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Results for “nonlinear mappings”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multiple-core-hole resonance spectroscopy with ultraintense X-ray pulses

Understanding the interaction of intense, femtosecond X-ray pulses with heavy atoms is crucial for gaining insights into the structure and dynamics of matter. One key aspect of nonlinear light–matter interaction was, so far, not studied systematically at free-electron lasers—its dependence on the photon energy. Here, we use resonant ion spectroscopy to map out the transient electronic structures occurring during the complex charge-up pathways of xenon. Massively hollow atoms featuring up to six simultaneous core holes determine the spectra at specific photon energies and charge states. We also illustrate how different X-ray pulse parameters, which are usually intertwined, can be partially disentangled. The extraction of resonance spectra is facilitated by the possibility of working with a constant number of photons per X-ray pulse at all photon energies and the fact that the ion yields become independent of the peak fluence beyond a saturation point. Our study lays the groundwork for spectroscopic investigations of transient atomic species in exotic, multiple-core-hole states that have not been explored previously.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Exploring the impacts of unprecedented climate extremes on forest ecosystems: hypotheses to guide modeling and experimental studies

Abstract. Climatic extreme events are expected to occur more frequently in the future, increasing the likelihood of unprecedented climate extremes (UCEs) or record-breaking events. UCEs, such as extreme heatwaves and droughts, substantially affect ecosystem stability and carbon cycling by increasing plant mortality and delaying ecosystem recovery. Quantitative knowledge of such effects is limited due to the paucity of experiments focusing on extreme climatic events beyond the range of historical experience. Here, we present a road map of how dynamic vegetation demographic models (VDMs) can be used to investigate hypotheses surrounding ecosystem responses to one type of UCE: unprecedented droughts. As a result of nonlinear ecosystem responses to UCEs that are qualitatively different from responses to milder extremes, we consider both biomass loss and recovery rates over time by reporting a time-integrated carbon loss as a result of UCE, relative to the absence of drought. Additionally, we explore how unprecedented droughts in combination with increasing atmospheric CO2 and/or temperature may affect ecosystem stability and carbon cycling. We explored these questions using simulations of pre-drought and post-drought conditions at well-studied forest sites using well-tested models (ED2 and LPJ-GUESS). The severity and patterns of biomass losses differed substantially between models. For example, biomass loss could be sensitive to either drought duration or drought intensity depending on the model approach. This is due to the models having different, but also plausible, representations of processes and interactions, highlighting the complicated variability of UCE impacts that still need to be narrowed down in models. Elevated atmospheric CO2 concentrations (eCO2) alone did not completely buffer the ecosystems from carbon losses during UCEs in the majority of our simulations. Our findings highlight the consequences of differences in process formulations and uncertainties in models, most notably related to availability in plant carbohydrate storage and the diversity of plant hydraulic schemes, in projecting potential ecosystem responses to UCEs. We provide a summary of the current state and role of many model processes that give way to different underlying hypotheses of plant responses to UCEs, reflecting knowledge gaps which in future studies could be tested with targeted field experiments and an iterative modeling–experimental conceptual framework.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1971

Global trajectory targeting via computer graphics

A technique is described in which the two-point boundary value problem (TPBVP) may be solved with the aid of interactive computer graphics. The particular TPBVP considered is the optimal electric propulsion space trajectory problem. An appropriate two-dimensional projection of the TPBVP mapping, or trajectory, is displayed on the computer's television screen, and a man-in-the-loop varies selected trajectory starting conditions in the fashion of a nonlinear walk until the viewed trajectory endpoint lies near a displayed target. Once global targeting is accomplished in this manner, program internal logic can easily handle local targeting to strongly solve the TPBVP.

Mann, F. I.↗
NASA NTRS1977

Optimum constrained image restoration filters

The research described centered on development of an optimum image restoration filter (IRF) minimizing the radius of gyration of the corrected or composite system point-spread function (P-SF) subject to contraints, and reducing 2-dimensional spatial smearing or blurring of an image. The constraints are imposed on the radius of gyration of the IRF P-SF, the total restored image noise power, and the shape of the composite system frequency spectrum. The image degradation corresponds to mapping many points from the original image into a single resolution element. The P-SF is obtained as solution to a set of simultaneous differential equations obeying nonlinear integral constraints. Truncation errors due to edge effects are controlled by constraining the radius of gyration of the IRF P-SF. An iterative technique suppresses sidelobes of the composite system P-SF.

