Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “differential analysis”

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 1,459 records · Page 81
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

On the dynamic collapse of a column impacting a rigid surface

Results are presented of an analytical investigation on the dynamic collapse of an elastic periodically supported column. The column has an attached mass at one end and impacts a rigid surface with prescribed velocity and angle of incidence at the other end. A first-order approximate nonlinear analysis is developed in which it is assumed that only first-order nonlinear terms need be retained. Differential equations are derived and solved numerically by explicit time integration in order to determine specific ranges of the basic nondimensional parameters for which the response characteristics are markedly different. To assess modeling sophistication relative to prediction accuracy, a comparison is made of the results from this approximate analysis with those of a finite element computer code based on a convected coordinate formulation.

Housner, J. M.↗
NASA NTRS2019

Modal Analysis of the Orion Capsule Two Parachute System

As discussed in Ref [1], it is apparent from flight tests that the system made up of two main parachutes and a capsule can undergo several distinct dynamical behaviors. The most significant and problematic of these is the pendulum mode in which the system develops a pronounced swinging motion with an amplitude of up to 24 deg. Large excursions away from vertical by the capsule could cause it to strike the ground at a large horizontal or vertical speed and jeopardize the safety of the astronauts during a crewed mission. In reference [1], Ali et al. summarized a series of efforts taken by the Capsule Parachute Assembly System (CPAS) Program to understand and mitigate the pendulum issue. The period of oscillation and location of the system's pivot point are determined from post-flight analysis. Other noticeable but benign modes include: 1) flyout (scissors) mode, where the parachutes move back and forth symmetrically with respect to the vertical axis similar to the motion of a pair of scissors; 2) maypole mode, where the two parachutes circle around the vertical axis at a nearly constant radius and period; and 3) breathing mode, in which deformation of the non-rigid canopies affects the axial acceleration of the system in an oscillatory manner. Because these modes are relatively harm- less, little effort has been devoted to analyzing them in comparison with the pendulum motion. Motions of the actual system made up of two parachutes and a capsule are extremely complicated due to nonlinearities and flexibility effects. Often it is difficult to obtain insight into the fundamental dynamics of the system by examining results from a multi-body simulation based on nonlinear equations of motion (EOMs). As a part of this study, the dynamics of each mode observed during flight is derived from first principles on an individual basis by making numerous simplifications along the way. The intent is to gain a better understanding into the behavior of the complex multi-body system by studying the reduced set of differential equations associated with each mode. This approach is analogous to the traditional modal analysis technique used to study airplane flight dynamics, in which the full nonlinear behavior of the airframe is decomposed into the phugoid and short period modes for the longitudinal dynamics and the spiral, roll-subsidence, and dutch-roll modes for the lateral dynamics. It is important to note that the study does not address the mechanisms that cause the system to transition from one mode to another, nor does it discuss motions during which two or more modes occur simultaneously.

Pei, J.↗
NASA NTRS1974

Energy transfer in volume-reflecting heat shields

An approximate analysis of radiative transfer in highly scattering materials was developed based on the Kubelka-Munk differential equations--a set of two differential equations representing the spatial rate of change of radiative half-fluxes within the scattering media. These approximate solutions of the Kubelka-Munk equations together with analytic solutions for the steady state temperature distribution for two types of boundary conditions are given. These solutions show the influence of back surface reflectance, scattering power, incident radiative flux parameter and boundary conductive flux parameter on overall reflectance and temperature distributions. This radiation field analysis, adapted to spherical geometry, was applied to the evaluation of the thermal performance of teflon and fritted quartz as heat protection materials for entry into the atmosphere of Jupiter.

Weston, K. C.↗
NASA NTRS1980

An analysis of turbulent diffusion flame in axisymmetric jet

The kinetic theory of turbulent flow was employed to study the mixing limited combustion of hydrogen in axisymmetric jets. The integro-differential equations in two spatial and three velocity coordinates describing the combustion were reduced to a set of hyperbolic partial differential equations in the two spatial coordinates by a binodal approximation. The MacCormick's finite difference method was then employed for solution. The flame length was longer than that predicted by the flame-sheet analysis, and was found to be in general agreement with a recent experimental result. Increase of the turbulence energy and scale resulted in an enhancement of the combustion rate and, hence, in a shorter flame length. Details of the numerical method as well as of the physical findings are discussed.

