Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Formal Methods”

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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

SU-F-BRD-15: Quality Correction Factors in Scanned Or Broad Proton Therapy Beams Are Indistinguishable

Purpose: The IAEA TRS-398 code of practice details the reference conditions for reference dosimetry of proton beams using ionization chambers and the required beam quality correction factors (kQ). Pencil beam scanning (PBS) requires multiple spots to reproduce the reference conditions. The objective is to demonstrate, using Monte Carlo (MC) calculations, that kQ factors for broad beams can be used for scanned beams under the same reference conditions with no significant additional uncertainty. We consider hereafter the general Alfonso formalism (Alfonso et al, 2008) for non-standard beam. Methods: To approach the reference conditions and the associated dose distributions, PBS must combine many pencil beams with range modulation and shaping techniques different than those used in passive systems (broad beams). This might lead to a different energy spectrum at the measurement point. In order to evaluate the impact of these differences on kQ factors, ion chamber responses are computed with MC (Geant4 9.6) in a dedicated scanned pencil beam (Q-pcsr) producing a 10×10cm2 composite field with a flat dose distribution from 10 to 16 cm depth. Ion chamber responses are also computed by MC in a broad beam with quality Q-ds (double scattering). The dose distribution of Q -pcsr matches the dose distribution of Q-ds. k-(Q-pcsr,Q-ds) is computed for a 2×2×0.2cm{sup 3} idealized air cavity and a realistic plane-parallel ion chamber (IC). Results: Under reference conditions, quality correction factors for a scanned composite field versus a broad beam are the same for air cavity dose response, k-(Q-pcsr,Q-ds) =1.001±0.001 and for a Roos IC, k-(Q-pcsr,Q-ds) =0.999±0.005. Conclusion: Quality correction factors for ion chamber response in scanned and broad proton therapy beams are identical under reference conditions within the calculation uncertainties. The results indicate that quality correction factors published in IAEA TRS-398 can be used for scanned beams in the SOBP of a high-energy proton beam. Jefferson Sorriaux is financed by the Walloon Region under the convention 1217662. Jefferson Sorriaux is sponsored by a public-private partnership IBA - Walloon Region.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

The challenges of theory-software translation

Background: Software is now ubiquitous within research. In addition to the general challenges common to all software development projects, research software must also represent, manipulate, and provide data for complex theoretical constructs. Ensuring this process of theory-software translation is robust is essential to maintaining the integrity of the science resulting from it, and yet there has been little formal recognition or exploration of the challenges associated with it. Methods: We thematically analyse the outputs of the discussion sessions at the Theory-Software Translation Workshop 2019, where academic researchers and research software engineers from a variety of domains, and with particular expertise in high performance computing, explored the process of translating between scientific theory and software. Results: We identify a wide range of challenges to implementing scientific theory in research software and using the resulting data and models for the advancement of knowledge. We categorise these within the emergent themes of design, infrastructure, and culture, and map them to associated research questions. Conclusions: Systematically investigating how software is constructed and its outputs used within science has the potential to improve the robustness of research software and accelerate progress in its development. We propose that this issue be examined within a new research area of theory-software translation, which would aim to significantly advance both knowledge and scientific practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Application of the Combined Judgmental and Randomly Placed Sampling Method

In the wake of the 2001 anthrax incidents in the United States, there has been considerable discussion about the role of judgmental and probabilistic sampling strategies, particularly in the context of clearance sampling. The Combined Judgmental and Random (CJR) methodology provides a statistical methodology that allows practitioners to leverage information from both judgmental and randomly selected sample locations and then quantify the confidence in negative results. The objective of the CJR sampling design is to demonstrate, with high probability, that a high percentage of the decision area (or population) is acceptable, given that none of the samples are unacceptable. The purpose of this document is to assist practitioners to appropriately use the CJR methodology and to implement this sampling design in Visual Sample Plan (VSP). We begin by defining some fundamental terms. A decision area is the geographical or spatial area (indoor or outdoor) about which practitioners wish to draw a conclusion on the basis of sampling and other relevant information. Decision areas typically include all or part of a building, but they may be any contaminated (or potentially contaminated) area for which characterization or clearance is required. In this report, a statistical sampling approach refers to any sampling approach based on a mathematical or statistical model that provides confidence or probability statements about the decision area. Statistical sampling approaches typically involve taking samples at random locations, or at the nodes of a randomly located grid or lattice that is superimposed on the decision area. The term probabilistic sampling is often used to describe statistical sampling designs that exclusively use randomly located samples. This terminology implies that probabilistic statements can only be made based upon the results of randomly placed samples. However, the CJR method utilizes a Bayesian model that gives rise to a formal probabilistic statement regarding the acceptability of the decision area based upon the information obtained from both judgmental and random samples. Judgmental samples play a vital role in the characterization and clearance process because they include the informed prior belief and expert knowledge of personnel involved in the sampling process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the connection between least squares, regularization, and classical shadows

Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS ``shadows'' completely analogous to those in CS---namely, point estimators calculated from the empirical frequencies of single measurements---we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies---differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying ``shadow'' umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A generalized method for high throughput in-situ experiment data analysis: An example of battery materials exploration

A generalized method is introduced to extract critical information from series of ranked correlated data. The method is generally applicable to all types of spectra evolving as a function of any arbitrary parameter. This approach is based on correlation functions and statistical scedasticity formalism. Numerous challenges in analyzing high throughput experimental data can be tackled using the herein proposed method. We applied this method to understand the reactivity pathway and formation mechanism of a Li-ion battery cathode material during high temperature synthesis using in-situ highenergy X-ray diffraction. We demonstrate that Pearson's correlation function can easily unravel all major phase transition and, more importantly, the minor structural changes which cannot be revealed by conventionally inspecting the series of diffraction patterns. Furthermore, a two-dimensional (2D) reactivity pattern calculated as the scedasticity along all measured reciprocal space of all successive diffraction pattern pairs unveils clearly the structural evolution path and the active areas of interest during the synthesis. The methods described here can be readily used for on-the-fly data analysis during various in-situ operando experiments in order to quickly evaluate and optimize experimental conditions, as well as for post data analysis and large data mining where considerable amount of data hinders the feasibility of the investigation through point-by-point inspection.

25 ENERGY STORAGE↗
DOE OSTI2015

Transition matrices and orbitals from reduced density matrix theory

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.

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

SU-E-T-516: Measurement of the Absorbed Dose Rate in Water Under Reference Conditions in a CyberKnife Unit

Purpose: This paper aims to measure the absorbed-dose-rate in a CyberKnife unit reference-field (6cm diameter) using three ionization chambers (IC) following the new IAEA/AAPM formalism and Gafchromic film (MD-V3-55 and EBT3) protocol according to our work reported previously. Methods: The absorbed-dose-rates were measured at 90cm and 70cm SSD in a 10cmx10cm field and at 70cm SSD in a 5.4cmx5.4cm equivalent to 6cm diameter field using a linac Varian iX. All measurements were performed at 10cm depth in water. The correction factors that account for the difference between the IC response on the reference field and the CyberKnife reference field, k-(Q-msr,Q)^(f-msr,f-ref), were evaluated and Gafchromic film were calibrated using the results obtained above. Under the CyberKnife reference conditions, the factors were used to measure the absorbed-dose-rate with IC according to the new formalism and the calibrated film was irradiated in water. The film calibration curve was used to evaluate the absorbed-dose-rate in the CyberKnife unit. Results: Difference up to 2.56% is observed between dose-rate measured with IC in the reference 10cmx10cm field, depending where the chamber was calibrated, which was not reflected in the correction factor k-(Q-msr,Q)^(f-msr,f-ref ) where variations of ~0.15%-0.5% were obtained. Within measurements uncertainties, maximum difference of 1.8% on the absorbed-dose-rate in the CyberKnife reference field is observed between all IC and the films Conclusion: Absorbed-dose-rate to water was measured in a CyberKnife reference field with acceptable accuracy (combined uncertainties ~1.32%-1.73%, k=1) using three IC and films. The MD-V3-55 film as well as the new IAEA/AAPM formalism can be considered as a suitable dosimetric method to measure absorbed-dose-rate to water in small and non-standard CyberKnife fields used in clinical treatments However, the EBT3 film is not appropriated due to the high uncertainty provided (combined uncertainty ~9%, k=1) This work is partially supported by Conacyt grant 127409 and PAPIITUNAM grant IN10581.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

An Eigenvector-Based Method of Radio Array Calibration and Its Application to the Tianlai Cylinder Pathfinder

