SEARCH · Search NASA

Results for “Differentiability”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2026

The Memory Scaling of Reverse-Mode Differentiation in Particle Accelerator Simulations with Space Charge

The recent development of differentiable simulation codes for particle accelerators has enabled gradient-based workflows that promise finer control and more realistic modeling of accelerator facilities. However, when using reverse-mode automatic differentiation, the memory usage continuously increases during the simulation, and can potentially exceed the available hardware memory - especially when costly space charge computation is included. To study the memory requirements for differentiable simulations, we have implemented space charge in Cheetah, a PyTorch-based beam tracking code that supports reverse-mode differentiation. We find that the memory usage for reverse-mode differentiation grows linearly with the number of macroparticles and cells, and that it is proportional to the number of space charge kicks involved in the simulation. This general scaling can be used to evaluate whether a given differentiable simulation is feasible given hardware memory constraints.

Dhamrait, Arjun↗

DOE OSTI2019

Application of symmetries to differential equations: symmetry reduction and solution transformation examples

In the following lecture notes, we provide an outline of what we mean by symmetries of differential equations and illustrate their utility in simplification of differential equations which may lead to solutions. Loosely, a symmetry of a differential equation is a local group of transformations acting on the space of independent and dependent variables that transform solutions of a differential equation to new solutions, i.e., if Δ(x,u,p)=0 denotes a differential equation with a solution prescribed by [x,u,p], then knowlege of a symmetry facilitates the attainment of a new solution, [$\tilde{x}$, $\tilde{u}$, $\tilde{p}$], such that Δ(x,u,p)=Δ($\tilde{x}$, $\tilde{u}$, $\tilde{p}$)=0. In Equations (1) and (2), x, u and p denote the independent variables, dependent variables and partial derivatives, respectively and the tildes denote the transformations. Equation (2) will subsequently be referred to as the symmetry criterion. We can apply the knowlede of the existence of a symmetry in two ways: 1) If not solution is known apriori, the symmetry can be applied to simplify the differential equation through the method of symmetry reduction. Often, the resultant simplification may enable a solution to be determined; 2) If we already possess a solution to a different equation, knowledge of an admissible symmetry enables us to generate new solutions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Absolute elastic differential electron scattering cross sections in the intermediate energy region. IV - CO

Using a crossed electron beam-molecular beam scattering geometry and a relative-flow technique, ratios of elastic differential cross sections of CO to those of He have been measured at electron impact energies of 3, 5, 7.5, 9.9, 15, 20, 30, 50, 75, and 100 eV. At each energy, an angular range of 15 to 130 deg has been covered. These ratios have been multiplied by previously known He elastic differential cross sections to obtain elastic differential cross sections for CO. Since pure rotational excitations were not resolved, the elastic differential cross sections are a sum of elastic and pure rotational excitations at room temperature. From a knowledge of differential cross sections (DCS), integral and momentum transfer cross sections have been calculated. Both the DCS and integral cross sections are compared at 50, 75, and 100 eV to a recent two-potential theory of e-molecule scattering. Present results show that the isoelectronic molecules CO and N2 have very similar magnitudes and shapes of their differential cross sections.

Tanaka, H.↗

NASA NTRS1985

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. A type of differentiating matrix based on local approximation on a sequence of sliding subgrids is considered. Previous derivations of this type of matrix have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The new formulation allows grids which have arbitrarily space points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids which include near-boundary points. Use of the differentiating matrix as an operator to solve eigenvalue problems involving ordinary differential equations is also considered.

Lakin, W. D.↗

NASA NTRS1986

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids through the expedient of including 'near boundary' points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.

Lakin, W. D.↗

NASA NTRS1991

A unified approach to the helioseismic forward and inverse problems of differential rotation

A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion.

