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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Field Harmonic Measurement of High-Gradient Permanent Magnet Quadrupoles for NSLS- II Upgrade

The National Synchrotron Light Source II (NSLS-II) is preparing for a major upgrade based on a new lattice concept, known as “Complex Bend,” to replace its existing double bend achromat (DBA) lattice. Here, this novel lattice will use high-gradient permanent magnet quadrupoles (PMQs) with small apertures in the range of 16–22 mm. A prototype complex bend branch with PMQs has been installed in the NSLS-II linac to evaluate the lattice's performance. An accurate and precise magnetic measurement system is required for field harmonic characterization and magnetic tuning of these PMQs. As part of this project a Rotating-Coil bench, based on a Printed Circuit Board (PCB) coil with a 12 mm diameter, has been configured to measure nine PMQs with bore diameter of 12.7 mm. This PCB coil has an active length of 270 mm, and is able to measure fields up to the 15th harmonic of the main field at a reference radius of 5 mm, while maintaining field quality levels within 10 ppm of the main field. This article presents the PCB coil setup, the harmonic measurement results and their temperature dependencies and repeatability. Simulation results on compensation of undesired multipoles using “IDBuilder”, a genetic algorithm-based optimizer code for magnetic tuning is included for field harmonic corrections.

36 MATERIALS SCIENCE↗
DOE OSTI2020

High-throughput phase-field simulations and machine learning of resistive switching in resistive random-access memory

Metal oxide-based Resistive Random-Access Memory (RRAM) exhibits multiple resistance states, arising from the activation/deactivation of a conductive filament (CF) inside a switching layer. Understanding CF formation kinetics is critical to achieving optimal functionality of RRAM. Here a phase-field model is developed, based on materials properties determined by ab initio calculations, to investigate the role of electrical bias, heat transport and defect-induced Vegard strain in the resistive switching behavior, using MO 2- x systems such as HfO 2- x as a prototypical model system. It successfully captures the CF formation and resultant bipolar resistive switching characteristics. High-throughput simulations are performed for RRAMs with different material parameters to establish a dataset, based on which a compressed-sensing machine learning is conducted to derive interpretable analytical models for device performance (current on/off ratio and switching time) metrics in terms of key material parameters (electrical and thermal conductivities, Vegard strain coefficients). These analytical models reveal that optimal performance (i.e., high current on/off ratio and low switching time) can be achieved in materials with a low Lorenz number, a fundamental material constant. This work provides a fundamental understanding to the resistive switching in RRAM and demonstrates a computational data-driven methodology of materials selection for improved RRAM performance, which can also be applied to other electro-thermo-mechanical systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Use of a segmented cell for the combinatorial development of platinum group metal-free electrodes for polymer electrolyte fuel cells

The development of novel platinum group metal (PGM)-free catalysts is a difficult task, particularly when coupled with the integration into a cathode catalyst layer (CCL). The optimization of such PGM-free electrode structures is often non-linear and iterative, making it a demanding task due to the high number of parameters that affect performance. To accelerate both materials discovery and electrode development, this work demonstrates the application of a high-resolution segmented cell (SC) with 121 segments of 0.413 cm 2 size for combinatorial high-throughput PGM-free catalyst screening and CCL optimization. The approach utilizes three flow-field strips with active areas of 4.45 cm 2 each, distributed over 11 segments. Electrodes with identical catalyst material and fabrication method result in reproducible data with typically less than 10% variation between each segment and match in performance with differential single cell data. High throughput testing of combinatorial sample sets, with varied PGM-free electrocatalyst materials or electrode composition, demonstrated the ability to rapidly discern high performing outliers, and establish or confirm trends in electrode optimization. The results indicated significant performance benefits of electrodes with ionomer content of 45 wt% over lower values, and of water rich inks with 82% water content over those with 50%.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2023

