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 451 records · Page 25

Symbolic methods for the evaluation of sum rules of Bessel functions

The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NWChem: Quantum Chemistry Simulations at Scale

Methods based on quantum mechanics equations have been developed since the 1930's with the purpose of accurately studying the electronic structure of molecules. However, it is only during the last two decades that intense development of new computational algorithms has opened the possibility of performing accurate simulations of challenging molecular processes with high-order many-body methods. A wealth of evidence indicates that the proper inclusion of instantaneous interactions between electrons (or the so-called electron correlation effects) is indispensable for the accurate characterization of chemical reactivity, molecular properties, and interactions of light with matter. The availability of reliable methods for benchmarking of medium-size molecular systems provides also a unique chance to propagate high-level accuracy across spatial scales through the multiscale methodologies. Some of these methods have potential to utilize computational resources in an effi*cient way since they are characterized by high numerical complexity and appropriate level of data granularity, which can be effi*ciently distributed over multi-processor architectures. The broad spectrum of coupled cluster (CC) methods falls into this class of methodologies. Several recent CC implementations clearly demonstrated the scalability of CC formalisms on architectures composed of hundreds thousand computational cores. In this context NWChem provides a collection of Tensor Contraction Engine (TCE) generated parallel implementations of various coupled cluster methods capable of taking advantage of many thousand of cores on leadership class parallel architectures.

chemistry↗

Finding Horndeski theories with Einstein gravity limits

The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or not. For this purpose, we develop a new and surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.

79 ASTRONOMY AND ASTROPHYSICS↗

Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis–Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Integrative Analysis of Metabolic Models – from Structure to Dynamics

The characterization of biological systems with respect to their behavior and functionality based on versatile biochemical interactions is a major challenge. To understand these complex mechanisms at systems level modeling approaches are investigated. Different modeling formalisms allow metabolic models to be analyzed depending on the question to be solved, the biochemical knowledge and the availability of experimental data. Here, we describe a method for an integrative analysis of the structure and dynamics represented by qualitative and quantitative metabolic models. Using various formalisms, the metabolic model is analyzed from different perspectives. Determined structural and dynamic properties are visualized in the context of the metabolic model. Interaction techniques allow the exploration and visual analysis thereby leading to a broader understanding of the behavior and functionality of the underlying biological system. The System Biology Metabolic Model Framework (SBM{sup 2} – Framework) implements the developed method and, as an example, is applied for the integrative analysis of the crop plant potato.

60 APPLIED LIFE SCIENCES↗

A framework for measuring weak-lensing magnification using the Fundamental Plane

ABSTRACT Galaxy–galaxy lensing is an essential tool for probing dark matter haloes and constraining cosmological parameters. While galaxy–galaxy lensing measurements usually rely on shear, weak-lensing magnification contains additional constraining information. Using the Fundamental Plane (FP) of elliptical galaxies to anchor the size distribution of a background population is one method that has been proposed for performing a magnification measurement. We present a formalism for using the FP residuals of elliptical galaxies to jointly estimate the foreground mass and background redshift errors for a stacked lens scenario. The FP residuals include information about weak-lensing magnification κ, and therefore foreground mass, since to first order, non-zero κ affects galaxy size but not other FP properties. We also present a modular, extensible code that implements the formalism using emulated galaxy catalogues of a photometric galaxy survey. We find that combining FP information with observed number counts of the source galaxies constrains mass and photo-z error parameters significantly better than an estimator that includes number counts only. In particular, the constraint on the mass is 17.0 per cent if FP residuals are included, as opposed to 27.7 per cent when only number counts are included. The effective size noise for a foreground lens of mass $M_\mathrm{ H}=10^{14}\, \mathrm{M}_\odot$, with a conservative selection function in size and surface brightness applied to the source population, is σκ, eff = 0.250. We discuss the improvements to our FP model necessary to make this formalism a practical companion to shear analyses in weak-lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Second-order spectral line shift comparisons

The second-order spectral line width formulae from the projection operator and kinetic theory methods were recently compared. It was shown that a systematic expansion of the projection operator width expression including initial correlations formally agrees with the second-order kinetic theory result. It is now shown that the second-order dynamic shifts are also formally the same. The static shifts, however, differ due to an ad hoc treatment of electron-electron correlations in the projection operator method. The approximation is necessary in order to screen the radiator-electron interactions. The differences, however, are expected to be small. Finally, the results suggest using the rigorous and more compact second-order width and shift expressions from the kinetic theory method as the starting point for spectral line shape calculations. At line center, however, the projection operator second-order expression for the width and shift simplifies and reduces to the kinetic theory result.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within “chemical accuracy” (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob’s ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 − N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Chemistry↗

