Results for “beyond standard model” — Page 5

NASA NTRS1992

Independent Constituents in Observatory Time Series in Characterizing the Secular Variation

By an ansatz of a finite set of N superimposed oscillations, observatory time series are fitted. This start model is optimized for the independence of the used 2N-dimensional functional system as a criterion. Here, the contributions of each of the dimensions to the volume of the corresponding 2N-dimensional parallelpiped of the functional space is to be evaluated. Independence and an equal standard for the constituents are achieved by the optimizing procedure varying the start values of frequencies in the fitting ansatz when quotients of successively constructed Gram-determinants are beyond a definite threshold and of nearly the same numerical value. Results for globally distributed observatories characterize the secular variation.

Webers, W.↗

NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗

NASA NTRS2010

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.

Lane, John E.↗

NASA NTRSDate not supplied

Enabling Interoperability in Earth System Digital Twins (ESDT): Integrating Observations, Models, and AI for Actionable Insights Through NASA'S Intelligent Systems Technology Program

NASA’s Intelligent Systems Technology Program (IST) is driving a paradigm shift in Earth science through the development of Earth System Digital Twins (ESDT). These integrated information systems create a dynamic "digital replica" of the Earth by harmonizing continuous, multi-source observations with high-fidelity models and state-of-the-art artificial intelligence (AI) that enable “What now?”, “What next?”, and “What if?” scenario building. These scenarios are reflected in NASA IST’s series of ESDTs, from the Coastal Zone Digital Twin that integrates complex data on the current state of the Chesapeake Bay to the Terrestrial Environmental Rapid-Replication and Assimilation Hydrometeorological (TerraHydro) AI-based ESDT that forecasts water movement across Earth’s surface, to the Agriculture Land Information System (AgLIS) which can be used to assess optimal planting dates and crop yield estimates. By bridging the gap between vast data archives and actionable insights, these projects enable a system-of-systems approach to understanding complex, interacting Earth processes. This poster will highlight recent innovations and future directions from NASA’s ESDT initiatives: Continuous Data Assimilation & Multi-Source Fusion. A core requirement of the ESDT work is the transition from static models to dynamic "living" replicas. This involves creating frameworks for the continual assimilation of near-real-time data from uncoordinated, heterogeneous sources, including satellite observations and airborne assets, and ground-based Internet of Things (IoT) sensors. These systems link design, operational status, and environmental data, ensuring the digital twin accurately reflects the current state of the physical Earth system. High-Fidelity Hybrid Modeling & Computational Acceleration to enable interactive "what-if" explorations, programs are moving beyond traditional, slow physical solvers by developing fast surrogate machine learning models and Deep Generative Models (DGMs). These hybrid approaches use neural networks to emulate complex physics, such as cloud feedback or ocean dynamics, at a fraction of the original computing cost, often leveraging advanced hardware like Graphics Processing Units (GPUs) to achieve the necessary scale. Federated Ecosystems & Interoperable Frameworks rather than building isolated tools, NASA IST is moving toward federated ESDTs and reusable analytic collaborative frameworks. This theme focuses on interoperability standards and common ontologies that allow specialized digital twins to interact and share data. This system-of-systems architecture supports multi-discipline investigations, such as analyzing how upstream watershed changes impact downstream urban flooding or how wildfire emissions affect regional air quality. By leveraging these advancements, ESDTs empower researchers and decision-makers to conduct real-time analysis and run complex hypothetical scenarios, ultimately improving our understanding of Earth’s evolving systems and informing critical real-world applications.

Earth System↗

NASA NTRS1991

Metal opacities and convective core overshooting in Population I stars

New stellar opacities computed by Rogers and Iglesias are found to lead to revised evolutionary models for stars of intermediate-to-high mass that show remarkably close agreement with observed stars, under otherwise standard physical assumptions. Most or all of the earlier discrepancies, except for the problem of predicted apsidal motion constants that are perhaps still too large, appear to have been resolved by using these new opacities with their increased metal line contribution. Thus, the implied interior metallicity of massive stars in the solar neighborhood now becomes 'normal'. Furthermore, the effective distance of convective overshooting beyond the classical convective core boundary is confirmed to be small and probably less than 0.2 times the local pressure scale height.