Chung, P. M.↗
NASA NTRS2000

Investigation of Mesoscale Variability in Convective Boundary Layer Development Using LASE

Throughout this research effort we have analyzed data collected from the Southern Great Plains 1997 (SGP) experiment to evaluate terms in the budget of water vapor in the atmospheric boundary layer (ABL). The analysis is centered on using data obtained from the Lidar Atmospheric Sensing Experiment (LASE) downward-looking differential absorption lidar (DIAL) that was flown on the NASA-P3 aircraft. The DIAL is able to measure vertical profiles of water vapor, as well as aerosol backscatter, throughout the ABL. Initial work on using the DIAL is summarized in the attached meeting preprint, which discusses results from a segment of the 12 July 1997 flight. Additional analysis has been carried out using both the DIAL data and in situ measurements to obtain more complete and detailed estimates of terms in the ABL water vapor budget. This includes data from the Canadian National Research Council Twin Otter aircraft, as well as from a spectrum of surface-based instruments. This work is expected to lead to a refereed article planned for submission to the Journal.

Lenschow, Donald H.↗
DOE OSTI2021

Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

42 ENGINEERING↗
NASA NTRS1995

Structural characterization and regulatory element analysis of the heart isoform of cytochrome c oxidase VIa

In order to investigate the mechanism(s) governing the striated muscle-specific expression of cytochrome c oxidase VIaH we have characterized the murine gene and analyzed its transcriptional regulatory elements in skeletal myogenic cell lines. The gene is single copy, spans 689 base pairs (bp), and is comprised of three exons. The 5'-ends of transcripts from the gene are heterogeneous, but the most abundant transcript includes a 5'-untranslated region of 30 nucleotides. When fused to the luciferase reporter gene, the 3.5-kilobase 5'-flanking region of the gene directed the expression of the heterologous protein selectively in differentiated Sol8 cells and transgenic mice, recapitulating the pattern of expression of the endogenous gene. Deletion analysis identified a 300-bp fragment sufficient to direct the myotube-specific expression of luciferase in Sol8 cells. The region lacks an apparent TATA element, and sequence motifs predicted to bind NRF-1, NRF-2, ox-box, or PPAR factors known to regulate other nuclear genes encoding mitochondrial proteins are not evident. Mutational analysis, however, identified two cis-elements necessary for the high level expression of the reporter protein: a MEF2 consensus element at -90 to -81 bp and an E-box element at -147 to -142 bp. Additional E-box motifs at closely located positions were mutated without loss of transcriptional activity. The dependence of transcriptional activation of cytochrome c oxidase VIaH on cis-elements similar to those found in contractile protein genes suggests that the striated muscle-specific expression is coregulated by mechanisms that control the lineage-specific expression of several contractile and cytosolic proteins.

Non-NASA Center↗
DOE OSTI2023

Multidimensional quantitative phenotypic and molecular analysis reveals neomorphic behaviors of p53 missense mutants

Abstract Mutations in the TP53 tumor suppressor gene occur in >80% of the triple-negative or basal-like breast cancer. To test whether neomorphic functions of specific TP53 missense mutations contribute to phenotypic heterogeneity, we characterized phenotypes of non-transformed MCF10A-derived cell lines expressing the ten most common missense mutant p53 proteins and observed a wide spectrum of phenotypic changes in cell survival, resistance to apoptosis and anoikis, cell migration, invasion and 3D mammosphere architecture. The p53 mutants R248W, R273C, R248Q, and Y220C are the most aggressive while G245S and Y234C are the least, which correlates with survival rates of basal-like breast cancer patients. Interestingly, a crucial amino acid difference at one position—R273C vs. R273H—has drastic changes on cellular phenotype. RNA-Seq and ChIP-Seq analyses show distinct DNA binding properties of different p53 mutants, yielding heterogeneous transcriptomics profiles, and MD simulation provided structural basis of differential DNA binding of different p53 mutants. Integrative statistical and machine-learning-based pathway analysis on gene expression profiles with phenotype vectors across the mutant cell lines identifies quantitative association of multiple pathways including the Hippo/YAP/TAZ pathway with phenotypic aggressiveness. Further, comparative analyses of large transcriptomics datasets on breast cancer cell lines and tumors suggest that dysregulation of the Hippo/YAP/TAZ pathway plays a key role in driving the cellular phenotypes towards basal-like in the presence of more aggressive p53 mutants. Overall, our study describes distinct gain-of-function impacts on protein functions, transcriptional profiles, and cellular behaviors of different p53 missense mutants, which contribute to clinical phenotypic heterogeneity of triple-negative breast tumors.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Parameter Identification for Battery Abuse Reaction Kinetics Models Using DSC Analysis [SWR-23-87]

This code estimates the parameters as inputs for NREL’s abuse reaction kinetics model using Differential scanning calorimetry (DSC) experimental data. The parameters for calculating the rates of abuse reactions among battery cell components at elevated temperatures include frequency factor, activation energy, and reaction orders. The least-squared method is employed to fit the reaction model to DSC data. The code is implemented in MATLAB.