Ritzwoller, Michael H.↗

NASA NTRS1992

Differential phase acoustic microscope for micro-NDE

A differential phase scanning acoustic microscope (DP-SAM) was developed, fabricated, and tested in this project. This includes the acoustic lens and transducers, driving and receiving electronics, scanning stage, scanning software, and display software. This DP-SAM can produce mechanically raster-scanned acoustic microscopic images of differential phase, differential amplitude, or amplitude of the time gated returned echoes of the samples. The differential phase and differential amplitude images provide better image contrast over the conventional amplitude images. A specially designed miniature dual beam lens was used to form two foci to obtain the differential phase and amplitude information of the echoes. High image resolution (1 micron) was achieved by applying high frequency (around 1 GHz) acoustic signals to the samples and placing two foci close to each other (1 micron). Tone burst was used in this system to obtain a good estimation of the phase differences between echoes from the two adjacent foci. The system can also be used to extract the V(z) acoustic signature. Since two acoustic beams and four receiving modes are available, there are 12 possible combinations to produce an image or a V(z) scan. This provides a unique feature of this system that none of the existing acoustic microscopic systems can provide for the micro-nondestructive evaluation applications. The entire system, including the lens, electronics, and scanning control software, has made a competitive industrial product for nondestructive material inspection and evaluation and has attracted interest from existing acoustic microscope manufacturers.

Waters, David D.↗

NASA NTRS1996

Differential Canard deflection for generation of yawing moment on the X-31 with and without the vertical tail

The feasibility of augmenting the available yaw control power on the X-31 through differential deflection of the canard surfaces was studied as well as the possibility of using differential canard control to stabilize the X-31 with its vertical tail removed. Wind-tunnel tests and the results of departure criteria and linear analysis showed the destabilizing effect of the reduction of the vertical tail on the X-31. Wind-tunnel testing also showed that differential canard deflection was capable of generating yawing moments of roughly the same magnitude as the thrust vectoring vanes currently in place on the X-31 in the post-stall regime. Analysis showed that the X-31 has sufficient aileron roll control power that with the addition of differential canard as a yaw controller, the wind-axis roll accelerations will remain limited by yaw control authority. It was demonstrated, however, that pitch authority may actually limit the maximum roll rate which can be sustained. A drop model flight test demonstrated that coordinated, wind axis rolls could be performed with roll rates as high as 50 deg/sec (full scale equivalent) at 50 deg angle of attack. Another drop model test was conducted to assess the effect of vertical tail reduction, and an analysis of using differential canard deflection to stabilize the tailless X-31 was performed. The results of six-degree-of-freedom, non-linear simulation tests were correlated with the drop model flights. Simulation studies then showed that the tailless X-31 could be controlled at angles of attack at or above 20 deg using differential canard as the only yaw controller.

Whiting, Matthew Robert↗

NASA NTRS1988

Kinetics of determination in the differentiation of isolated mesophyll cells of Zinnia elegans to tracheary elements

Mechanically isolated mesophyll cells of Zinnia elegans L. cv Envy differentiate to tracheary elements when cultured in inductive medium containing 0.5 micromolar alpha-naphthaleneacetic acid and 0.5 micromolar benzyladenine. The cells do not differentiate when cultured in medium in which the concentration of auxin and/or cytokinin has been reduced to 0.005 micromolar. Cells require an initial 24-hour exposure to inductive cytokinin and 56-hour exposure to inductive auxin for differentiation at 72 hours of culture. Freshly isolated Zinnia cells can be maintained in medium having low concentrations of both auxin and cytokinin for only 1 day without significant loss of potential to differentiate upon transfer to inductive medium. Initial culture for up to 2 days in medium having high auxin and low cytokinin, or low auxin and high cytokinin, allows full differentiation on the third day after transfer to inductive medium and potentiates the early differentiation of some cells.

