Search NASA⌕ Search

SEARCH · Search NASA

Results for “mathematical regularization”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Singular inverse square potential in coordinate space with a minimal length

The problem of a particle of mass m in the field of the inverse-square potential α∕r{sup 2} is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate representation, for a specific form of the generalized uncertainty relation, we solve the deformed Schrödinger equation analytically in terms of confluent Heun functions. We explicitly show the regularizing effect of the minimal length on the singularity of the potential. We discuss the problem of bound states in detail and we derive an expression for the energy spectrum in a natural way from the square integrability condition; the results are in complete agreement with the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

(U) LNK3DNT Capability in SENSMG Tested with Transport Correction

The SENSMG multigroup neutron sensitivity code can read materials and geometry from redoin and lnk3dnt files written by the PARTISN multigroup discrete ordinates code or the MCNP6 Monte Carlo code. Reference 5 described an initial version of this capability. Reference 6 introduced two important extensions: 1) Reaction-rate ratios are now allowed as responses with redoin/lnk3dnt inputs; and 2) Sensitivities of reaction-rate ratios to mass densities and interface locations are now calculated (for all problems, not just redoin/lnk3dnt problems). In this report, we document the testing of the redoin/lnk3dnt capability when used with transport correction. PARTISN’s transport corrections are described in Ref. 3, and Refs. 7 and 8 discuss the calculation of cross-section sensitivities when transport corrections are applied. References 7 and 8 verify SENSMG for problems with transport correction using central differences. This report verifies the capability with redoin/lnk3dnt inputs by comparison with regular SENSMG inputs. Unlike Refs. 5 and 6, in this report we use a spherical test problem because the sensitivity of the response with respect to the highest-order scattering is zero in cylinders due to the use of flux moments in the inner products.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1997

Extension of a Kolmogorov Atmospheric Turbulence Model for Time-Based Simulation Implementation

The development of any super/hypersonic aircraft requires the interaction of a wide variety of technical disciplines to maximize vehicle performance. For flight and engine control system design and development on this class of vehicle, realistic mathematical simulation models of atmospheric turbulence, including winds and the varying thermodynamic properties of the atmosphere, are needed. A model which has been tentatively selected by a government/industry group of flight and engine/inlet controls representatives working on the High Speed Civil Transport is one based on the Kolmogorov spectrum function. This report compares the Dryden and Kolmogorov turbulence forms, and describes enhancements that add functionality to the selected Kolmogorov model. These added features are: an altitude variation of the eddy dissipation rate based on Dryden data, the mapping of the eddy dissipation rate database onto a regular latitude and longitude grid, a method to account for flight at large vehicle attitude angles, and a procedure for transitioning smoothly across turbulence segments.

McMinn, John D.↗
NASA NTRS1994

Correlation of finite element free vibration predictions using random vibration test data

Finite element analysis is regularly used during the engineering cycle of mechanical systems to predict the response to static, thermal, and dynamic loads. The finite element model (FEM) used to represent the system is often correlated with physical test results to determine the validity of analytical results provided. Results from dynamic testing provide one means for performing this correlation. One of the most common methods of measuring accuracy is by classical modal testing, whereby vibratory mode shapes are compared to mode shapes provided by finite element analysis. The degree of correlation between the test and analytical mode shapes can be shown mathematically using the cross orthogonality check. A great deal of time and effort can be exhausted in generating the set of test acquired mode shapes needed for the cross orthogonality check. In most situations response data from vibration tests are digitally processed to generate the mode shapes from a combination of modal parameters, forcing functions, and recorded response data. An alternate method is proposed in which the same correlation of analytical and test acquired mode shapes can be achieved without conducting the modal survey. Instead a procedure is detailed in which a minimum of test information, specifically the acceleration response data from a random vibration test, is used to generate a set of equivalent local accelerations to be applied to the reduced analytical model at discrete points corresponding to the test measurement locations. The static solution of the analytical model then produces a set of deformations that once normalized can be used to represent the test acquired mode shapes in the cross orthogonality relation. The method proposed has been shown to provide accurate results for both a simple analytical model as well as a complex space flight structure.

Chambers, Jeffrey A.↗
DOE OSTI2018

On the Five-Moment Hamburger Maximum Entropy Reconstruction

We consider the Maximum Entropy Reconstruction (MER) as a solution to the five-moment truncated Hamburger moment problem in one dimension. In the case of five monomial moment constraints, the probability density function (PDF) of the MER takes the form of the exponential of a quartic polynomial. This implies a possible bimodal structure in regions of moment space. An analytical model is developed for the MER PDF applicable near a known singular line in a centered, two-component, third- and fourth-order moment (μ{sub 3}, μ{sub 4}) space, consistent with the general problem of five moments. The model consists of the superposition of a perturbed, centered Gaussian PDF and a small-amplitude packet of PDF-density, called the outlying moment packet (OMP), sitting far from the mean. Asymptotic solutions are obtained which predict the shape of the perturbed Gaussian and both the amplitude and position on the real line of the OMP. The asymptotic solutions show that the presence of the OMP gives rise to an MER solution that is singular along a line in (μ{sub 3}, μ{sub 4}) space emanating from, but not including, the point representing a standard normal distribution, or thermodynamic equilibrium. We use this analysis of the OMP to develop a numerical regularization of the MER, creating a procedure we call the Hybrid MER (HMER). Compared with the MER, the HMER is a significant improvement in terms of robustness and efficiency while preserving accuracy in its prediction of other important distribution features, such as higher order moments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ 2 ) in the L∞(Ω) norm, which is optimal considering the O(δ 2 ) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Finally, based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ 2 ) convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cluster Configuration Spaces of Finite Type