Yang, Chuanbo↗
DOE OSTI2022

Development and Analysis of Optimal Multilevel Solvers on Advanced Computers. Final Report

Constrained optimization in the context of time dependent, partial differential equations (PDE) leads to a symmetric, block-tridiagonal system of nonlinear equations that must be solved repeatedly in an iterative solution strategy. The blocks represent spatial discretization, while the connection between the blocks represents a forward and backward integration in time. The focus of this project is to apply a parallel-in-time (PiT) solution technique to the large block-triangular system.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

The modified equation approach to the stability and accuracy analysis of finite-difference methods

The stability and accuracy of finite-difference approximations to simple linear partial differential equations are analyzed by studying the modified partial differential equation. Aside from round-off error, the modified equation represents the actual partial differential equation solved when a numerical solution is computed using a finite-difference equation. The modified equation is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations. The connection between 'heuristic' stability theory based on the modified equation approach and the von Neumann (Fourier) method is established. In addition to the determination of necessary and sufficient conditions for computational stability, a truncated version of the modified equation can be used to gain insight into the nature of both dissipative and dispersive errors.

Warming, R. F.↗
NASA NTRS1978

The velocity dispersion in Saturn's rings

The collisional dynamics of a differentially rotating disk of particles are considered. The investigation is to some extent an analytic counterpart of the numerical studies of Brahic (1977). Following Brahic, it is assumed that the particles are identical, indestructible, imperfectly elastic, smooth spheres. Gravitational interactions between the particles are neglected. The main result of the reported analysis is the derivation of the relation between the coefficient of restitution and the optical depth for a differentially rotating disk of identical, inelastic, smooth spheres. Questions concerning the applicability of the obtained results to Saturn's rings are studied. It is felt that the calculations should give accurate quantitative results if the rings' filling factor is small. If this assumption is not justified, the calculations should be at least qualitatively correct.

Goldreich, P.↗
DOE OSTI2022

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass ε for the latent variables and solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. Here, we propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass ε is made small with $\mathscr{O}$(ε) error for the atomic degrees of freedom and with $\mathscr{O}$($\sqrt{ε}$) error for the latent variables, when the dimension of the latent variable d' is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathscr{O}$(ε) for the latent variables as well. Numerical results verify that both estimates are sharp not only for d'=1, but also for arbitrary d'. In the setting of general d', we do obtain convergence, but with the non-sharp rate of $\mathscr{O}$($\sqrt{ε}$) for both the atomic and latent variables.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Multimodal Atomic Force Microscopy for the Characterization of Metallic Particulates

This study investigates the utility of multimodal, or functional, atomic force microscopy (AFM) for the characterization of individual particles and particle ensembles. In single-particle analyses, AFM imaging modes provided orthogonal insights into mechanical and magnetic properties that are not accessible through conventional electron microscopy. Although the experiments were inherently delicate and time-intensive, with an observed sample loss rate of approximately 30%, these techniques enabled the qualitative differentiation of grain structures and magnetic domains, underscoring the challenges of experimental robustness. For particle ensembles, AFM enabled the extraction of reliable 2D and 3D particle size distributions. However, efforts to chemically differentiate particles based on mechanical property contrasts were limited by scaling effects and the qualitative nature of the data. Overall, multimodal AFM offers valuable complementary information, but its application requires careful consideration of methodological limitations, particularly for sample integrity, calibration, and scalability of mechanical and magnetic measurements. This report is organized to first address the application of AFM to single-particle analysis using various imaging modalities, followed by its potential role in ensemble-level particle screening and differentiation.

36 MATERIALS SCIENCE↗
NASA NTRS1971

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Rosenbaum, J. S.↗
NASA NTRS1978

On least squares approximations to indefinite problems of the mixed type

A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

Fix, G. J.↗
NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