Search NASA⌕ Search

SEARCH · Search NASA

Results for “Spatial Behavior”

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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Satellite-Derived Management Zones

The term "satellite-derived management zones" (SAMZ) denotes agricultural management zones that are subdivisions of large fields and that are derived from images of the fields acquired by instruments aboard Earth-orbiting satellites during approximately the past 15 years. "SAMZ" also denotes the methodology and the software that implements the methodology for creating such zones. The SAMZ approach is one of several products of continuing efforts to realize a concept of precision agriculture, which involves optimal variations in seeding, in application of chemicals, and in irrigation, plus decisions to farm or not to farm certain portions of fields, all in an effort to maximize profitability in view of spatial and temporal variations in the growth and health of crops, and in the chemical and physical conditions of soils. As used here, "management zone" signifies, more precisely, a subdivision of a field within which the crop-production behavior is regarded as homogeneous. From the perspective of precision agriculture, management zones are the smallest subdivisions between which the seeding, application of chemicals, and other management parameters are to be varied. In the SAMZ approach, the main sources of data are the archives of satellite imagery that have been collected over the years for diverse purposes. One of the main advantages afforded by the SAMZ approach is that the data in these archives can be reused for purposes of precision agriculture at low cost. De facto, these archives contain information on all sources of variability within a field, including weather, crop types, crop management, soil types, and water drainage patterns. The SAMZ methodology involves the establishment of a Web-based interface based on an algorithm that generates management zones automatically and quickly from archival satellite image data in response to requests from farmers. A farmer can make a request by either uploading data describing a field boundary to the Web site or else drawing the boundary on a reference image. Hence, a farmer can start to engage in precision farming shortly after gaining access to the Web site, without the need for incurring the high costs of conventional precision-agriculture data-collection practices that include collecting soil samples, mapping electrical conductivity of soil, and compiling multiyear crop-yield data. Given the boundary of a field, a SAMZ server computes the zones within the field in a three-stage process. In the first stage, a vector-valued image of the field is constructed by assembling, from the archives, the equivalent of a stack of the available images of the field (see figure). In the second stage, the vector-valued image is analyzed by use of a wavelet transform that detects spatial variations considered significant for precision farming while suppressing small-scale heterogeneities that are regarded as insignificant. In the third stage, a segmentation algorithm assembles the zones from smaller regions that have been identified in the wavelet analysis.

Lepoutre, Damien↗
DOE OSTI2024

Behavior, Energy, Autonomy, Mobility Modeling Framework (BEAM) v1.0

The Behavior, Energy, Autonomy, and Mobility (BEAM) model is an integrated, agent-based travel demand simulation framework. Individual agents express preferences through a utility- maximizing evolutionary algorithm that minimizes each individual’s cost and time spent traveling via diverse modal options, including the competition for scarce supply resources such as parking spaces and charging infrastructure. BEAM simulates the essential elements that compose a dynamic transportation system. From the road network, parking and charging infrastructure, to the transit system and a synthetic population with plans and preferences, the virtual system is an amalgamation of multiple spatially resolved layers that together represent an integrated transportation system. BEAM is an extension to the MATSim (Multi-Agent Transportation Simulation) model, where agents employ reinforcement learning across successive simulated days to maximize their personal utility through plan mutation (exploration) and selecting between previously executed plans (exploitation). The BEAM model shifts some of the behavioral emphasis in MATSim from across-day planning to within- day planning, where agents dynamically respond to the state of the system during the mobility simulation. In BEAM, agents can plan across all major modes of travel including driving, walking, biking, transit, and demand-responsive ride hailing. It is designed to integrate with other open source transportation models, such as ActivitySim.