Non-NASA Center↗

NASA NTRS1998

Fibronectin is a survival factor for differentiated osteoblasts

The skeletal extracellular matrix produced by osteoblasts contains the glycoprotein fibronectin, which regulates the adhesion, differentiation and function of various adherent cells. Interactions with fibronectin are required for osteoblast differentiation in vitro, since fibronectin antagonists added to cultures of immature fetal calvarial osteoblasts inhibit their progressive differentiation. To determine if fibronectin plays a unique role in fully differentiated osteoblasts, cultures that had already formed mineralized nodules in vitro were treated with fibronectin antagonists. Fibronectin antibodies caused >95% of the cells in the mature cultures to display characteristic features of apoptosis (nuclear condensation, apoptotic body formation, DNA laddering) within 24 hours. Cells appeared to acquire sensitivity to fibronectin antibody-induced apoptosis as a consequence of differentiation, since antibodies failed to kill immature cells and the first cells killed were those associated with mature nodules. Intact plasma fibronectin, as well as fragments corresponding to the amino-terminal, cell-binding, and carboxy-terminal domains of fibronectin, independently induced apoptosis of mature (day-13), but not immature (day-4), osteoblasts. Finally, transforming growth factor-beta1 partially protected cells from the apoptotic effects of fibronectin antagonists. Thus, in the course of maturation cultured osteoblasts switch from depending on fibronectin for differentiation to depending on fibronectin for survival. These data suggest that fibronectin, together with transforming growth factor-beta1, may affect bone formation, in part by regulating the survival of osteoblasts.

NASA Center ARC↗

DOE OSTI2024

Regularized Differentiation for Bioburden Density Estimation in Planetary Protection

In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Co-benefits of subnationally differentiated carbon pricing policies in China: Alleviation of heavy PM 2.5 pollution and improvement in environmental equity

Carbon policies differentiated according to regional disparities have been recognized and recommended. However, the air quality co-benefits of differentiated policies remain unclear. Here we combine a multi-regional dynamic computable general equilibrium (CGE) model and an extend response surface model (ERSM) to investigate the impact of nationally uniform and subnationally differentiated carbon pricing policies on fine particulate matter (PM 2.5 ) concentrations in China. All policies examined lead to the same accumulated national CO 2 emissions (2020–2050), with the 2030 emissions attaining China's national abatement target. We find that, when subnational policies differentiated according to provincial PM 2.5 concentrations are implemented, the higher-than-average carbon price over more polluted provinces results in twice as much reduction in CO 2 and air pollutant emissions in 2050 as the national policy. As a result, the subnational policies cause larger PM 2.5 concentration reductions in these provinces (9%–18%) than the national policy (7%–11%). Also, the subnational policies eliminate high PM 2.5 exposure of over 45 μg/m 3 which 12% people suffer from under the national policy. Overall, the subnational policies substantially reduce regional disparity in PM 2.5 pollution and hence improve environmental equity. The results suggest that subnationally differentiated carbon policies are a promising instrument to mitigate severe pollution and promote environmental equity.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Redox and mineral controls on Fe and Ti isotopic fractionations during calc-alkaline magmatic differentiation

Titanium and Fe isotopic compositions of lavas from a calc-alkaline differentiation suite and corresponding mineral separates from the Rindjani Volcano, Indonesia show that Fe and Ti isotopic fractionations between minerals and melts are lower than those recorded in other suites at all stages of differentiation. Here, the limited isotopic fractionation for Ti is likely due to low-Ti magnetite and clinopyroxene being the dominant carriers of Ti in Rindjani lavas, as these minerals are thought to have limited equilibrium Ti isotopic fractionation relative to silicate magmas. Other magmatic differentiation suites controlled by removal of Ti-rich magnetite and characterized by a lesser role of clinopyroxene have larger Ti isotopic fractionations. This effect is an indirect consequence of the elevated Fe 3+ /Fe 2+ ratio of calc-alkaline magmas such as Rindjani, which promotes Fe 3+ incorporation into magnetite at the expense of Fe 2+ -Ti 4+ pairs, such that increased oxygen fugacity will subdue Ti isotopic fractionation in global magmatic series. Similarly, we find negligible Fe isotopic fractionation in Rindjani bulk rocks and mineral separates, unlike previous studies. This is also likely due to the oxidized nature of the Rindjani differentiation suite, which leads to similar Fe 3+ /Fe 2+ ratios in melt and minerals and decreases overall mineral-melt Fe fractionation factors. Paired Ti and Fe isotopic analyses may therefore represent a powerful tool to assess oxygen fugacity during differentiation, independent from Fe 3+ determinations of erupted samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A review of preserving privacy in data collected from buildings with differential privacy