OPTOM: Optimization of Parabolic Trough - Operations & Maintenance

The US Department of Energy’s SunShot goals look to reduce the cost of Concentrating Solar Power (CSP) technology to 5¢/kWh for baseload plants. This is about a 50% reduction from current costs. To achieve this cost target, a significant reduction in operation and maintenance (O&M) costs of 40 to 50% is likely needed. Advances are needed in the O&M practices of CSP plants if the technology is to achieve the SunShot cost goals. Digitization of plant performance and O&M data has become a new best practice in the world of renewable energy asset management. Owners and operators of large photovoltaic and wind power plants are working to digitize performance and O&M data at their existing assets, to improve their management of the facilities, to increase performance, reduce O&M costs, and lower the overall life cycle cost of ownership. CSP power plants are behind the curve of other technologies on the digitization of plant information to aid in the plant asset management. This project directly addresses the objective of digitizing the O&M data of the solar field, focusing on three areas: 1) creating a framework for sharing data and information, 2) creating a system for monitoring and managing the maintenance of the solar field collectors, and 3) developing analytic tools to identify issues in the solar field. According to the NREL CSP Best Practices Study, the current practice at many CSP plants is to rely on paper lists, spreadsheets, and email for monitoring and managing problems and maintenance in the solar field. The key element to digitize solar field O&M is the creation of a centralized data archive that all users and systems can interface with. This project developed a centralized relational database framework that allows users and applications to access and share data. Conventional power plants utilize Computerized Maintenance Management Systems (CMMSs) to track the corrective, preventive (scheduled), and predictive maintenance of equipment and subsystems in the power plant. CSP plants use these systems in the power block, but while these systems specialize at tracking maintenance on up to thousands of pieces of equipment, they are not well suited for tracking the tens or hundreds of thousands of components in large commercial CSP or photovoltaic solar fields. In this project we developed a new software application referred to as FieldStatus (TM). This is a specialized database program that is used to track the status of each collector and its components. This application is designed to complement the existing CMMS to enable improved tracking and management of maintenance activities in the solar field. One of the major maintenance tasks for solar fields is maintaining the cleanliness of the mirrors. Although seemingly a relatively straight forward task, it has often proven challenging to maintain high levels of cleanliness in an efficient and cost-effective manner. This project developed new tools and metrics for monitoring and optimizing solar field cleaning resources and overall solar field cleanliness.

14 SOLAR ENERGY↗
DOE OSTI2026

Advanced flip-coil system for magnetic field integral measurements of insertion devices

A novel flip-coil measurement system has been developed for the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Laboratory. This paper describes the design, implementation, and commissioning of the new measurement bench, highlighting its key features, including improved mechanical stability, advanced data acquisition, and enhanced reproducibility. The system enables precise characterization of field integrals and multipole components, ensuring the optimal performance of Insertion Devices (IDs) before installation in the NSLS-II storage ring. The flip-coil system incorporates an innovative approach to minimize mechanical and electrical errors, which significantly improves the reproducibility of measurements. In addition, the system features a state-of-the-art data acquisition system that enables real-time monitoring and analysis, further enhancing the efficiency and accuracy of the measurement process. Furthermore, preliminary tests have demonstrated that the new system meets the stringent requirements for magnetic field characterization of advanced insertion devices, making it an essential tool for future ID commissioning and quality assurance at NSLS-II.

36 MATERIALS SCIENCE↗
NASA NTRS1989

The role of optimization in the next generation of computer-based design tools

There is a close relationship between design optimization and the emerging new generation of computer-based tools for engineering design. With some notable exceptions, the development of these new tools has not taken full advantage of recent advances in numerical design optimization theory and practice. Recent work in the field of design process architecture has included an assessment of the impact of next-generation computer-based design tools on the design process. These results are summarized, and insights into the role of optimization in a design process based on these next-generation tools are presented. An example problem has been worked out to illustrate the application of this technique. The example problem - layout of an aircraft main landing gear - is one that is simple enough to be solved by many other techniques. Although the mathematical relationships describing the objective function and constraints for the landing gear layout problem can be written explicitly and are quite straightforward, an approximation technique has been used in the solution of this problem that can just as easily be applied to integrate supportability or producibility assessments using theory of measurement techniques into the design decision-making process.