Lazarus, Jessica↗
NASA NTRS1986

Seasonal variations of troposheric ozone at Natal, Brazil

An analysis of ozone measurements from Natal, Brazil (6 deg S, 35 W), with a focus on the seasonal behavior in the troposphere, is presented. The amplitude of seasonal cycle at Natal is much larger than at Panama (9 deg N), the only other tropical site for which similar data are available. Concentrations of ozone in the middle troposphere in the southern spring are unexpectedly high, 60-70 ppb, similar to values found at northern midlatitudes in summer, and larger by 20-30 ppb than values found at Panama and at southern midlatitudes. It is suggested that photochemical production of ozone associated with emissions of CO, hydrocarbons, and NO(x) from biomass burning may contribute significantly to the high values of ozone, but note that stratospheric intrusions could also play a role. The data available at present do not permit a definitive evaluation of the relative importance of these two sources of ozone. The data from Natal, in combination with recent aircraft and surface data, show that tropical ozone exhibits strong spatial and temporal inhomogeneities. The distribution of tropospheric ozone appears to be considerably more complex than the traditional view, which suggested a northern midlatitude maximum and north/-south hemispheric asymmetry. The seasonal cycle in the total column of ozone at Natal appears to mirror the behavior of the tropospheric contribution to the ozone column rather than the stratospheric contribution, and this may account for differences in the annual cycle of the total column at Natal versus other tropical locations.

Logan, J. A.↗
DOE OSTI2026

Can classical DEM simultaneously capture compressibility and flowability of milled biomass?

Accurate prediction of the rheological behavior of biomass is essential for the design and operation of hoppers, feeders, and storage systems in biorefineries. This study examines whether the classical, coarse-grained discrete element method (DEM) formulation can simultaneously reproduce the compressibility and flowability of milled herbaceous biomass, using Miscanthus × giganteus as a representative material. The model represents particles as rigid spheres interacting through Hertz-Mindlin elastic-frictional contacts augmented with an area-dependent cohesion term. Laboratory cyclic compression and wedge-shaped hopper discharge experiments were used as calibration benchmarks. Although the model can independently reproduce each behavior by appropriately tuning particle Young's modulus E and cohesion energy density k, an extensive parametric investigation comprising more than 600 simulations reveals that the optimal parameter regions for compression and hopper flow are distinct and non-overlapping in (E, k) space. Surrogate surface analysis further shows that the corresponding objective-function valleys exhibit similar trends but are approximately parallel and spatially offset, precluding a unified calibration within the explored domain. Sensitivity analysis indicates that compressibility is governed predominantly by stiffness and cohesion, whereas the slope of the mass flow rate-opening relation in hopper discharge is primarily controlled by tangential friction. Extensions incorporating particle size distribution and clumped-sphere representations do not eliminate the incompatibility. These results systematically reveal, for the first time, the structural limitation of simplified DEM formulations in representing biomass rheological behavior, underscoring the necessity for models incorporating additional physical mechanisms, such as particle deformability or enhanced interlocking, to achieve unified predictive capability for biomass handling behavior.

09 BIOMASS FUELS↗
DOE OSTI2019

Behavior, Energy, Autonomy, Mobility Modeling Framework

The Behavior, Energy, Autonomy, and Mobility (BEAM) model is an integrated, agent-based travel demand simulation framework. Individual agents express preferences through a utility-maximizing evolutionary algorithm that minimizes each individual's cost and time spent traveling via diverse modal options, including the competition for scarce supply resources such as parking spaces and charging infrastructure. BEAM simulates the essential elements that compose a dynamic transportation system. From the road network, parking and charging infrastructure, to the transit system and a synthetic population with plans and preferences, the virtual system is an amalgamation of multiple spatially resolved layers that together represent an integrated transportation system. BEAM is an extension to the MATSim (Multi-Agent Transportation Simulation) model, where agents employ reinforcement learning across successive simulated days to maximize their personal utility through plan mutation (exploration) and selecting between previously executed plans (exploitation). The BEAM model shifts some of the behavioral emphasis in MATSim from across-day planning to within-day planning, where agents dynamically respond to the state of the system during the mobility simulation. In BEAM, agents can plan across all major modes of travel including driving, walking, biking, transit, and demand-responsive ride hailing.