Stothers, Richard B.↗

NASA NTRS2014

Application and Evaluation of Control Modes for Risk-Based Engine Performance Enhancements

The engine control system for civil transport aircraft imposes operational limits on the propulsion system to ensure compliance with safety standards. However, during certain emergency situations, aircraft survivability may benefit from engine performance beyond its normal limits despite the increased risk of failure. Accordingly, control modes were developed to improve the maximum thrust output and responsiveness of a generic high-bypass turbofan engine. The algorithms were designed such that the enhanced performance would always constitute an elevation in failure risk to a consistent predefined likelihood. This paper presents an application of these risk-based control modes to a combined engine/aircraft model. Through computer and piloted simulation tests, the aim is to present a notional implementation of these modes, evaluate their effects on a generic airframe, and demonstrate their usefulness during emergency flight situations. Results show that minimal control effort is required to compensate for the changes in flight dynamics due to control mode activation. The benefits gained from enhanced engine performance for various runway incursion scenarios are investigated. Finally, the control modes are shown to protect against potential instabilities during propulsion-only flight where all aircraft control surfaces are inoperable.

emergency operation↗

NASA NTRS2014

Application and Evaluation of Control Modes for Risk-Based Engine Performance Enhancements

The engine control system for civil transport aircraft imposes operational limits on the propulsion system to ensure compliance with safety standards. However, during certain emergency situations, aircraft survivability may benefit from engine performance beyond its normal limits despite the increased risk of failure. Accordingly, control modes were developed to improve the maximum thrust output and responsiveness of a generic high-bypass turbofan engine. The algorithms were designed such that the enhanced performance would always constitute an elevation in failure risk to a consistent predefined likelihood. This paper presents an application of these risk-based control modes to a combined engine/aircraft model. Through computer and piloted simulation tests, the aim is to present a notional implementation of these modes, evaluate their effects on a generic airframe, and demonstrate their usefulness during emergency flight situations. Results show that minimal control effort is required to compensate for the changes in flight dynamics due to control mode activation. The benefits gained from enhanced engine performance for various runway incursion scenarios are investigated. Finally, the control modes are shown to protect against potential instabilities during propulsion-only flight where all aircraft control surfaces are inoperable.

aircraft engine performance↗

NASA NTRS2015

Application and Evaluation of Control Modes for Risk-Based Engine Performance Enhancements

The engine control system for civil transport aircraft imposes operational limits on the propulsion system to ensure compliance with safety standards. However, during certain emergency situations, aircraft survivability may benefit from engine performance beyond its normal limits despite the increased risk of failure. Accordingly, control modes were developed to improve the maximum thrust output and responsiveness of a generic high-bypass turbofan engine. The algorithms were designed such that the enhanced performance would always constitute an elevation in failure risk to a consistent predefined likelihood. This paper presents an application of these risk-based control modes to a combined engine/aircraft model. Through computer and piloted simulation tests, the aim is to present a notional implementation of these modes, evaluate their effects on a generic airframe, and demonstrate their usefulness during emergency flight situations. Results show that minimal control effort is required to compensate for the changes in flight dynamics due to control mode activation. The benefits gained from enhanced engine performance for various runway incursion scenarios are investigated. Finally, the control modes are shown to protect against potential instabilities during propulsion-only flight where all aircraft control surfaces are inoperable.

emergency operation↗

NASA NTRSDate not supplied

Enabling Biological Discovery Through Biospecimen Sharing: The Nasa Biological Institutional Scientific Collection