Riemer, T. E.↗
NASA NTRS1980

Dynamic analysis of noncontacting face seals

The dynamic behavior of a noncontacting coned face seal is analyzed taking into account various design parameters and operating conditions. The primary seal ring motion is expressed by a set of nonlinear equations for three degrees of freedom. These equations, which are solved numerically, allow identification of two dimensionless groups of parameters that affect the seal dynamic behavior. Stability maps for various seals are presented. These maps contain a stable-to-unstable transition region in which the ring wobbles at half the shaft frequency. The effect of various parameters on seal stability is discussed and an empirical expression for critical stability is offered.

Etsion, I.↗
DOE OSTI2024

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

Abstract For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.

Physics↗
DOE OSTI2020

Seismicity and Stress Associated With a Fluid-Driven Fracture: Estimating the Evolving Geometry

A coupled approach, combining the theory of rate- and state-dependent friction and methods from poroelasticity, forms the basis for a quantitative relationship between displacements and fluid leak-off from a growing fracture and changes in the rate of seismic events in the region surrounding the fracture. Poroelastic Green's functions link fracture aperture changes and fluid flow from the fracture to changes in the stress field and pore pressure in the adjacent formation. The theory of rate- and state-dependent friction provides a connection between Coulomb stress changes and variations in the rate of seismic events. Numerical modeling indicates that the Coulomb stress changes can vary significantly between formations with differing properties. The relationship between the seismicity rate changes and the changes in the formation stresses and fluid pressure is nonlinear, but a transformation produces a quantity that is linearly related to the aperture changes and fluid leak-off from the fracture. The methodology provides a means for mapping changes in seismicity into fracture aperture changes and to image an evolving fracture. An application to observed microseismicity associated with a hydrofracture reveals asymmetric fracture propagation within two main zones, with extended propagation in the upper zone. Furthermore, the time-varying volume of the fracture agrees with the injected volume, given by the integration of rate changes at the injection well, providing validation of the estimated aperture changes.

58 GEOSCIENCES↗
DOE OSTI2022

Ferroelectricity in a semiconducting all-inorganic halide perovskite

Ferroelectric semiconductors are rare materials with both spontaneous polarizations and visible light absorptions that are promising for designing functional photoferroelectrics, such as optical switches and ferroelectric photovoltaics. The emerging halide perovskites with remarkable semiconducting properties also have the potential of being ferroelectric, yet the evidence of robust ferroelectricity in the typical three-dimensional hybrid halide perovskites has been elusive. Here, we report on the investigation of ferroelectricity in all-inorganic halide perovskites, CsGeX 3 , with bandgaps of 1.6 to 3.3 eV. Their ferroelectricity originates from the lone pair stereochemical activity in Ge (II) that promotes the ion displacement. This gives rise to their spontaneous polarizations of ~10 to 20 μC/cm 2 , evidenced by both ab initio calculations and key experiments including atomic-level ionic displacement vector mapping and ferroelectric hysteresis loop measurement. Furthermore, characteristic ferroelectric domain patterns on the well-defined CsGeBr 3 nanoplates are imaged with both piezo-response force microscopy and nonlinear optical microscopic method.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Viscoelastic-Mapping of Cellulose Nanofibrils Using Low-Total-Force Contact Resonance Force Microscopy (LTF-CRFM)

Low-total-force contact resonance force microscopy (LTF-CRFM), an atomic force microscopy method, is introduced as a non-destructive means to quantify the local viscoelastic loss tangent (tan..delta..) of supported cellulose nanofibrils (CNFs). The method limits static and dynamic forces during measurement to minimize substrate and geometry effects and to reduce the potential for stress-induced CNF damage. LTF-CRFM uses Brownian motion to achieve the thermally-limited lowest dynamic force, while approaching adhesive pull-off to achieve the low static force. LTF-CRFM measurements were shown to generate analyzable data without evidence of nonlinear artifacts and without damage to the CNF over static forces ranging from 11.6 to 84.6 nN. The measured tan..delta.. of CNFs was 0.015 +/- 0.0094, which is the first reported tan..delta.. measurement of an isolated CNF. Finally, LTF-CRFM successfully mapped tan..delta.. along the length of CNFs to determine that kink defects along the CNF do not impart a local viscoelastic property change at the spatial resolution of the measurement.