For each Dynkin diagram $D$, we define a ''cluster configuration space'' ${\mathcal{M}}_D$ and a partial compactification ${\widetilde {\mathcal{M}}}_D$. For $D = A_{n-3}$, we have ${\mathcal{M}}_{A_{n-3}} = {\mathcal{M}}_{0,n}$, the configuration space of $n$ points on ${\mathbb P}^1$, and the partial compactification ${\widetilde {\mathcal{M}}}_{A_{n-3}}$ was studied in this case by Brown. The space ${\widetilde {\mathcal{M}}}_D$ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on ${\widetilde {\mathcal{M}}}_D$ are generated by coordinates $u_\gamma$, in bijection with the cluster variables of type $D$, and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Galerkin finite element method for time-fractional stochastic diffusion equations

In this paper, Galerkin finite element method for solving the time-fractional stochastic diffusion equations with multiplicative noise is proposed and investigated. The pathwise regularity properties of solutions to the semidiscrete Galerkin approximations are demonstrated and the convergence of optimal rates are derived. And also we construct the fully discrete scheme which is based on the approximations of the Mittag–Leffler function and analyze the error estimates of convergence in L{sub 2}-norm space. Finally, numerical results are conducted to confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Concentric Spherical GNN for 3D Representation Learning

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Design of Test Support Hardware for Advanced Space Suits

As a member of the Space Suit Assembly Development Engineering Team, I designed and built test equipment systems to support the development of the next generation of advanced space suits. During space suit testing it is critical to supply the subject with two functions: (1) cooling to remove metabolic heat, and (2) breathing air to pressurize the space suit. The objective of my first project was to design, build, and certify an improved Space Suit Cooling System for manned testing in a 1‐G environment. This design had to be portable and supply a minimum cooling rate of 2500 BTU/hr. The Space Suit Cooling System is a robust, portable system that supports very high metabolic rates. It has a highly adjustable cool rate and is equipped with digital instrumentation to monitor the flowrate and critical temperatures. It can supply a variable water temperature down to 34 deg., and it can generate a maximum water flowrate of 2.5 LPM. My next project was to design and build a Breathing Air System that was capable of supply facility air to subjects wearing the Z‐2 space suit. The system intakes 150 PSIG breathing air and regulates it to two operating pressures: 4.3 and 8.3 PSIG. It can also provide structural capabilities at 1.5x operating pressure: 6.6 and 13.2 PSIG, respectively. It has instrumentation to monitor flowrate, as well as inlet and outlet pressures. The system has a series of relief valves to fully protect itself in case of regulator failure. Both projects followed a similar design methodology. The first task was to perform research on existing concepts to develop a sufficient background knowledge. Then mathematical models were developed to size components and simulate system performance. Next, mechanical and electrical schematics were generated and presented at Design Reviews. After the systems were approved by the suit team, all the hardware components were specified and procured. The systems were then packaged, fabricated, and thoroughly tested. The next step was to certify the equipment for manned used, which included generating a Hazard Analysis and giving a presentation to the Test Readiness Review Board. Both of these test support systems will perform critical roles in the development of next‐generation space suits. They will used on a regular basis to test the NASA's new Z‐2 Space Suit. The Space Suit Cooling System is now the primary cooling system for all advanced suit tests.

Watters, Jeffrey A.↗
DOE OSTI2023

Phishing in the Wild: An Ecologically Valid Study of the Phishing Tactics and Human Factors that Predict Susceptibility to a Phishing Attack

In this research, 153 employees at a National Laboratory received one of one of four different phishing emails. All of the emails were similar in content, but systematically varied according to the number and combination of phishing tactics in the message. Participants were unaware they would be receiving the email, which was sent during regular business hours. After receiving the emails, participants completed online questionnaires designed to measure possible predictors of phishing attack susceptibility. Finally, the significant predictors included how suspicious participants were of the email and their reported level of distress related to their work prior to completing the study.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: Boeing Helicopters airframe finite element modeling

Mathematical models based on the finite element method of structural analysis, as embodied in the NASTRAN computer code, are routinely used by the helicopter industry to calculate airframe static internal loads used for sizing structural members. Historically, less reliance has been placed on the vibration predictions based on these models. Beginning in the early 1980's NASA's Langley Research Center initiated an industry wide program with the objective of engendering the needed trust in vibration predictions using these models and establishing a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process. Emphasis in this paper is placed on the successful modeling of the Army/Boeing CH-47D which showed reasonable correlation with test data. A principal finding indicates that improved dynamic analysis requires greater attention to detail and perhaps a finer mesh, especially the mass distribution, than the usual stress model. Post program modeling efforts show improved correlation placing key modal frequencies in the b/rev range with 4 percent of the test frequencies.

