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Results for “Linearity preservation”

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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Creation of Self-Semi-Interpenetrating Network Structures in PIM-1 Membranes for Enhanced Physical Aging Resistance

A series of self-semi-interpenetrating network (ssIPN) thin films based on PIM-1 structure were developed by end-cross-linking telechelic PIM-1 oligomers end-capped with curable carboxylic acid groups to form model networks, which are penetrated by linear high-molecular-weight PIM-1 chains. ssIPN films with systematically varied network content ranging from 10 to 30 wt % were comprehensively examined on their microstructure and gas permeation properties. Fresh PIM-1 ssIPN films exhibited gas separation performances close to those of as-cast linear PIM-1, where the films closely followed the upper bound trade-off line, gaining as much selectivity as they lose gas permeability as the network content increases. This indicates that gas permeability is largely preserved despite cross-linking. Wide-angle X-ray scattering supported this observation, with peaks shifting toward lower d-spacing as oligomer content increased, suggesting tighter chain packing with higher cross-linkable oligomer loading. In physical aging studies over two months, all ssIPN films outperform linear PIM-1 for H 2 /CH 4 and O 2 /N 2 separations. Notably, the PIM-1 ssIPN with 10 wt % network content showed the best physical aging resistance, with negligible permeability loss even after one month. Finally, these findings highlight a promising macromolecular strategy for enhancing the physical aging resistance of microporous polymer membranes for gas separation.

PIM-1↗
DOE OSTI2023

Architecture-Preserving Provable Repair of Deep Neural Networks

Deep neural networks (DNNs) are becoming increasingly important components of software, and are considered the state-of-the-art solution for a number of problems, such as image recognition. However, DNNs are far from infallible, and incorrect behavior of DNNs can have disastrous real-world consequences. This paper addresses the problem of architecture-preserving V-polytope provable repair of DNNs. A V-polytope defines a convex bounded polytope using its vertex representation. V-polytope provable repair guarantees that the repaired DNN satisfies the given specification on the infinite set of points in the given V-polytope. An architecture-preserving repair only modifies the parameters of the DNN, without modifying its architecture. The repair has the flexibility to modify multiple layers of the DNN, and runs in polynomial time. It supports DNNs with activation functions that have some linear pieces, as well as fully-connected, convolutional, pooling and residual layers. To the best our knowledge, this is the first provable repair approach that has all of these features. We implement our approach in a tool called APRNN. Using MNIST, ImageNet, and ACAS Xu DNNs, we show that it has better efficiency, scalability, and generalization compared to PRDNN and REASSURE, prior provable repair methods that are not architecture preserving.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2015

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

Tangent Linear Model↗
DOE OSTI2024

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

In Dzanic (2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Finally, some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High-brightness electron injectors for high-duty cycle X-ray free electron lasers

The successful development in the last two decades of X-ray free electron lasers (FELs) with their revolutionary brightness performance has been tightly dependent on the parallel development of electron guns and injectors capable of providing the high-brightness electron beams required by FELs lasing at these short wavelengths. The ultimate brightness delivered by a linear accelerator (linac) is already set at its injector and the remaining part of the accelerator can be only designed to preserve the injector performance. The technology to be used for the accelerator part of an X-Ray FEL strongly depends on the duty-cycle at which the FEL operates. Normal-conducting, room-temperature, copper-based radio frequency (RF) technology is typically used for low duty-cycles of up to approximately 10 −3 . For higher duty-cycles and up to continuous wave (CW) operation, the linac must rely on superconductive RF technology because, with the higher duty-cycle, the increasingly higher power dissipated in normal conducting RF structures becomes excessive for the warm technology. The situation changes in the lower energy part of the accelerator, where injector schemes, based on direct current, normal-conducting, and superconducting RF electron guns, are demonstrating the beam quality performance required by high-duty-cycle X-ray FELs. In this paper we start with a description of the requirements for such injectors, followed by an overview of the pursued technologies and schemes, and by a discussion on the main differences in terms of beam dynamics between low and high duty-cycle injectors.

Sannibale, Fernando↗
NASA NTRS1993

Green vegetation, nonphotosynthetic vegetation, and soils in AVIRIS data

The problem of distinguishing between green vegetation, nonphotosynthetic vegetation (NPV, such as dry grass, leaf litter, and woody material), and soils in imaging-spectrometer data is addressed by analyzing an image taken by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over the Jasper Ridge Biological Preserve (California) on September 20, 1989, using spectral mixture analysis. Over 98 percent of the spectral variation could be explained by linear mixtures of three endmembers, green vegetation, shade, and soil. NPV, which could not be distinguished from soil when included as an endmember, was discriminated by residual spectra that contained cellulose and lignin absorptions. Distinct communities of green vegetation were distinguished by (1) nonlinear mixing effect caused by transmission and scattering by green leaves, (2) variations in a derived canopy-shade spectrum, and (3) the fraction of NPV.