Understanding biological impacts from spaceflight hazards and the subsequent development of countermeasures are a high priority to enable humanity to venture back to the Moon, and then to Mars and beyond. Experiments have been conducted with model organisms flown to space and analogous investigations terrestrially, to identify biological mechanistic impacts from spaceflight hazards and to develop mitigation countermeasures, thus contributing towards basic and applied science goals. However, sending organisms into space is a costly endeavor. To maximize scientific return, all biospecimens not required by spaceflight-relevant Principal Investigators are harvested, preserved, and archived in the NASA Biological Institutional Scientific Collection (NBISC). Biospecimens are collected and preserved according to well-established standard operating procedures to maintain scientific quality and are available on-request by the international scientific community. NBISC currently stores over 32,000 biospecimens from Shuttle, International Space Station, and ground-based space analog investigations. Tissue sharing has resulted in at least 33 publications since 2011 and 51 requests since 2016. Many requests for NBISC biospecimens come from first-time investigators who subsequently submit grants as their point-of-entry into the field of spaceflight biology and health. The NBISC biorepository is part of the NASA ‘Open Science for Life in Space’ collaborative group of projects, which includes NASA Genelab, the Space Biology Program’s Biospecimen Sharing Program, Physical Sciences Informatics, and the Ames Life Sciences Data Archive. NBISC biospecimens have been awarded to NASA Genelab, who then generated various open access science ‘omics datasets through the GeneLab Sample Processing laboratory, with resulting data widely used for biological study. Other NBISC biospecimen awards have led to studies on fecal microbiome analysis, DNA damage analysis using single-cell DNA sequencing, enzymatic-pathway identification involved in spaceflight muscle atrophy, and characterization of ocular morphological changes. Of note, NBISC is expanded to include a new Space Microbial Culture Collection (SMCC) for the collection, identification, documentation, long-term preservation, and distribution of space-related microbial isolates.

Biospecimens↗

NASA NTRS2000

XMM-Newton Observations of the Cluster of Galaxies Sersic 159-03

The cluster of galaxies Sersic 159-03 was observed with the XMM-Newton X-ray observatory as part of the Guaranteed Time program. X-ray spectra taken with the EPIC and RGS instruments show no evidence for the strong cooling flow derived from previous X-ray observations. There is a significant lack of cool gas below 1.5 keV as compared to standard isobaric cooling flow models. While the oxygen is distributed more or less uniformly over the cluster, iron shows a strong concentration in the center of the cluster, slightly offset from the brightness center but within the central cD galaxy. This points to enhanced type Ia supernova activity in the center of the cluster. There is also an elongated iron-rich structure ex- tending to the east of the cluster, showing the inhomogeneity of the iron distribution. Finally, the temperature drops rapidly beyond 4' from the cluster center.

Kaastra, J. S.↗

NASA NTRS2014

Tidal Heating in Multilayered Terrestrial Exoplanets

The internal pattern and overall magnitude of tidal heating for spin-synchronous terrestrial exoplanets from 1 to 2.5 R(sub E) is investigated using a propagator matrix method for a variety of layer structures. Particular attention is paid to ice-silicate hybrid super-Earths, where a significant ice mantle is modeled to rest atop an iron-silicate core, and may or may not contain a liquid water ocean. We find multilayer modeling often increases tidal dissipation relative to a homogeneous model, across multiple orbital periods, due to the ability to include smaller volume low viscosity regions, and the added flexure allowed by liquid layers. Gradations in parameters with depth are explored, such as allowed by the Preliminary Earth Reference Model. For ice-silicate hybrid worlds, dramatically greater dissipation is possible beyond the case of a silicate mantle only, allowing non-negligible tidal activity to extend to greater orbital periods than previously predicted. Surface patterns of tidal heating are found to potentially be useful for distinguishing internal structure. The influence of ice mantle depth and water ocean size and position are shown for a range of forcing frequencies. Rates of orbital circularization are found to be 10-100 times faster than standard predictions for Earth-analog planets when interiors are moderately warmer than the modern Earth, as well as for a diverse range of ice-silicate hybrid super-Earths. Circularization rates are shown to be significantly longer for planets with layers equivalent to an ocean-free modern Earth, as well as for planets with high fractions of either ice or silicate melting.

celestial mechanics↗

NASA NTRS1994

Beyond maximum entropy: Fractal Pixon-based image reconstruction

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.

Puetter, Richard C.↗

NASA NTRS1992

Stellar evolution in blue populous clusters of the Small Magellanic Cloud and the problems of envelope semiconvection and convective core overshooting

New theoretical evolutionary sequences of models for stars with low metallicities, appropriate to the Small Magellanic Cloud, are derived with both standard Cox-Stewart opacities and the new Rogers-Iglesias opacities. Only those sequences with little or no convective core overshooting are found to be capable of reproducing the two most critical observations: the maximum effective temperature displayed by the hot evolved stars and the difference between the average bolometric magnitudes of the hot and cool evolved stars. An upper limit to the ratio of the mean overshoot distance beyond the classical Schwarzschild core boundary to the local pressure scale height is set at 0.2. It is inferred from the frequency of cool supergiants in NGC 330 that the Ledoux criterion, rather than the Schwarzschild criterion, for convection and semiconvection in the envelopes of massive stars is strongly favored. Residuals from the fitting for NGC 330 suggest the possibility of fast interior rotation in the stars of this cluster. NGC 330 and NGC 458 have ages of about 3 x 10 exp 7 and about 1 x 10 exp 8 yr, respectively.