Gabel, R.↗
DOE OSTI2016

Diffusion and transport in locally disordered driven lattices

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Separation of continuous lines mutually overlapping and smoothed by the instrumental function

Direct and inverse spectroscopy problems concerning superposition of overlapping continuous spectral lines, as well as smoothing of the total spectrum by the instrumental function, are considered. The direct problem is formulated in two stages: initially, the total spectrum is formed by lines with a given intensity distribution, and, then, a smoothed by the spectrometer instrumental function and noisy spectrum is obtained. The inverse problem is also formulated in two stages: initially, the Fredholm integral equation of the first kind is solved by the Tikhonov regularization method (an ill-posed problem), and, then, the problem of reconstruction of separate line-component shapes from the total spectrum is solved, which is the problem of line separation (division). The individual line components are modeled by Gaussians and Lorentzians. Numerical illustrations are shown. Gaussian and dispersion (Lorentz) instrumental functions are considered.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation

Here we propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those methods. Our derivation assures convergence for convex problems whose feasible set is compact, subject to some standard regularity conditions and a mild “fairness” condition on subproblem selection. The method’s convergence guarantees are deterministic and do not require randomization, in contrast to other proposed asynchronous variations of progressive hedging. Computational experiments described in an online appendix show the method to outperform progressive hedging on large-scale problems in a highly parallel computing environment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

User input verification and test driven development in the NJOY21 nuclear data processing code

Before physically-meaningful data can be used in nuclear simulation codes, the data must be interpreted and manipulated by a nuclear data processing code so as to extract the relevant quantities (e.g. cross sections and angular distributions). Perhaps the most popular and widely-trusted of these processing codes is NJOY, which has been developed and improved over the course of 10 major releases since its creation at Los Alamos National Laboratory in the mid-1970’s. The current phase of NJOY development is the creation of NJOY21, which will be a vast improvement from its predecessor, NJOY2016. Designed to be fast, intuitive, accessible, and capable of handling both established and modern formats of nuclear data, NJOY21 will address many issues that many NJOY users face, while remaining functional for those who prefer the existing format. Although early in its development, NJOY21 is quickly providing input validation to check user input. By providing rapid and helpful responses to users while writing input files, NJOY21 will prove to be more intuitive and easy to use than any of its predecessors. Furthermore, during its development, NJOY21 is subject to regular testing, such that its test coverage must strictly increase with the addition of any production code. This thorough testing will allow developers and NJOY users to establish confidence in NJOY21 as it gains functionality. This document serves as a discussion regarding the current state input checking and testing practices of NJOY21.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Maximizing Efficiency and Quality: Leveraging Automated Testing for Laboratory Commissioning

The traditional commissioning process uses sampling to select equipment for functional acceptance testing when large quantities of equipment are present. Although this approach is generally effective in identifying wide-spread issues, it has several shortcomings: it fails to evaluate equipment not included in the sample, provides only a one-time validation of equipment operation, and the standard documentation is a simple checklist of pass/fail questions. During the construction and commissioning process of the new Research and Innovation Laboratory (RAIL) in Golden, CO, the National Renewable Energy Laboratory team engaged Group14 Engineering to implement a Connected Commissioning process using fault detection and diagnostic software for automated functional acceptance testing. This presentation highlights the advantages offered by automated functional testing in this critical laboratory setting: (1) sampling 100% of BAS-connected equipment during functional testing, (2) testing results backed by data beyond the traditional pass/fail checklist, and (3) an automated test process that can be regularly executed by the building management team for ongoing commissioning throughout the life of the building. The presentation will also cover technical challenges associated with Connected Commissioning and the important conversations with key stakeholders that need to occur well before functional acceptance testing in order to successfully implement the automated testing processes.

automated testing↗
DOE OSTI2018

Detecting and quantifying materials in containers utilizing an inverse algorithm with adaptive regularization

A method, system and computer program product for automatically detecting and quantifying materials in containers (e.g., luggage, storage containers, equipment or componentry for processing or handling). An X-ray radiograph of a container is generated. A set of materials of interest (e.g., plutonium, steel) is selected to determine if the object comprises or contains materials of interest. An estimate of the areal densities or thicknesses of each of the selected materials of interest is obtained by minimizing an objective function with respect to the areal densities or thicknesses for each of the selected materials of interest. Adaptive regularization is implemented in the objective function to improve optimization results by adding a constraint to the objective function, where the constraint penalizes the objective function for solutions that do not line up with a prior belief about the solution form (e.g., the solution should not be negative or especially noisy).

97 MATHEMATICS AND COMPUTING↗