Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solution regularity”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Genetic Evolution of Shape-Altering Programs for Supersonic Aerodynamics

Two constrained shape optimization problems relevant to aerodynamics are solved by genetic programming, in which a population of computer programs evolves automatically under pressure of fitness-driven reproduction and genetic crossover. Known optimal solutions are recovered using a small, naive set of elementary operations. Effectiveness is improved through use of automatically defined functions, especially when one of them is capable of a variable number of iterations, even though the test problems lack obvious exploitable regularities. An attempt at evolving new elementary operations was only partially successful.

Kennelly, Robert A., Jr.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-13664-DND

The safety of aerospace vehicles is largely dependent on the ability of modern non-destructive evaluation (NDE) tools to accurately detect structural damage before a critical flaw size is reached. However, existing NDE technologies are inherently limited by the physical response of the materials being inspected making the detection of small cracks or pre-crack damage difficult. One innovative solution to this problem is to create a multifunctional metallic material that can be used in structural applications and contains second phase sensory particles that significantly enhance the ability of conventional NDE techniques to detect incipient damage during use and at regularly scheduled inspections. Ferromagnetic shape-memory alloys (FSMAs) are an ideal material for use as this second phase material as they undergo a uniform and repeatable change in both magnetic properties and crystallographic structure when strained. These changes are more readily detected than small cracks, thereby, allowing for enhanced detection of damage by conventional NDE techniques. In this study, a multifunctional metallic material was produced by embedding the sensory material particles within an aluminum alloy to form a sensory alloy. The NDE response of the FSMA and the sensory alloy during tension/compression and fatigue loading have been investigated. These results suggest that sensory alloys can be utilized for improved on-board structural health monitoring and to improve the accuracy and reduce time for ground-based inspection.

T. A. Wallace↗
NASA NTRSDate not supplied

Rational Design of Nanoplasmonic Array Geometries for Biosensing

Background: Molecular diagnostics provide early and accurate diagnosis, which is essential for the prevention and treatment of infectious as well as chronic diseases. These tests are designed to detect disease-specific bioanalytes such as nucleic acid (DNA or RNA) or protein (antigens, antibodies) biomarkers. In the context of infectious disease diagnosis, nucleic acid-based detection methods are known to provide more specific and sensitive results. Here, the presence of a unique sequence belonging to the pathogenic genomic material is targeted to identify species, organism, genera and/or antimicrobial resistant gene markers. The majority of the common nucleic acid based diagnostic techniques require amplification (polymerase chain reaction, isothermal amplification etc.) of the pathogenic genetic material prior to detection impacting diagnostic speed, complexity, and cost thereby limiting ease of use. Thus, the development of simplified nucleic acid-based diagnostics that can be even used in resource-poor settings may hugely benefit patients across the globe. Nanopath is a molecular diagnostics company utilizing a solid-state nanosensor to enable sequence-specific detection of target nucleic acids without the need of amplification. These nanostructures enable ultra-sensitive biomarker detection using geometric, feature-dependent properties highly dependent on the local dielectric environment, allowing them to be sensitive to low concentration binding events. This paper describes an application of this approach to provide highly relevant clinical information within a single doctor’s office visit. Intro: The Nanopath team is in collaboration with NASA (National Aeronautics and Space Administration) and NIST (National Institute of Standards and Technology) to push the bounds of the fundamental physics associated with their biosensing platform. The ability of metals to support electromagnetic surface waves gives rise to surface plasmons when optically illuminated. This property, and its strong sensitivity to changes in the local refractive index, allows for the use of metal nanoparticles as ultra-sensitive transducers. In prior work by members of this team, ensembles of randomly oriented nanoparticles (i.e., colloidal nanorods dispersed on chip) were employed for sequence-specific nucleic acid sensing (1-3). While these particle sensors have the advantage of rapid fabrication, they suffer from low sensitivity and quality factor due to the random particle dispersity. In contrast, in this study we employ ordered array nanoparticle ensembles which can be used to improve sensor sensitivity and figure-of-merit. Study Methods Overview: In this talk, we detail the results of sensing experiments and computational simulations to outline a rational design of the structure of these plasmonic nanoparticle arrays for biomolecular sensing. Through simulation and experiment, we iteratively tailor nanostructure dimension to provide high quality signal and large resonance shifts upon modeled nucleic acid binding. In particular, full-wave electromagnetic simulations were conducted using Lumerical photonic simulation software in which periodic boundary conditions were applied in the x- and y- dimensions for each of the nanoplasmonic sensor geometries. To simulate the resonance response to changes in the bulk solution in contact with the sensor surface, the refractive index of the surrounding media was changed appropriately. Nucleic acid hybridization events were modeled using either using spherical structures approximating the relevant radius of genomic material as estimated by polymer models, or as conformal layers with the known refractive indices for nucleic acids. On the basis of initial simulations, nanosensors were fabricated using traditional electron-beam lithography protocols at NIST. To evaluate consensus between simulations and experiments, bulk sensing experiments were carried out in which the resonance peaks were obtained by submerging the sensors in refractive index standards. Key nanosensor characteristics including resonance peak locations, resonance peak shifts as a function of refractive index, and figure of merit (FOM) of extinction curves were examined between the experimental and simulation results prior to proceeding with simulations on additional geometries and more complex solution conditions, and further device fabrication. This iterative process is repeated toward a rational design of nanoplasmonic array geometries for biosensing optimizing response for targeted disease detection. In summary, this study puts forth a methodology for rational design and characterization of regularly spaced nanoparticle arrays for optics-based biosensing. The results of this study will allow for more informed design of nanostructure geometries towards sequence-specific nucleic acid detection. These improved designs have the potential to improve clinical sensitivity and limit-of-detection across disease indication.