Stothers, Richard B.↗

NASA NTRS2024

Additively Manufactured Plastic Plasma Spectrometer

We report results in development and testing of a low resource top hat electrostatic analyzer (ESA) for space plasma measurements. This device has been additively manufactured (3D-printed) using fused deposition modeling. The classic top hat design is composed of four plastic pieces, without any surface coatings. The three conducting electrodes are printed from carbon nanotube infused polyether ether ketone (CNT-PEEK). The fourth piece, an insulating electrode support, uses pure PEEK. This ESA is designed to detect electrons in space from 10eV up to 30 keV. We demonstrate that the printed CNT-PEEK is sufficiently electrically conductive to support the fast high voltage slewing often required for high time resolution measurements. The plastic ESA has been successfully vibrated beyond standard pre-flight levels, tested under keV electron beam illumination over a wide range of temperatures, and tested under UV illumination, simulating the solar Ly-α flux. In comparison with an identical machined aluminum ESA, our CNT-PEEK ESA provides nominal energy/angle band passes, closely matching simulation. These band passes imply minimal impact from surface charging at beam energies of 2-3 keV, although more investigation is needed. We also find that the CNT-PEEK ESA provides far superior out-of-band electron rejection and UV photon rejection compared to the machined aluminum ESA. We do not detect any problems with trapped gases or outgassing. This development offers potential for significant mass savings, implementation of otherwise unattainable geometric configurations, and dramatic simplification in manufacturing and assembly processes required for development of space plasma instruments.

Quetzal Larrick↗

NASA NTRSDate not supplied

NextSTEP Appendix A Modular ECLSS Effort Lessons Learned

NASA’s Artemis program provides the first steps for earth-independent exploration starting with crewed habitats in cislunar space and progressing toward crewed landings on the lunar surface that will prepare systems and crews for the exploration of Mars. The Next Space Technology for Exploration Partnerships (NextSTEP) is a public-private partnership model that facilitates commercial development of deep space exploration capabilities in support of more extensive human spaceflight missions in and beyond cislunar space. NASA issued the original NextSTEP Broad Agency Announcement (BAA) to U.S. industry in late 2014 and issued the second BAA (NextSTEP-2) in April 2016. The first appendix under NextSTEP-2, Appendix A, focused on developing deep space habitation concepts, engineering design and development, and risk reduction efforts leading to a habitation capability in cislunar space. NASA solicited concepts to develop and refine the evolvable, modular architecture, functional allocation options, standards, and common interfaces required to enable interoperability of the aggregate system to provide long duration deep space transit habitation, specifically enhancements and testing of deep space Environmental Control and Life Support Systems (ECLSS). Collins Aerospace, formerly UTC Aerospace Systems (UTAS), was awarded a Phase 1 and subsequent Phase 2 contract to “develop concepts that group ECLS systems into logical modules maximizing the use of common components and the development of unique methods and design concepts that support in-flight maintenance and repair for future exploration systems.” This paper summarizes the work accomplished under this effort, the lessons that can be applied to development of forthcoming habitation elements, and the gaps remaining to achieve a more resilient, maintainable, repairable and adaptable system capable of installation on a wide variety of habitat platforms. A primary accomplishment of this effort is the development and maturation of a modular palletization concept to enable standard rack interfaces, post-launch outfitting, and decoupling of structural supports that withstand launch environments from those needed for lower on-orbit loads in order to reduce installed mass and repurposing of panels within the habitat. In the course of the effort, Collins assessed numerous architecture trades, including the use of condensing and noncondensing heat exchangers, the ability of modular units to accommodate various habitat volumes and thermal loading, and the most appropriate order of and timing of delivery of regenerative ECLSS hardware to orbital habitats. In addition to the modularity of hardware elements, Collins developed software approaches for distributed/modular command, control, and communication systems and innovative Bayesian fault detection and isolation techniques. Finally, the effort explored advanced maintainability and supportability concepts including the definition of maintenance units (MUs) in place of the traditional Orbital Replacement Units (ORUs), increasing parts commonality to reduce the number and type of spare parts, the use of augmented reality to guide crews during maintenance and repair procedures, and how crews would prepare for and recover from long durations of habitat dormancy. Now that the NextSTEP Modular ECLSS effort has come to a close, it’s important to identify the lessons learned and where they can be leveraged to improve NASA’s broader program of ECLSS technology development and demonstration and ultimately how they can increase the performance of future surface and orbital habitats.