Roberts, D. A.↗
NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗
DOE OSTI2020

A fully implicit, scalable, conservative nonlinear relativistic Fokker–Planck 0D-2P solver for runaway electrons

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic ‘runaway’ electrons (~ MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. As such, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker–Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron–ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham–Lorentz–Dirac reaction term. However, our implementation improves on these earlier studies by (1) ensuring exact conservation properties for electron collisions, (2) strictly preserving positivity, and (3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams–Karney potentials, and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Spatiotemporally dynamic implicit large eddy simulation using machine learning classifiers

In this article, we utilize machine learning to dynamically determine if a point on the computational grid requires implicit numerical dissipation for large eddy simulation (LES). The decision making process is learnt through a priori training on quantities derived from direct numerical simulation (DNS) data. In particular, we compute eddy-viscosities obtained through the coarse-graining of DNS quantities and utilize their projection onto a Gaussian distribution to categorize areas that may require dissipation. If our learning determines that closure is necessary, an upwinded scheme is utilized for computing the non-linear Jacobian. In contrast, if it is determined that closure is unnecessary, a symmetric and second-order accurate energy and enstrophy preserving Arakawa scheme is utilized instead. This results in a closure framework that precludes the specification of any model-form for the small scale contributions of turbulence but deploys an appropriate numerical dissipation from explicit closure driven hypotheses. Here, this methodology is deployed for the Kraichnan turbulence test-case and assessed through various statistical quantities such as angle-averaged kinetic energy spectra and vorticity structure functions. Our framework thus establishes a link between the use of explicit LES ideologies for closure and numerical dissipation-based modeling of turbulence leading to improved statistical fidelity of a posteriori simulations.

42 ENGINEERING↗
DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗
NASA NTRS1976

Conservation properties of numerical integration methods for systems of ordinary differential equations

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Rosenbaum, J. S.↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Emittance preservation for the electron arm in a single PWFA-LC stage using quasi-adiabatic plasma density ramp matching sections

Plasma-based acceleration (PBA) is being considered for a next generation linear collider (LC). In some PBA-LC designs for the electron arm, the extreme beam parameters are expected to trigger background ion motion within the witness beam, which can lead to longitudinally varying nonlinear focusing forces and result in an unacceptable emittance growth of the beam. To mitigate this, we propose to use quasi-adiabatic plasma density ramps as matching sections at the entrance and exit of each stage. We match the witness electron beam to the low density plasma entrance, where the beam initially has a large matched spot size so the ion motion effects are relatively small. As the beam propagates in the plasma density upramp, it is quasi-adiabatically focused, and its distribution maintains a non-Gaussian equilibrium distribution in each longitudinal slice throughout the process, even when severe ion collapse has occurred. This only causes small amounts of slice emittance growth. The phase mixing between slices with different betatron frequencies leads to additional projected emittance growth within the acceleration stage. A density downramp at the exit of an acceleration section can eliminate much of the slice and projected emittance growth as the beam and ion motion adiabatically defocuses and decreases, respectively. Simulation results from QuickPIC with Azimuthal Decomposition show that within a single acceleration stage with a 25 GeV energy gain, this concept can limit the projected emittance growth to only ∼2% for a 25 GeV, 100 nm emittance witness beam and ∼20% for a 100 GeV, 100 nm normalized emittance witness beam. The trade-off between the adiabaticity of the plasma density ramp and the initial ion motion at the entrance for a given length of the plasma density ramp is also discussed.

Physics↗
NASA NTRS1993

Giant radiating dyke swarms on Earth and Venus

On Earth, giant radiating dyke swarms are usually preserved as fan-shaped fragments which have been dismembered from their original configuration by subsequent plate tectonic rifting events. Analysis of the largest fragments and consideration of their original configuration has led to the idea that many swarms are plume related, and that dyke swarms radiate away from plume centers. Magellan radar data reveal abundant intact giant radiating swarms on Venus which are similar in scale and pattern to those on Earth. The absence of intense weathering and plate tectonic processes on Venus accounts for the preservation of the primary radiating patterns. It is characteristic of both Earth and Venus that giant radiating dikes are emplaced laterally for distances of at least 2000 km away from plume centers. At distances beyond the influence of the plume on both Earth and Venus, the radiating dyke pattern is often swept into a linear pattern aligned with the regional stress field. There is tremendous potential synergism between the characterization and analysis of terrestrial dyke swarms (where significant erosion has revealed their structure and emplacement directions at depth) and the giant swarms of Venus (where the complete circumferential structure is preserved, and the surface fracture systems above near surface dikes and the nature of the central source regions are revealed). In this study, we report on the characteristics of radial dyke swarms on Earth and Venus and draw some preliminary comparisons from the two perspectives. In summary, on both planets there is evidence for plume-related magmatic centers associated with vertical and lateral injection of magma over considerable distances (up to at least 2000 km). The abundance of very broadly radiating swarms on Venus supports the notion that the swarms on Earth were radiating over broad sectors at the time of intrusion but were dissected by later events. The Venus data show that a swarm can change from radiating (proximal) to regional (distal) subparallel orientations. An implication for Earth is that many regional linear swarms which do not have a radiating pattern may be due to fragmentation of the swarm during later plate tectonic rifting. Completion of the global classification and census of Venus features, comparison to the terrestrial synthesis, and documentation of the mode of emplacement of dikes in these environments (buffered and unbuffered conditions) should lead to additional general insight into mechanisms of formation and evolution and their relation to plumes.