BIOMASS FUELS↗
NASA NTRS2012

Improved Displacement Transfer Functions for Structure Deformed Shape Predictions Using Discretely Distributed Surface Strains

In the formulations of earlier Displacement Transfer Functions for structure shape predictions, the surface strain distributions, along a strain-sensing line, were represented with piecewise linear functions. To improve the shape-prediction accuracies, Improved Displacement Transfer Functions were formulated using piecewise nonlinear strain representations. Through discretization of an embedded beam (depth-wise cross section of a structure along a strain-sensing line) into multiple small domains, piecewise nonlinear functions were used to describe the surface strain distributions along the discretized embedded beam. Such piecewise approach enabled the piecewise integrations of the embedded beam curvature equations to yield slope and deflection equations in recursive forms. The resulting Improved Displacement Transfer Functions, written in summation forms, were expressed in terms of beam geometrical parameters and surface strains along the strain-sensing line. By feeding the surface strains into the Improved Displacement Transfer Functions, structural deflections could be calculated at multiple points for mapping out the overall structural deformed shapes for visual display. The shape-prediction accuracies of the Improved Displacement Transfer Functions were then examined in view of finite-element-calculated deflections using different tapered cantilever tubular beams. It was found that by using the piecewise nonlinear strain representations, the shape-prediction accuracies could be greatly improved, especially for highly-tapered cantilever tubular beams.

Ko, William L.↗
DOE OSTI2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗
NASA NTRS1991

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗
NASA NTRS1997

Design of Neural Networks for Fast Convergence and Accuracy: Dynamics and Control

A procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed, such that once properly trained, they provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component/spacecraft design changes and measures of its performance or nonlinear dynamics of the system/components. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The proposed method should work for applications wherein an arbitrary large source of training data can be generated. Two numerical examples are performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗
DOE OSTI2021

Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids

In this work, we introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system's behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Generation of ultrahigh-brightness pre-bunched beams from a plasma cathode for X-ray free-electron lasers

The longitudinal coherence of X-ray free-electron lasers (XFELs) in the self-amplified spontaneous emission regime could be substantially improved if the high brightness electron beam could be pre-bunched on the radiated wavelength-scale. Here, we show that it is indeed possible to realize such current modulated electron beam at angstrom scale by exciting a nonlinear wake across a periodically modulated plasma-density downramp/plasma cathode. The density modulation turns on and off the injection of electrons in the wake while downramp provides a unique longitudinal mapping between the electrons’ initial injection positions and their final trapped positions inside the wake. The combined use of a downramp and periodic modulation of micrometers is shown to be able to produces a train of high peak current (17 kA) electron bunches with a modulation wavelength of 10’s of angstroms - orders of magnitude shorter than the plasma density modulation. The peak brightness of the nano-bunched beam can be $\textit{O}$(10 21 A/m 2 /rad 2 ) orders of magnitude higher than current XFEL beams. Such prebunched, high brightness electron beams hold the promise for compact and lower cost XEFLs that can produce nanometer radiation with hundreds of GW power in a 10s of centimeter long undulator.

47 OTHER INSTRUMENTATION↗
NASA NTRS2023

Using Regionalized Air Quality Model Performance and Bayesian Maximum Entropy Data Fusion to Map Global Surface Ozone Concentration and Associated Uncertainty

Estimates of ground-level ozone concentrations have been improved through data fusion of observations and atmospheric chemistry models. Our previous global ozone estimates for the Global Burden of Disease study corrected for bias uniformly across continents and then corrected near monitoring stations using the Bayesian Maximum Entropy (BME) framework for data fusion. Here, we use the Regionalized Air Quality Model Performance (RAMP) framework to correct model bias over a much larger spatial range than BME can, accounting for the spatial inhomogeneity of bias and nonlinearity as a function of modeled ozone. RAMP bias correction is applied to a composite of 9 global chemistry-climate models, based on the nearest set of monitors. These estimates are then fused with observations using BME, which matches observations at measurement stations, with the influence of observations declining with distance in space and time. We create global ozone maps for each year from 1990 to 2017 at fine spatial resolution. RAMP is shown to create unrealistic discontinuities due to the spatial clustering of ozone monitors, which we overcome by applying a weighting for RAMP based on the number of monitors nearby. Incorporating RAMP before BME has little effect on model performance near stations, but strongly increases R 2 by 0.15 at locations farther from stations, shown through a checkerboard cross-validation. Corrections to estimates differ based on location in space and time, confirming heterogeneity. We quantify the likelihood of exceeding selected ozone levels, finding that parts of the Middle East, India, and China are most likely to exceed 55 parts per billion (ppb) in 2017. About 96% of the global population was exposed to ozone levels above the World Health Organization guideline of 60 µg m −3 (30 ppb) in 2017. Our annual fine-resolution ozone estimates may be useful for several applications including epidemiology and assessments of impacts on health, agriculture, and ecosystems.

Ozone↗
DOE OSTI2024

Enhancing the Range and Reliability of the Spacer Layer Imaging Method

The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.

EHL film geometry↗
DOE OSTI2025

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials’ symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response.

36 MATERIALS SCIENCE↗