovoltaic (PV) Cybersecurity: A vision for improving cyber maturity of distributed and utility-scale solar energy installations

As the solar energy sector continues to expand, its integration into the broader energy infrastructure presents both unprecedented opportunities and new risks. The increasing reliance on digital technologies and interconnected systems in solar energy creates an expanded attack surface for motivated cyber adversaries. Cyberattacks have the potential to cause disruptions in energy production, damage to equipment, financial losses, and compromises in national security. Therefore, ensuring robust cybersecurity measures is paramount to protect the integrity, availability, confidentiality, and access control of solar energy systems. However, there are still key gaps and challenges to be addressed in industry and research, which stakeholders must race to address as they combat a growing number of real-world cyber incidents that affect solar energy systems and a growing number of vulnerabilities discovered and disclosed in key types of equipment. This roadmap explore the current state of solar PV cybersecurity and the gaps and challenges still to be addressed.

14 - SOLAR ENERGY↗
DOE OSTI2020

Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model

This paper presents a novel methodology to use direct numerical simulation (DNS) to study the impact of isotropic homogeneous turbulence on the condensational growth of cloud droplets. As shown by previous DNS studies, the impact of turbulence increases with the computational domain size, that is, with the Reynolds number, because larger eddies generate higher and longer-lasting supersaturation fluctuations that affect growth of individual cloud droplets. The traditional DNS can only simulate a limited range of scales because of the excessive computational cost that comes from resolving all scales involved, that is, from large scales at which the turbulent kinetic energy (TKE) is introduced down to the Kolmogorov microscale, and from following every single droplet. The novel approach is referred to as the “scaled-up DNS”. The scaling up is done in two parts, first by increasing both the computational domain and the Kolmogorov microscale and second by using super-droplets instead of real droplets. To ensure proper dissipation of TKE and scalar variance at small scales, molecular transport coefficients are appropriately scaled up with the grid length. For the scaled-up domains, say, meters and tens of meters, one needs to follow billions of real droplets. This is not computationally feasible, and so-called super-droplets are applied in scaled-up DNS simulations. Each super-droplet represents an ensemble of identical real droplets, and the number of real droplets represented by a super-droplet is referred to as the multiplicity attribute. After simple tests showing the validity of the methodology, scaled-up DNS simulations are conducted for five domains, the largest of 64 3 m 3 volume using a DNS of 256 3 grid points and various multiplicities. All simulations are carried out with vanishing mean vertical velocity and with no mean supersaturation, similarly to past DNS studies. As expected, the supersaturation fluctuations as well as the spread in droplet size distribution increase with the domain size, with the droplet radius variance increasing in time t as t 1∕2 as identified in previous DNS studies. Scaled-up simulations with different multiplicities document numerical convergence of the scaled-up solutions. Finally, we compare the scaled-up DNS results with a simple stochastic model that calculates supersaturation fluctuations based on the vertical velocity fluctuations updated using the Langevin equation. Overall, the results document similar scaling to previous small-domain DNS simulations and support the notion that the stochastic subgrid-scale model is a valuable tool for the multi-scale simulation of droplet spectral evolution applying a large-eddy simulation model.

54 ENVIRONMENTAL SCIENCES↗