Ernst, Richard E.↗
DOE OSTI2025

Quantum Time Dynamics Mediated by the Yang–Baxter Equation and Artificial Neural Networks

Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANNs) and the Yang–Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANNs for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the data set for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Limit cycle oscillations in the zonal-flow-catalyzed interactions of ion-temperature-gradient turbulence

Limit-cycle oscillations are studied for ion temperature gradient turbulence, which, in the absence of large diamagnetic (mean) shear flows, saturates through energy transfer from unstable modes to large-scale stable modes via zonal-flow intermediary modes. Oscillations of zonal flow and turbulence levels are strongly constrained by the reactive, largely non-dissipative character of the zonal flows. Since existing predator–prey models for observed oscillations in experiments do not include energy transfer through zonal flows to stable modes, low-order fluid models with this physics are constructed and investigated. A simple three-wave truncation produces low-amplitude zonal flows that slowly oscillate around a zero mean, with turbulence oscillations between coupled wavenumbers that exceed linear frequencies by orders of magnitude. This inconsistency with experimental observations is caused by the weak non-linear drive of zonal flows in three-wave systems and the lack of multiple-wavenumber turbulent interactions. A more comprehensive model that preserves multiple wavenumber interactions within the context of conservative zonal-flow-mediated energy transfer to stable modes accurately reflects observed dynamics when the phase between stable and unstable modes is occasionally randomized.

Li, P. -Y. (ORCID:0000000295254171)↗
NASA NTRS2007

Alfven Waves and Turbulence in the Solar Atmosphere and Solar Wind

We solve the problem of propagation and dissipation of Alfvenic turbulence in a model solar atmosphere consisting of a static photosphere and chromosphere, transition region, and open corona and solar wind using a phenomenological model for the turbulent dissipation based on wave reflection. We show that most of the dissipation for a given wave frequency spectrum occurs in the lower corona, and the overall rms amplitude of the fluctuations evolves in a way consistent with observations. The frequency spectrum for a Kolmogorov-like slope is not found to change dramatically from the photosphere to the solar wind; however, it does preserve signatures of transmission throughout the lower atmospheric layers, namely, oscillations in the spectrum at high frequencies reminiscent of the resonances found in the linear case. These may disappear once more realistic couplings for the nonlinear terms are introduced or if time-dependent variability of the lower atmospheric layer is introduced.

turbulence↗
NASA NTRS2020

Searching for Evidence of Life in Deep Time and Space

Cyanobacterial mats provide insights into ancient benthic microbial communities and their biosignatures. Thick mats occupy hypersaline saltern ponds at Guerrero Negro, Baja California, Mexico. Mat biota maintains rapid rates of biogeochemical processes under steep and rapidly changing environmental gradients. Cycling of C, O, and S all increased identically with temperature, indicating the tight coupling of these cycles. An enormous microbial diversity exhibits a highly structured spatial distribution of populations. Combined universal clone libraries from all mat layers indicated Bacteria/Archaea/Eukarya ratios of 57:7:1. More than 10,000 unique bacterial sequences were present. The relative abundance of Archaea increased with depth - below 10 cm, solvent-extractable archaeal lipids were twice as abundant as bacterial lipids. Only 15 species of Eukarya were found among 890 clones analyzed. Degradation of the mats’ insoluble macromolecular organic fraction (IMOM) by hydropyrolysis released a complex variety of linear, branched and polycyclic alkane structures, e.g., hopanes, methylhopanes and steranes. Covalent binding of these biosignatures into IMOM aids their long-term geological preservation. Mars rover missions revealed evidence of long-lived fluvial lacustrine systems and organics in associated mudstones. NASA’s Mars 2020 rover mission will examine sediments in Jezero crater, including a delta and shoreline carbonate deposits, environments that on Earth have sustained microbial mats.

Des Marais, David J.↗