NextSTEP↗

NASA NTRSDate not supplied

NextSTEP Appendix A Modular ECLSS Effort Lessons Learned

NASA’s Artemis program provides the first steps for earth-independent exploration starting with crewed habitats in cislunar space and progressing toward crewed landings on the lunar surface that will prepare systems and crews for the exploration of Mars. The Next Space Technology for Exploration Partnerships (NextSTEP) is a public-private partnership model that facilitates commercial development of deep space exploration capabilities in support of more extensive human spaceflight missions in and beyond cislunar space. NASA issued the original NextSTEP Broad Agency Announcement (BAA) to U.S. industry in late 2014 and issued the second BAA (NextSTEP-2) in April 2016. The first appendix under NextSTEP-2, Appendix A, focused on developing deep space habitation concepts, engineering design and development, and risk reduction efforts leading to a habitation capability in cislunar space. NASA solicited concepts to develop and refine the evolvable, modular architecture, functional allocation options, standards, and common interfaces required to enable interoperability of the aggregate system to provide long duration deep space transit habitation, specifically enhancements and testing of deep space Environmental Control and Life Support Systems (ECLSS). Collins Aerospace, formerly UTC Aerospace Systems (UTAS), was awarded a Phase 1 and subsequent Phase 2 contract to “develop concepts that group ECLS systems into logical modules maximizing the use of common components and the development of unique methods and design concepts that support in-flight maintenance and repair for future exploration systems.” This paper summarizes the work accomplished under this effort, the lessons that can be applied to development of forthcoming habitation elements, and the gaps remaining to achieve a more resilient, maintainable, repairable and adaptable system capable of installation on a wide variety of habitat platforms. A primary accomplishment of this effort is the development and maturation of a modular palletization concept to enable standard rack interfaces, post-launch outfitting, and decoupling of structural supports that withstand launch environments from those needed for lower on-orbit loads in order to reduce installed mass and repurposing of panels within the habitat. In the course of the effort, Collins assessed numerous architecture trades, including the use of condensing and noncondensing heat exchangers, the ability of modular units to accommodate various habitat volumes and thermal loading, and the most appropriate order of and timing of delivery of regenerative ECLSS hardware to orbital habitats. In addition to the modularity of hardware elements, Collins developed software approaches for distributed/modular command, control, and communication systems and innovative Bayesian fault detection and isolation techniques. Finally, the effort explored advanced maintainability and supportability concepts including the definition of maintenance units (MUs) in place of the traditional Orbital Replacement Units (ORUs), increasing parts commonality to reduce the number and type of spare parts, the use of augmented reality to guide crews during maintenance and repair procedures, and how crews would prepare for and recover from long durations of habitat dormancy. Now that the NextSTEP Modular ECLSS effort has come to a close, it’s important to identify the lessons learned and where they can be leveraged to improve NASA’s broader program of ECLSS technology development and demonstration and ultimately how they can increase the performance of future surface and orbital habitats.

NextSTEP↗

NASA NTRS1989

Scattering by a two dimensional groove in a ground plane

Higher order boundary conditions involve derivatives of the fields beyond the first and were recently shown to be more effective than traditional first order conditions in modeling dielectric coatings and layers. In this report an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented. Deficiencies of such higher order boundary conditions are addressed and a correction is proposed for the present case. As part of the process of examining and improving the accuracy of the proposed generalized boundary conditions, an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition.

Barkeshli, K.↗

NASA NTRS1990

TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions

Higher order boundary conditions involve derivatives of the fields beyond the first and were recently shown to be more effective than traditional first order conditions in modeling dielectric coatings and layers. In this report an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented. Deficiencies of such higher-order boundary conditions are addressed and a correction is proposed for the present case. As part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions, an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition.

Barkeshli, Kasra↗