sensor↗
NASA NTRSDate not supplied

Total Variation Majorization Minimization (TV-MM) Approach to Radiometer Brightness Temperature Gridding and Reconstruction

This paper presents the implementation of an algorithm to enhance the image resolution of the Earth's surface brightness temperature (T B ) data measured by radiometers such as the one onboard of the Soil Moisture Active Passive (SMAP) mission. A key step in radiometer T B processing is the conversion of the swath-based calibrated antenna temperature (T A ) measurements to the Level 3 Earth-centered grid. The simplest algorithm to transform this data from swath to gridded format is called drop-in-the-bucket which simply averages surrounding noisy T A samples to form a T B value at the gridded location. This method reduces noise, however produces low resolution products. To obtain a higher resolution product, SMAP uses other techniques such the Backus-Gilbert (BG) algorithm, which is the conventional method used in microwave radiometry. Although this method performs the required interpolation, it is not effective in denoising and removing blurring effects due to antenna filtering of the radiometer image data. Our motivation for this development is to further improve the resolution through post-processing of the radiometer T B image, a highly cost-effective method of image enhancement. The approach adapted in this work is based on the minimization of the Total Variation (TV) regularized objective function that is used extensively in solving general ill-posed linear inverse problems in image processing. Since the TV-based objective function is convex but not everywhere differentiable, there exists many numerical algorithms that can estimate the solution and the one selected for this work is called Majorization- Minimization (MM). By applying this algorithm, simulation experiments were performed based on synthetic data from the Geophysical model as well as real SMAP data to demonstrate the effectiveness of the technique. Results were then compared against the BG method.

Wing Lee↗
NASA NTRSDate not supplied

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗
DOE OSTI2020

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

Abstract We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle‐based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid‐based advection in other regions of the flow. A novel Backward Semi‐Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C 1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B‐spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut‐cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

Gagniere, S.↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
DOE OSTI2020

In-situ Detection of Glovebox Glove Degradation Prior to Glove Failure; Effects on Safety, Waste, and Operational Costs - 20402

Glovebox glove pressure decay leak testing and analysis of the data can greatly improve glovebox safety, minimize Transuranic (TRU) glove waste, and minimize operational cost. It is well known, the weakest point of containment on a glovebox is the glove. Mitigating unplanned openings in gloves is critical to minimizing operational and safety costs in glovebox operations. Mitigating unplanned glove openings due to glove failures will be discussed in this paper. The lack of an engineered solution to determine a gloves operational life in nuclear operations, has lead to use of theoretical and manual subjective methods to determine the life and safety of a glovebox glove. Whether the glove is inspected visually prior to use, or gloves are changed regularly to theoretically avoid failure, both the operators PPE and the room are being exposed to contamination, or un-necessary amounts of TRU glove waste are being generated. Millions of dollars yearly in operational costs are spent on glove failures due to loss of production, incident analysis, regulatory audits, clean up, and paperwork. In a nuclear application, a glove failure could contaminate an operator and laboratory, shut down the operation for weeks, potentially create a regulatory audit, and potentially create a media frenzy; the damages to the organization can be astronomical. Elimination of glove failures is possible by tracking glove material degradation and setting limits to allow glove change when it becomes necessary, prior to glove failure. Analytical pressure decay leak testing allows the detection of material degradation, and in turn the ability to limit operational glove failures. A German based company called MK Versuchsanlagen, e.K., has developed an advanced Glove Integrity Testing System. The system, with its use of proprietary RFID and special software technology, is unique in its capabilities. The system is capable to perform highly accurate regular glove testing on any size glovebox line in minimal time. The system records and can analyze a tremendous amount of system data that in turn can determine, for example, a safe glove change time prior to a glove material failure. This paper will show how an advanced Glove Integrity Testing System can detect glove material degradation and help determine a safe change point prior to glove failure. Pressure decay curves of new gloves and recorded effects of accelerated aging on the glove over time will be shown. The use of this technology in nuclear facilities can greatly improve glovebox operational safety, minimize glovebox glove TRU waste, and save organizations tremendous costs in downtime, clean up, documentation, and potential regulatory review. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS2024

Mars Climate Monitoring Mission

For future missions to Mars, Nasa wants a better understanding of the regular weather patterns on Mars. Current models of martian weather are not up to the task of predicting weather that could impair future martian prospects. To improve our models, we need accurate data, measured directly from orbiters or surface stations, like rovers or probes. One solution is to send a web of permanent surface weather stations to various locations on the surface, in order to get accurate data about large-scale martian weather patterns. Such data could be used to improve our models which could greatly aid in improving the safety of future exploration. Such a mission, though, would have countless moving parts, from launch till landing. We created this short animation to demonstrate how such a mission might be carried out, what it might tell us, and how that information could prove critically useful for future martian exploration, including human missions to the surface.