Rogan, J. Edward↗
NASA NTRS2012

HURON (HUman and Robotic Optimization Network) Multi-Agent Temporal Activity Planner/Scheduler

HURON solves the problem of how to optimize a plan and schedule for assigning multiple agents to a temporal sequence of actions (e.g., science tasks). Developed as a generic planning and scheduling tool, HURON has been used to optimize space mission surface operations. The tool has also been used to analyze lunar architectures for a variety of surface operational scenarios in order to maximize return on investment and productivity. These scenarios include numerous science activities performed by a diverse set of agents: humans, teleoperated rovers, and autonomous rovers. Once given a set of agents, activities, resources, resource constraints, temporal constraints, and de pendencies, HURON computes an optimal schedule that meets a specified goal (e.g., maximum productivity or minimum time), subject to the constraints. HURON performs planning and scheduling optimization as a graph search in state-space with forward progression. Each node in the graph contains a state instance. Starting with the initial node, a graph is automatically constructed with new successive nodes of each new state to explore. The optimization uses a set of pre-conditions and post-conditions to create the children states. The Python language was adopted to not only enable more agile development, but to also allow the domain experts to easily define their optimization models. A graphical user interface was also developed to facilitate real-time search information feedback and interaction by the operator in the search optimization process. The HURON package has many potential uses in the fields of Operations Research and Management Science where this technology applies to many commercial domains requiring optimization to reduce costs. For example, optimizing a fleet of transportation truck routes, aircraft flight scheduling, and other route-planning scenarios involving multiple agent task optimization would all benefit by using HURON.

Hua, Hook↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Request for the establishment of quantum information foundries

Quantum information science still requires basic science research to achieve its full potential. However, scientists require access to fabricated device samples if we are to utilize the full toolset for solving the pressing issues in the field such as materials, device layout, or optimal error correction methods.Currently, access to samples is either prohibitively expensive, or requires close collaboration with one of the few groups in the world developing these systems. A dedicated quantum foundry could,in principle,provide affordable samples designed with current best practices to a host of scientists who otherwise do not have access. We detail several different foundry models which we believe will assist the community in developing the science for both the underlying processes, as well as the more advanced chip layout and circuit design. Opening access to the broader community has the potential to significantly lower the barrier to entry and vastly improve the ability for researchers in fields ranging from condensed matter to materials characterization to systems engineering to contribute to accelerating the advance of quantum information science and technology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2006

Global Positioning System (GPS) Precipitable Water in Forecasting Lightning at Spaceport Canaveral

This paper evaluates the use of precipitable water (PW) from Global Positioning System (GPS) in lightning prediction. Additional independent verification of an earlier model is performed. This earlier model used binary logistic regression with the following four predictor variables optimally selected from a candidate list of 23 candidate predictors: the current precipitable water value for a given time of the day, the change in GPS-PW over the past 9 hours, the KIndex, and the electric field mill value. This earlier model was not optimized for any specific forecast interval, but showed promise for 6 hour and 1.5 hour forecasts. Two new models were developed and verified. These new models were optimized for two operationally significant forecast intervals. The first model was optimized for the 0.5 hour lightning advisories issued by the 45th Weather Squadron. An additional 1.5 hours was allowed for sensor dwell, communication, calculation, analysis, and advisory decision by the forecaster. Therefore the 0.5 hour advisory model became a 2 hour forecast model for lightning within the 45th Weather Squadron advisory areas. The second model was optimized for major ground processing operations supported by the 45th Weather Squadron, which can require lightning forecasts with a lead-time of up to 7.5 hours. Using the same 1.5 lag as in the other new model, this became a 9 hour forecast model for lightning within 37 km (20 NM)) of the 45th Weather Squadron advisory areas. The two new models were built using binary logistic regression from a list of 26 candidate predictor variables: the current GPS-PW value, the change of GPS-PW over 0.5 hour increments from 0.5 to 12 hours, and the K-index. The new 2 hour model found the following for predictors to be statistically significant, listed in decreasing order of contribution to the forecast: the 0.5 hour change in GPS-PW, the 7.5 hour change in GPS-PW, the current GPS-PW value, and the KIndex. The new 9 hour forecast model found the following five independent variables to be statistically significant, listed in decreasing order of contribution to the forecast: the current GPSPW value, the 8.5 hour change in GPS-PW, the 3.5 hour change in GPS-PW, the 12 hour change in GPS-PW, and the K-Index. In both models, the GPS-PW parameters had better correlation to the lightning forecast than the K-Index, a widely used thunderstorm index. Possible future improvements to this study are discussed.

