Search NASA⌕ Search

SEARCH · Search NASA

Results for “fixed points”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Hyperspectral traits (TSWIFT) UC Davis Populus trichocarpa Common Garden

This dataset provides tower-based hyperspectral remote sensing measurements of individualPopulustrees collected with the TSWIFT system to support genetic analyses of canopy photosynthetic traits over time under drought. From 2022-08-18 to 2022-10-18, spectra were repeatedly acquired from the same targeted canopy area of each tree using fixed pointing coordinates. The dataset includes hyperspectral measurements from 400–900 nm and ultraspectral measurements from 730–780 nm. These spectra enable calculation of reflectance-based vegetation indices and other spectral traits, including solar-induced fluorescence (SIF) retrievals from the ultraspectral region. Because measurements were collected exclusively over a drought treatment plot, derived phenotypes are intended for drought-context genetic association and prediction analyses.

09 BIOMASS FUELS↗
DOE OSTI2024

Defining Detection Limits for Continuous Monitoring Systems for Methane Emissions at Oil and Gas Facilities

Networks of fixed-point continuous monitoring systems are becoming widely used in the detection and quantification of methane emissions from oil and gas facilities in the United States. Regulatory agencies and operators are developing performance metrics for these systems, such as minimum detection limits. Performance characteristics, such as minimum detection limits, would ideally be expressed in emission rate units; however, performance parameters such as detection limits for a continuous monitoring system (CMS) will depend on meteorological conditions, the characteristics of emissions at the site where the CMS is deployed, the positioning of CMS devices in relation to the emission sources, and the amount of time allowed for the CMS to detect an emission source. This means that certifying the performance of a CMS will require test protocols with well-defined emission rates and durations; initial protocols are now being used in field tests. Field testing results will vary, however, depending on meteorological conditions and the time allowed for detection. This work demonstrates methods for evaluating CMS performance characteristics using dispersion modeling and defines an approach for normalizing test results to standard meteorological conditions using dispersion modeling.

Chen, Qining (ORCID:0000000316908091)↗
DOE OSTI2020

Robust Learning with Implicit Residual Networks

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power, and allows for control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet does not introduce new parameters and can potentially lead to a reduction in the number of required layers due to improved forward stability. Finally, we derive the memory-efficient training algorithm, propose a stochastic regularization technique, and provide numerical results in support of our findings.

Reshniak, Viktor↗
DOE OSTI2021

Stability Analysis of Parameter Varying Genetic Toggle Switches Using Koopman Operators

The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in describing circuit dynamics in rapidly dividing cells, assuming fixed or time-invariant kinetic rates. There is a growing interest in being able to model and extend synthetic biological function for growth conditions such as stationary phase or during nutrient starvation. As cells transition from one growth phase to another, kinetic rates become time-varying parameters. In this paper, we propose a novel class of parameter varying nonlinear models that can be used to describe the dynamics of genetic circuits, including the toggle switch, as they transition from different phases of growth. We show that there exists unique solutions for this class of systems, as well as for a class of systems that incorporates the microbial phenomena of quorum sensing. Further, we show that the domain of these systems, which is the positive orthant, is positively invariant. We also showcase a theoretical control strategy for these systems that would grant asymptotic monostability of a desired fixed point. We then take the general form of these systems and analyze their stability properties through the framework of time-varying Koopman operator theory. A necessary condition for asymptotic stability is also provided as well as a sufficient condition for instability. A Koopman control strategy for the system is also proposed, as well as an analogous discrete time-varying Koopman framework for applications with regularly sampled measurements.

Harrison, Jamiree (ORCID:0000000265351579)↗
DOE OSTI2022

Qubit Regularization and Qubit Embedding Algebras

Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling

Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn 85 opacity set. The implicit systems arise from the discretization of a nonrelativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems — a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixedpoint iteration and Newton’s method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Here, numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2021

dlmcfpt.c1

The DLMC VAP uses inertial data from the ARM NAV system to transform the Doppler lidar beam angles (az and el) from the lidar's frame of reference to an Earth-fixed frame such the azimuth angle is measured clockwise from true north and the elevation angle is measured from the local horizon. Additionally, the VAP compensates the observed radial (air) velocity data for the effects of the platform velocity (i.e. corrected_radial_velocity = observed_radial_velocity-platform_radial_velocity). The VAP was developed specifically for MOSAiC. The dlmcfpt.c1 product contains the fixed point, or staring data. The dlmcusr.c1 product contains a user defined scan which is anything the operator wants it to be.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

dlmcusr.c1

The DLMC VAP uses inertial data from the ARM NAV system to transform the Doppler lidar beam angles (az and el) from the lidar's frame of reference to an Earth-fixed frame such the azimuth angle is measured clockwise from true north and the elevation angle is measured from the local horizon. Additionally, the VAP compensates the observed radial (air) velocity data for the effects of the platform velocity (i.e. corrected_radial_velocity = observed_radial_velocity-platform_radial_velocity). The VAP was developed specifically for MOSAiC. The dlmcfpt.c1 product contains the fixed point, or staring data. The dlmcusr.c1 product contains a user defined scan which is anything the operator wants it to be.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

dlfpt2.b1

Doppler Lidar - Partial Fixed Pointing mode

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1962

Periodic Motions in Banach Space and Applications to Functional-Differential Equations

In establishing the existence of periodic solutions for nonautonomous differential equations of the form x = g(x, t), where g is periodic in t of period ω for fixed x, it is often convenient to consider the translation operator T(x(t)) = x(t + ω). If corresponding to each initial vector chosen in an appropriate region there corresponds a unique solution of our equation, then periodicity may be established by proving the existence of a fixed point under T. This same technique is also useful for more general functional equations and can be extended in a number of interesting ways. In this paper we shall consider a variable type of translation operator which is useful in investigating periodicity for autonomous differential and functional equations where the period involved is less obvious.

Jones, G. Stephen↗
NASA NTRS1965

Instrument calibrates low gas-rate flowmeters

Electronically measuring the transit time of a soap bubble carried by the gas stream between two fixed points in a burette calibrates flowmeters used for measuring low gas-flow rates.

Copeland, A. C.↗
NASA NTRS1968

Motion under a periodic cubic force.

Periodic cubic differential equation of motion solved with special reference to location of fixed points and stability of solutions

Bartlett, J. H.↗
NASA NTRS1972

Calculation of free-fall trajectories using numerical optimization methods.

An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.

Hull, D. G.↗
NASA NTRS1973

Digital random-number generator

For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.

Brocker, D. H.↗