We propose an eigenvector-based formalism for the calibration of radio interferometer arrays. In the presence of a strong dominant point source, the complex gains of the array can be obtained by taking the first eigenvector of the visibility matrix. We use the stable principle component analysis method to help separate outliers and noise from the calibrator signal to improve the performance of the method. This method can be applied with poorly known beam model of the antenna, is insensitive to outliers or imperfections in the data, and has low computational complexity. It thus is particularly suitable for the initial calibration of the array, which can serve as the initial point for more accurate calibrations. We demonstrate this method by applying it to the cylinder pathfinder of the Tianlai experiment, which aims to measure the dark energy equation of state using the baryon acoustic oscillation features in the large-scale structure by making intensity mapping observation of the redshifted 21 cm emission of the neutral hydrogen (H i). The complex gain of the array elements and the beam profile in the east–west direction (short axis of the cylinder) are successfully obtained by applying this method to the transit data of bright radio sources.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical transformations to efficiently compute the formation and energetics of small polarons A different approach based on a Landau-Pekar energy functional has been proposed in the recent literature. Here in this work, we analyze and compare these two methods in detail. We show that the small polaron energy is identical in the two formalisms when using the same polaron wave function. We also show that our canonical transformation formalism can predict polaron band structures and can properly treat zero- and finite-temperature lattice vibration effects, although at present using a fixed polaron wave function. Conversely, the energy functional approach can compute the polaron wave function, but as we show here, it neglects lattice vibrations and cannot address polaron self-localization and thermal band narrowing. Taken together, this work relates two different methods developed recently to study polarons from first-principles, highlighting their merits and shortcomings and discussing them both in a unified formalism.

36 MATERIALS SCIENCE↗
DOE OSTI2014

SU-F-18C-04: A Combination of Monoenergetic Reconstruction and Stoichiometric Calibration for Tissue Characterization Using Dual Energy Computed Tomography

Purpose: Dual energy computed tomography (DECT) pre-reconstruction methods require the prior knowledge of the X-ray source spectrum to allow extracting physical parameters needed for radiation therapy dose calculation, such as electron density (ED) and the effective atomic number (EAN). While DECT stoichiometric calibration may provide reliable performance for typical radiation therapy clinical conditions, it is yet to be adapted to prereconstruction methods. The presence of noise and inaccurate spectrum description may lead to systematic errors and artifacts which compromise the accuracy of treatment planning. Methods: A new technique is investigated which consists in applying a DECT stoichiometric calibration method to a set of monoenergetic images obtained with a DECT prereconstruction method. To evaluate the performance of this extended method, a simulation environment is developed to generate DECT scans under well controlled conditions, to reconstruct monoenergetic images of a tissue-equivalent phantom from transformed sinograms and to extract ED and EAN maps using a DECT formalism. Result: Under simulated clinical conditions, the accuracy in determining ED with the extended method versus a pre-reconstruction method alone is shown to be better than 0.35% versus 0.5%, respectively. In the presence of a realistic noise level, EAN determination presents a relative mean error that drops from 2.5% to 0.5% once the calibration is applied. Considering a spectrum alteration by a 1 mm Cu layer, EAN errors are up to 30% for the pre-reconstruction method alone versus less than 3% for the extended method. Conclusion: This study shows that combining pre-reconstruction DECT methods with a stoichiometric calibration considerably improves the accuracy and reliability of tissue characterization for radiation therapy in a clinical context. The presented method could potentially be adapted as gold standard for dose calculation methods based on DECT.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2018

An Eigenvector-based Method of Radio Array Calibration and Its Application to the Tianlai Cylinder Pathfinder

We propose an eigenvector-based formalism for the calibration of radio interferometer arrays. In the presence of a strong dominant point source, the complex gains of the array can be obtained by taking the first eigenvector of the visibility matrix. We use the stable principle component analysis (SPCA) method to help separate outliers and noise from the calibrator signal to improve the performance of the method. This method can be applied with poorly known beam model of the antenna, and is insensitive to outliers or imperfections in the data, and has low computational complexity. It thus is particularly suitable for the initial calibration of the array, which can serve as the initial point for more accurate calibrations. We demonstrate this method by applying it to the cylinder pathfinder of the Tianlai experiment, which aims to measure the dark energy equation of state using the baryon acoustic oscillation (BAO) features in the large scale structure by making intensity mapping observation of the redshifted 21~cm emission of the neutral hydrogen (HI). The complex gain of the array elements and the beam profile in the East-West direction (short axis of the cylinder) are successfully obtained by applying this method to the transit data of bright radio sources.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Huzinaga projection embedding for efficient and accurate energies of systems with localized spin-densities