Kehrer, Kristen C.↗
DOE OSTI2022

Radio-Frequency Rapid Thermal Processing Enabling Spatial Phase Transformation and Nanocrystallization of Soft Magnetic Amorphous Alloys

Thermal processing of soft magnetic amorphous and nanocrystalline alloys is explored under the influence of radio-frequency induction-heating techniques. Direct induction-heating concepts based on longitudinal and transverse flux heating are examined and the details of electromagnetic fields interaction with metallic strips are discussed by analytical calculations as well as finite element analysis. Initial experimental results confirming spatial control of phase transformations and nanocrystallization within a single strip of Finemet Fe-based amorphous ribbons are reported. Here, the degree to which primary and secondary crystallization temperature are achieved depends on the spacing between the ribbon relative to the induction coil as well as the coil design and configuration. For transverse coil configurations, the local temperature and therefore microstructural evolution is different across the lateral dimension of processed ribbons, with reduced gap sizes producing enhanced peak temperatures and larger temperature distributions with greater spatial variation in microstructure. In addition, indirect susceptor-based induction heating under tension is performed and the impact of microstructure is demonstrated. Herein, potential for exploiting spatially optimized phase transformations is illustrated through electromagnetic field–assisted processing in a scalable manufacturing process with amorphous and nanocrystalline soft magnetic alloys.

36 MATERIALS SCIENCE↗
NASA NTRS1966

Low-thrust guidance study Final report

Computer algorithm to determine minimum-time optimal control for continuous low-thrust propulsion systems operating in inverse-square gravity field

GRAVITATIONAL FIELD↗
NASA NTRS2005

NASA Tech Briefs, September 2005

Topivs include: Diamond-Coated Carbon Nanotubes for Efficient Field Emission; Improved Anode Coatings for Direct Methanol Fuel Cells; Advanced Ablative Insulators and Methods of Making Them; PETIs as High-Temperature Resin-Transfer-Molding Materials; Stable Polyimides for Terrestrial and Space Uses; Low-Density, Aerogel-Filled Thermal-Insulation Tiles; High-Performance Polymers Having Low Melt Viscosities; Nonflammable, Hydrophobic Aerogel Composites for Insulation; Front-Side Microstrip Line Feeding a Raised Antenna Patch; Medium-Frequency Pseudonoise Georadar; Facilitating Navigation Through Large Archives; Program for Weibull Analysis of Fatigue Data; Comprehensive Micromechanics-Analysis Code - Version 4.0; Component-Based Visualization System; Software for Engineering Simulations of a Spacecraft; LabVIEW Interface for PCI-SpaceWire Interface Card; Path Following with Slip Compensation for a Mars Rover; International Space Station Electric Power System Performance Code-SPACE; Software for Automation of Real-Time Agents, Version 2; Software for Optimizing Plans Involving Interdependent Goals; Computing Gravitational Fields of Finite-Sized Bodies; Custom Sky-Image Mosaics from NASA's Information Power Grid; ANTLR Tree Grammar Generator and Extensions; Generic Kalman Filter Software; Alignment Stage for a Cryogenic Dilatometer; Rugged Iris Mechanism; Treatments To Produce Stabilized Aluminum Mirrors for Cryogenic Uses; Making AlNx Tunnel Barriers Using a Low-Energy Nitrogen-Ion Beam; Making Wide-IF SIS Mixers with Suspended Metal-Beam Leads; Sol-Gel Glass Holographic Light-Shaping Diffusers; Automated Counting of Particles To Quantify Cleanliness; Phase Correction for GPS Antenna with Nonunique Phase Center; Compact Infrasonic Windscreen; Broadband External-Cavity Diode Laser; High-Efficiency Solar Cells Using Photonic-Bandgap Materials; Generating Solid Models from Topographical Data; Computationally Lightweight Air-Traffic-Control Simulation; Spool Valve for Switching Air Flows Between Two Beds; Partial Model of Insulator/ Insulator Contact Charging; Asymmetric Electrostatic Radiation Shielding for Spacecraft; and Reusable Hybrid Propellant Modules for Outer-Space Transport.