Mars↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2021

Non-Wilsonian ultraviolet completion via transseries

We study some of the implications for the perturbative renormalization program when augmented with the Borel–Ecalle resummation. We show the emergence of a new kind of nonperturbative fixed point for the scalar [Formula: see text] model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cutoff, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel–Laplace resummation of the renormalons in nonasymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.

Physics↗
DOE OSTI2023

Refining Processing Engines from SAPHIRE: Initialization of Fault Tree/Event Tree Solver

SAPHIRE has been extensively employed for over 35 years to model risk-important systems and quantify risk models. As a well-established and thoroughly documented Probabilistic Risk Assessment (PRA) tool, SAPHIRE has continuously tracked computational trends and received regular updates. Despite its ongoing evolution, there remains a need for further enhancements, particularly in dealing with the quantification of exceptionally large models. These improvements could take the form of algorithmic advancements, harnessing the power of parallel computing, and exploring the potential benefits of cloud computing solutions. Considering these aspirations, the notion of a remote solve option was introduced and subsequently evolved into a dedicated project within the SAPHIRE development team. A significant outcome of this initiative is SAPHSOLVE, an engine extracted from the SageRisk API designed specifically for remote solving capabilities. The ongoing project is nearing its culmination, marked by a series of discoveries that have brought undocumented aspects to light. Among these revelations is the intricacy of the input and output format for the SAPHSOLVE engine. This document serves the crucial purpose of meticulously delineating the precise formats for both input and output, as they form an indispensable foundation. The importance of documenting these formats cannot be overstated, as it is a pivotal step in facilitating rigorous testing and comparison. Whether it involves scrutinizing SAPHSOLVE results against those of the internal integrated solver or other external solvers, the ability to construct models or transform existing ones into a compatible SAPHSOLVE format is imperative. Chapter 1 offers a succinct introduction to both SAPHIRE and SAPHSOLVE, followed by Chapter 2 which outlines the roadmap for enhancing SAPHSOLVE. The core of this report is Chapter 3, which intricately elucidates the intricacies of the input and output file formats. To provide a tangible illustration of these formats, a rudimentary example has been compiled and is available in Appendix. SAPHSOLVE represents a novel external solving mechanism developed by the SAPHIRE team, although it has not yet reached the full spectrum of capabilities possessed by SAPHIRE's internal solver. However, the SAPHIRE team has set a comprehensive course for incorporating the functionalities of SAPHSOLVE. A comprehensive outlook on the future of SAPHSOLVE is expounded upon in Chapter 4.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems

We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

The sensitivity of various mode sets for probing differential rotation shear zones

The potential of future data sets from global oscillations network group (GONG) and solar oscillations investigation (SOI) for resolving long-lived azimuthal jets and shearing flows, is investigated. Various artificial data sets are constructed, containing noise resembling that of a one-year observation run. These are inverted using a two dimensional regularized least squares inversion. The ability of this method to form well localized averages of the rotation rate, as measured by the averaging kernels, is investigated using an extensive mode set and subsets. It is shown that it is possible to keep the noise in the solution down to a few nHz in much of the solar interior, while obtaining a reasonable resolution for a GONG-like data set. At low latitudes in the middle of the convection zone, an angular resolution of less than 10 deg and a radial resolution of about 0.04 solar radii, are obtained. The averaging kernels depend on the mode set, and a reduction in the number of modes tends to introduce small-scale near surface structures into the averaging kernels which would adversely affect the inferred rotation rate.

Christensen-Dalsgaard, Joergen↗
NASA NTRS2004

Unique Approaches to Analysis of Time-Variable Gravity from GRACE

We have developed an innovative analysis strategy for analysis of GRACE data. We have developed a capability to recover local/regional gravity changes using non-global functional representations (Le. surface anomalies vs. global spherical harmonics) h m the GRACE data. Our approach can take regularly or irregularly shaped regions, populate them with surface anomaly blocks of suitable area and solve for the resulting mass flux with respect to a mean field. The surface mass or gravity anomalies benefit from the application of spatial and temporal constraints to add stability to the solution. In this paper we discuss the analysis of four months of GRACE Level 1B data (accelerometry, intersatellite data, attitude information and precise orbits) from July to October 2003, recently released to the GRACE Science Team. We compare and contrast this local approach to gravity recovery, with the more conventional approach using global spherical harmonics. We review simulations of this technique which allow us to pinpoint optimum strategies for applications of this local gravity recovery approach.

Lemoine, Frank G.↗
DOE OSTI2023

Peculiarities of beta functions in sigma models

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in β functions in supersymmetric Yang-Mills theories.

Sigma Models↗
NASA NTRS1988

Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor

A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.

Lim, Joon W.↗