Significant amounts of data are collected in buildings. While these data have great potential for maximizing the energy efficiency of buildings in general, only a small portion of the data are accessible to researchers, government, and industry for analyses. Concerns about privacy are one of the major barriers prohibiting access to these data. Privacy preservation techniques are generally applied to this problem not only to preserve underlying privacy but also to improve the usefulness of data. Among various privacy preserving techniques, differential privacy has become one of the more popular solutions since its introduction in 2006. Differential privacy is a mathematical measure for protecting privacy so that one's privacy cannot be incurred by participating in a database. Additionally, although significant research improvements have been made for more than a decade, applying differential privacy to data collected in buildings is still an immature field of study. Because implementing differential privacy on a certain use case is not straightforward and can be achieved with various configurations, it is important to understand variation of configurations with different use cases around data collected from buildings. This literature review aims to introduce what has been done to implement differential privacy in data collected in buildings, and to discuss associated challenges and potential future research opportunities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Analysis of ionizing radiation induced DNA damage response in human adult stem cells and differentiated neurons

Findings of neurodegenerative features associated with human radiosensitive syndromes such as Ataxia telangiectasia suggest that DNA repair efficiency is crucial for maintaining the functional integrity of central nervous system. To gain a better understanding of ionizing radiation (IR) induced DNA damage response in undifferentiated and differentiated neural cell types and to evaluate the role of ATM in DNA double strand break (DSB) repair, an in vitro human neural cell differentiation model system was utilized in this study. As compared to adult stem cells, differentiated neurons displayed an attenuated DSB repair response (as judged by the persistence of 53BP1 foci) after IR exposure and the attenuation was even more pronounced in stem cells and neurons after suppression of ATM (Ataxia Telangiectasia Mutated) gene product suggesting the importance of ATM for an optimal DSB repair efficiency in human neural cell types. In corroboration with an attenuated DNA damage response, a sharp decline in the expression levels of several DSB repair genes was observed in neurons. Furthermore, our results suggest that cellular differentiation modulates the expression of several genes thereby compromising the DSB repair fidelity in post mitotic neurons. Further studies are required to verify whether or not ATM mediated exacerbation of DNA repair deficiency in differentiated neurons leads to neurodegeneration.

53 binding protein 1↗

DOE OSTI2021

Down-regulation of A3AR signaling by IL-6-induced GRK2 activation contributes to Th17 cell differentiation

Highlights: • Cyclic AMP-PKA signaling is involved in Th17 cell differentiation. • IL-6 stimulation triggers the internalization of A{sub 3}AR and promotes cAMP production in T cells. • IL-6 induces A{sub 3}AR internalization in a GRK2 dependent manner. • GRK2 is a potential therapeutic target for treating Th17 driving immune diseases. IL-6-triggered Th17 cell expansion is responsible for the pathogenesis of many immune diseases including rheumatoid arthritis (RA). Traditionally, IL-6 induces Th17 cell differentiation through JAK-STAT3 signaling. In the present work, PKA inhibition reduces in vitro induction of Th17 cells, while IL-6 stimulation of T cells facilitates the internalization of A{sub 3}AR and increased cAMP production in a GRK2 dependent manner. Inhibition of GRK2 by paroxetine (PAR) or genetic depletion of GRK2 restored A{sub 3}AR distribution and prevented Th17 cell differentiation. Furthermore, in vivo PAR treatment effectively reduced the splenic Th17 cell proportion in a rat model of collagen-induced arthritis (CIA) which was accompanied by a significant improvement in clinical manifestations. These results indicate that IL-6-induced Th17 cell differentiation not only occurs through JAK-STAT3-RORγt but is also mediated through GRK2-A{sub 3}AR-cAMP-PKA-CREB/ICER-RORγt. This elucidates the significance of GRK2-controlled cAMP signaling in the differentiation of Th17 cells and its potential application in treating Th17-driven immune diseases such as RA.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