Source record↗
NASA NTRS2006

Automated Antenna Design with Evolutionary Algorithms

Current methods of designing and optimizing antennas by hand are time and labor intensive, and limit complexity. Evolutionary design techniques can overcome these limitations by searching the design space and automatically finding effective solutions. In recent years, evolutionary algorithms have shown great promise in finding practical solutions in large, poorly understood design spaces. In particular, spacecraft antenna design has proven tractable to evolutionary design techniques. Researchers have been investigating evolutionary antenna design and optimization since the early 1990s, and the field has grown in recent years as computer speed has increased and electromagnetic simulators have improved. Two requirements-compliant antennas, one for ST5 and another for TDRS-C, have been automatically designed by evolutionary algorithms. The ST5 antenna is slated to fly this year, and a TDRS-C phased array element has been fabricated and tested. Such automated evolutionary design is enabled by medium-to-high quality simulators and fast modern computers to evaluate computer-generated designs. Evolutionary algorithms automate cut-and-try engineering, substituting automated search though millions of potential designs for intelligent search by engineers through a much smaller number of designs. For evolutionary design, the engineer chooses the evolutionary technique, parameters and the basic form of the antenna, e.g., single wire for ST5 and crossed-element Yagi for TDRS-C. Evolutionary algorithms then search for optimal configurations in the space defined by the engineer. NASA's Space Technology 5 (ST5) mission will launch three small spacecraft to test innovative concepts and technologies. Advanced evolutionary algorithms were used to automatically design antennas for ST5. The combination of wide beamwidth for a circularly-polarized wave and wide impedance bandwidth made for a challenging antenna design problem. From past experience in designing wire antennas, we chose to constrain the evolutionary design to a monopole wire antenna. The results of the runs produced requirements-compliant antennas that were subsequently fabricated and tested. The evolved antenna has a number of advantages with regard to power consumption, fabrication time and complexity, and performance. Lower power requirements result from achieving high gain across a wider range of elevation angles, thus allowing a broader range of angles over which maximum data throughput can be achieved. Since the evolved antenna does not require a phasing circuit, less design and fabrication work is required. In terms of overall work, the evolved antenna required approximately three person-months to design and fabricate whereas the conventional antenna required about five. Furthermore, when the mission was modified and new orbital parameters selected, a redesign of the antenna to new requirements was required. The evolutionary system was rapidly modified and a new antenna evolved in a few weeks. The evolved antenna was shown to be compliant to the ST5 mission requirements. It has an unusual organic looking structure, one that expert antenna designers would not likely produce. This antenna has been tested, baselined and is scheduled to fly this year. In addition to the ST5 antenna, our laboratory has evolved an S-band phased array antenna element design that meets the requirements for NASA's TDRS-C communications satellite scheduled for launch early next decade. A combination of fairly broad bandwidth, high efficiency and circular polarization at high gain made for another challenging design problem. We chose to constrain the evolutionary design to a crossed-element Yagi antenna. The specification called for two types of elements, one for receive only and one for transmit/receive. We were able to evolve a single element design that meets both specifications thereby simplifying the antenna and reducing testing and integration costs. The highest performance antenna found using a getic algorithm and stochastic hill-climbing has been fabricated and tested. Laboratory results correspond well with simulation. Aerospace component design is an expensive and important step in space development. Evolutionary design can make a significant contribution wherever sufficiently fast, accurate and capable software simulators are available. We have demonstrated successful real-world design in the spacecraft antenna domain; and there is good reason to believe that these results could be replicated in other design spaces.