We demonstrate the accuracy and efficiency of the restricted open-shell and unrestricted formulation of the absolutely localized Huzinaga projection operator embedding method. Restricted open-shell and unrestricted Huzinaga projection embedding in the full system basis is formally exact to restricted open-shell and unrestricted Kohn–Sham density functional theory, respectively. By utilizing the absolutely localized basis, we significantly improve the efficiency of the method while maintaining high accuracy. Furthermore, the absolutely localized basis allows for high accuracy open-shell wave function methods to be embedded into a closed-shell density functional theory environment. The open-shell embedding method is shown to calculate electronic energies of a variety of systems to within 1 kcal/mol accuracy of the full system wave function result. For certain highly localized reactions, such as spin transition energies on transition metals, we find that very few atoms are necessary to include in the wave function region in order to achieve the desired accuracy. This extension further broadens the applicability of our absolutely localized Huzinaga level-shift projection operator method to include open-shell species. Here, we apply our method to several representative examples, such as spin splitting energies, catalysis on transition metals, and radical reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Solving the nuclear pairing model with neural network quantum states

In this work, we present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the groundstate wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically-exact full configuration interaction values.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Mapping valence electron distributions with multipole density formalism using 4D-STEM

Recent advancement in aberration correction and detector technology opened a door to various applications using 4D-STEM, which yields a diffraction pattern for each scanning position within a crystal unit-cell in scanning transmission electron microscopy (STEM) and generates incredible amounts of data in momentum space. Currently 4D-STEM analysis relies on the center-of-mass of the diffraction patterns in electric field and charge density mapping. It only derives the total projected charge density and is limited to phase objects, e.g. extremely thin samples. Here, we propose a new analytical method to accurately map aspherical valence electron distributions with atom-centered multipolar functions formalism using the whole 4D-STEM dataset. We demonstrate that, with the full dynamical calculations for various sample thicknesses, the method is sensitive not only to the miniscule charge transfer, but also to the atomic site symmetry and aspherical electron orbitals. The process of the refinement is much more robust and reliable than quantitative convergent beam electron diffraction.

4D-STEM↗
DOE OSTI2015

Spin-flip configuration interaction singles with exact spin-projection: Theory and applications to strongly correlated systems

Spin-flip approaches capture static correlation with the same computational scaling as the ordinary single reference methods. Here, we extend spin-flip configuration interaction singles (SFCIS) by projecting out intrinsic spin-contamination to make it spin-complete, rather than by explicitly complementing it with spin-coupled configurations. We give a general formalism of spin-projection for SFCIS, applicable to any spin states. The proposed method is viewed as a natural unification of SFCIS and spin-projected CIS to achieve a better qualitative accuracy at a low computational cost. While our wave function ansatz is more compact than previously proposed spin-complete SF approaches, it successfully offers more general static correlation beyond biradicals without sacrificing good quantum numbers. It is also shown that our method is invariant with respect to open-shell orbital rotations, due to the uniqueness of spin-projection. We will report benchmark calculations to demonstrate its qualitative performance on strongly correlated systems, including conical intersections that appear both in ground-excited and excited-excited degeneracies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Higher-order temporal integration for the incompressible Navier–Stokes equations in bounded domains

Here, this paper compares and contrasts higher-order, semi-implicit temporal integration strategies for the incompressible Navier–Stokes methods based on spectral deferred corrections applied to certain gauge or auxiliary variable formulations of the equations. Particular focus is placed on the imposition of boundary conditions in the semi-implicit formulation, the accurate treatment of the pressure term, and the smoothness of the numerical solution for different formulations. The main result presented here is the formulation and numerical validation of a single-step, semi-implicit method called spectral deferred pressure corrections, which can in theory obtain arbitrary formal order of accuracy in time. Lastly, numerical results demonstrate up to eighth-order accuracy, scenarios where optimal temporal accuracy is attained, and scenarios where order reduction is observed due to time-dependent boundary conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Three-body resonances in the φ 4 theory

We study the properties of three-body resonances using a lattice complex scalar φ4 theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Note on two formulations of Crank-Nicolson method for Navier-Stokes equations

Here, we consider two formulations of the Crank-Nicolson (CN) method for the Navier-Stokes equations (NSE). The “natural” way of implementing CN for NSE is formally second order accurate in time for both velocity and pressure, whereas another formulation approximates pressure with only first order accuracy in time. Both versions of the method are applied to the benchmark problem of computing drag and lift in the flow around a cylinder. We show that the presumably more accurate version of the CN can create a solution with nonphysical oscillations and give incorrect predictions for the maximal drag coefficient, whereas the other formulation of the method predicts the drag and lift coefficients more accurately and does not introduce nonphysical oscillations. We locate the source of the issue and suggest several remedies.

Crank-Nicolson↗