PyDII: A python framework for computing equilibrium intrinsic point defect concentrations and extrinsic solute site preferences in intermetallic compounds

Point defects play an important role in determining the structural stability and mechanical behavior of intermetallic compounds. To help quantitatively understand the point defect properties in these compounds, we developed PyDII, a Python program that performs thermodynamic calculations of equilibrium intrinsic point defect concentrations and extrinsic solute site preferences in intermetallics. The algorithm implemented in PyDII is built upon a dilute-solution thermodynamic formalism with a set of defect excitation energies calculated from first-principles density-functional theory methods. The analysis module in PyDII enables automated calculations of equilibrium intrinsic antisite and vacancy concentrations as a function of composition and temperature (over ranges where the dilute solution formalism is accurate) and the point defect concentration changes arising from addition of an extrinsic substitutional solute species. To demonstrate the applications of PyDII, we provide examples for intrinsic point defect concentrations in NiAl.

36 MATERIALS SCIENCE↗

Implementation of High-Order Multireference Coupled-Cluster Methods on Intel Many Integrated Core Architecture

Here we discuss the implementation of multireference coupled-cluster formalism with singles, doubles, and noniterative triples (MRCCSD(T)), which is capable of taking advantage of the processing power of the Intel Xeon Phi coprocessor. We discuss the integration of two levels of parallelism underlying the MRCCSD(T) implementation with computational kernels designed to offload the computationally intensive parts of the MRCCSD(T) formalism to Intel Xeon Phi coprocessors. Special attention is given to the enhancement of the parallel performance by task reordering that has improved load balancing in the noniterative part of the MRCCSD(T) calculations. We also discuss aspects regarding efficient optimization and vectorization strategies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields

We report that since the 1950s, a large body of work has been published on connecting the curvature of a crystal lattice to geometrically necessary dislocations densities of a crystal lattice. Studying dislocation transmission through grains and across their boundaries requires the lattice curvature to be preserved. However, traditional crystal plasticity models and their numerical implementations do not formally preserve lattice curvature. In this paper, a continuous crystal lattice orientation finite element method (LOFEM) is proposed to rectify this impediment to the inclusion of dislocation-based constitutive models. The methodology is first presented, and then it is demonstrated for tension and compression deformations of a copper polycrystal. It is shown that under the same deformation histories, the lattice continuity constraint alters the evolving state in comparison to the traditional approach, including retarding the rate at which the crystallographic texture strengthens under monotonic deformation. Lastly, taking advantage of the finite element representation of the lattice orientation, the Nye tensor is computed on lattices misoriented by deformation and is subsequently used to compute evolving dislocation density distributions.

36 MATERIALS SCIENCE↗

Robust Estimation of Electron Density From Anatomic Magnetic Resonance Imaging of the Brain Using a Unifying Multi-Atlas Approach

Purpose: To develop a reliable method to estimate electron density based on anatomic magnetic resonance imaging (MRI) of the brain. Methods and Materials: We proposed a unifying multi-atlas approach for electron density estimation based on standard T1- and T2-weighted MRI. First, a composite atlas was constructed through a voxelwise matching process using multiple atlases, with the goal of mitigating effects of inherent anatomic variations between patients. Next we computed for each voxel 2 kinds of conditional probabilities: (1) electron density given its image intensity on T1- and T2-weighted MR images; and (2) electron density given its spatial location in a reference anatomy, obtained by deformable image registration. These were combined into a unifying posterior probability density function using the Bayesian formalism, which provided the optimal estimates for electron density. We evaluated the method on 10 patients using leave-one-patient-out cross-validation. Receiver operating characteristic analyses for detecting different tissue types were performed. Results: The proposed method significantly reduced the errors in electron density estimation, with a mean absolute Hounsfield unit error of 119, compared with 140 and 144 (P<.0001) using conventional T1-weighted intensity and geometry-based approaches, respectively. For detection of bony anatomy, the proposed method achieved an 89% area under the curve, 86% sensitivity, 88% specificity, and 90% accuracy, which improved upon intensity and geometry-based approaches (area under the curve: 79% and 80%, respectively). Conclusion: The proposed multi-atlas approach provides robust electron density estimation and bone detection based on anatomic MRI. If validated on a larger population, our work could enable the use of MRI as a primary modality for radiation treatment planning.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Stochastic variational quantization and maximum entropy principle