Hornby, Gregory S.↗
DOE OSTI2022

Quantitative Study of Plasmonic Gold Nanostar Geometry Toward Optimal SERS Detection

Abstract Complex shapes of gold nanostars (GNS) have been the major obstacle to the comprehensive understanding of the rich plasmonic phenomena of GNS. We conducted extensive, systematic numerical study of far-field and near-field spectral responses of GNS for varying geometrical parameters (e.g., number of spikes, spike tip angle, and spike-to-core ratio) to elucidate the relationship between the optical property and the geometry of GNS. We found that symmetric configurations of GNS spikes generated both dipole and quadrupole localized surface plasmon (LSP) modes, their hybridization resulted in the final near-field intensity at the spike tips, and there existed a specific GNS geometry that optimized the hybridization and thus the E-field intensity for any given wavelength. From these results, we further identified the shapes of GNS that generated the strongest Surface Enhanced Raman Scattering (SERS) enhancement factors in the visible and NIR spectral range. Hence, our results provide guiding principles in determining the optimal geometry of GNS for SERS applications with any choice of excitation wavelength.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Pressure Response Optimization of an Eddy Current-Driven Flyer Plate Valve for the ITER Shattered Pellet Injection System

One technique for mitigating disruptions in a tokamak is shattered pellet injection (SPI). SPI is a process in which a large solid pellet consisting of deuterium, neon, or argon is desublimated in a pipe gun barsrel and launched downstream. Pellets are shattered just before entering the plasma by an impact with an angled tube. Injection of these materials into the plasma radiates stored thermal energy, limits current decay rates, suppresses the generation of runaway electrons, and dissipates runaway electrons if necessary. A critical element of the SPI system is a fast-acting valve that releases high-pressure gas to dislodge and accelerate pellets directly, or indirectly via a mechanical punch. A prototype valve sized for the ITER SPI system has been designed and fabricated. A pulsed high-voltage power supply energizes the valve’s internal magnetic coil, which induces eddy currents in the adjacent flyer plate resulting in a repulsive force between the flyer plate and the coil. The flyer plate action lifts a valve seat, allowing high-pressure gas to flow from the valve plenum to the downstream (breech) location of the pellet or mechanical punch. All of the valve’s internal components are designed to operate in ITER-level static background magnetic fields. Here, a study was conducted to optimize the downstream pressure response for a range of valve sizes and operating pressures. In particular, the study analyzes the breech pressure response associated with varying plenum pressures as well as varying breech volumes. A computational fluid dynamics simulation was built in STAR-CCM+ and validated against data from laboratory experiments. The resulting simulation outputs, in the form of downstream responses for a variety of initial plenum pressures and breech volumes, will be used as a complement to experimental data to ensure the pressure pulse is suitable for pellet survivability. These data, combined with studies on pellet shear strength and shock response, will be applied to optimization of overall operating parameters of the ITER SPI system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Minimax confidence intervals in geomagnetism

The present paper uses theory of Donoho (1989) to find lower bounds on the lengths of optimally short fixed-length confidence intervals (minimax confidence intervals) for Gauss coefficients of the field of degree 1-12 using the heat flow constraint. The bounds on optimal minimax intervals are about 40 percent shorter than Backus' intervals: no procedure for producing fixed-length confidence intervals, linear or nonlinear, can give intervals shorter than about 60 percent the length of Backus' in this problem. While both methods rigorously account for the fact that core field models are infinite-dimensional, the application of the techniques to the geomagnetic problem involves approximations and counterfactual assumptions about the data errors, and so these results are likely to be extremely optimistic estimates of the actual uncertainty in Gauss coefficients.

Stark, Philip B.↗