In this note, we discuss the stochastic variational method (SVM) to derive the action principle of Schrödinger equation. In this formalism, the wave function is introduced as one of convenient ways to express the action. This work is a reformulation of Nelson—Yasue’s stochastic quantization scheme and its variational formulation by Yasue, and will furnish possible way to deal with more complicated system such as quantum field theory, suggesting an origin of quantum mechanics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Estimating the joint distribution of rate parameters across multiple reactions in the absence of experimental data

Here, a procedure for determining the joint uncertainty of Arrhenius parameters across multiple combustion reactions of interest is demonstrated. This approach is capable of constructing the joint distribution of the Arrhenius parameters arising from the uncertain measurements performed in specific target experiments without having direct access to the underlying experimental data. The method involves constructing an ensemble of hypothetical data sets with summary statistics consistent with the available information reported by the experimentalists, followed by a fitting procedure that learns the structure of the joint parameter density across reactions using this consistent hypothetical data as evidence. The procedure is formalized in a Bayesian statistical framework, employing maximum-entropy and approximate Bayesian computation methods and utilizing efficient Markov chain Monte Carlo techniques to explore data and parameter spaces in a nested algorithm. We demonstrate the application of the method in the context of experiments designed to measure the rates of selected chain reactions in the H 2 -O 2 system and highlight the utility of this approach for revealing the critical correlations between the parameters within a single reaction and across reactions, as well as for maximizing consistency when utilizing rate parameter information in predictive combustion modeling of systems of interest.

97 MATHEMATICS AND COMPUTING↗

Real-time neutron multiplicity and source localization for criticality safety during fuel debris removal

Advancing neutron detection and analysis techniques for complex radiation environments is an ongoing focus in nuclear instrumentation and monitoring. This proposal presents research and development of a generalized real-time neutron monitoring and analysis system, applicable to any detector capable of producing time-tagged neutron count data. While the work is demonstrated using the Neutron Multiplication Analysis Detector (NoMAD), a modular 15-tube helium-3 (He-3) array, due to its availability, spatial resolution, and flexible deployment, the methods developed are extensible to other systems, including organic scintillators and fast digital detectors. This research investigates two complementary analytical techniques for real-time characterization of neutron emitting sources: neutron multiplicity estimation based on the Hage-Cifarelli formalism and spatial localization using supervised machine learning applied to spatial count rate patterns. These methods are designed to operate under dynamic, evolving conditions such as fuel debris retrieval or reactor startup, where neutron-emitting material geometries may be partially unknown or changing over time. By integrating statistical neutron emission data with spatial localization, this research aims to develop and evaluate methods for real time neutron monitoring, source characterization, and material verification. Key contributions include implementation of a low-latency data pipeline for continuous neutron multiplicity analysis, development and validation of machine learning models for spatial inference, and experimental evaluation of system performance under variable measurement conditions. The outcomes are intended to support applications in nuclear safeguards, verification, emergency response, and reactor startup.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Exnihilo Transport Methods Manuals Revision 0

Exnihilo is a transport code system that contains both deterministic and stochastic (Monte Carlo) solvers. The deterministic solvers are contained in the Denovo package while the Monte Carlo solvers are implemented in the Shift package. This document explains the mathematical and numerical methods employed within Exnihilo. It is not a users guide, nor is it a code developer's manual. Naturally, there is cross-over between the code implementation and mathematical description of any given method, and these are included for the purpose of greater understanding where appropriate. The purpose of this document is to formally describe the equations that are solved by the various packages inside of Exnihilo. In general, linkages are not made between a given numerical method and the Exnihilo code base. This is largely due to the fact that the Exnihilo code base changes far more rapidly than the actual methods that it is solving. Thus, this documentation would go rapidly out of date if cross-references were made between the methods and the code that implements them. Instead, developers are encouraged to look at the Doxygen-produced code documentation that explains what each translation unit in the code is doing. Where necessary we will make distinctions between methods that are implemented in Exnihilo and methods that are documented to provide better understanding of the broader field and provide context for the chosen methods in Exnihilo.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