Bae, Sangjae↗
DOE OSTI2023

Fitting Matérn smoothness parameters using automatic differentiation

The Mat$\acute{e}$rn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities such as interpolants and forecasts. Unfortunately, derivatives of the Mat$\acute{e}$rn covariance function with respect to $\nu$ require derivatives of the modified second-kind Bessel function $K$ $\nu$ with respect to $\nu$. While closed form expressions of these derivatives do exist, they are prohibitively difficult and expensive to compute. For this reason, many software packages require fixing $\nu$ as opposed to estimating it, and all existing software packages that attempt to offer the functionality of estimating $\nu$ use finite difference estimates for $\partial$ $\nu$ $K$ $\nu$ . In this work, we introduce a new implementation of $K$$\nu$ that has been designed to provide derivatives via automatic differentiation (AD), and whose resulting derivatives are significantly faster and more accurate than those computed using finite differences. Here, we provide comprehensive testing for both speed and accuracy and show that our AD solution can be used to build accurate Hessian matrices for second-order maximum likelihood estimation in settings where Hessians built with finite difference approximations completely fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Computational modeling of microalgal biofilm growth in heterogeneous rotating algal biofilm reactors (RABRs) for wastewater treatment

Rotating algal biofilm reactors (RABRs) are innovative systems designed to cultivate microalgae biofilms efficiently. In this paper, we have developed a novel mathematical model to accurately capture the growth dynamics of algae biofilms within RABR. By considering the spatial heterogeneity of the RABR, we introduce a PDE-based model that addresses the spatial variations across the substratum, enabling a more accurate simulation of biofilm growth in RABRs. The photosynthesis process is modeled through reactive kinetics, driving the growth of the algae biofilm. To analyze the system's behavior, we employ finite difference numerical methods to solve the complex PDE model. We then conduct extensive numerical simulations to understand algae biofilm growth in the RABR environment under various operational factors and environmental conditions. One primary focus in these simulations is to investigate the impact of various harvesting strategies, harvesting frequencies, light intensity, and light exposure on the overall biomass productivity of the algae biofilm. The numerical results provide valuable insights into optimizing algae biofilm growth and designing harvesting techniques in RABR systems. Our proposed novel mathematical model provides an effective platform for the theoretical investigation and design of RABRs for wastewater treatment.

09 BIOMASS FUELS↗
DOE OSTI2020

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Modeling of transverse stimulated Raman scattering in KDP/DKDP in large-aperture plates suitable for polarization control

Transverse stimulated Raman scattering (TSRS) in potassium dihydrogen phosphate (KDP) and deuterated potassium dihydrogen phosphate (DKDP) plates for large-aperture, inertial confinement fusion (ICF)-class laser systems is a well-recognized limitation giving rise to parasitic energy conversion and laser-induced damage. The onset of TSRS is manifested in plates exposed to the ultraviolet section of the beam. TSRS amplification is a coherent process that grows exponentially and is distributed nonuniformly in the crystal and at the crystal surfaces. To understand the growth and spatial distribution of TSRS energy in various configurations, a modeling approach has been developed to simulate the operational conditions relevant to ICF-class laser systems. Specific aspects explored in this work include (i) the behavior of TSRS in large-aperture crystal plates suitable for third-harmonic generation and use as wave plates for polarization control in current-generation ICF-class laser system configurations; (ii) methods, and their limitations, of TSRS suppression and (iii) optimal geometries to guide future designs.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Reward-Based Participant Management for Crowdsourcing Rainfall Monitoring: An Agent-Based Model Simulation

Crowdsourcing incorporates common citizens as rich sources of data and is promising for environmental monitoring. Here, we propose and test the idea of incorporating incentives to crowdsourcing management for rainfall monitoring. In particular, we model the allocation of incentives (quantitatively measurable and limited rewards) among crowdsourcing participants for a theoretical rainfall monitoring case. For this purpose, we develop an integrated model comprising a reward allocation component to represent the decision-making process of a central manager, an agent-based model to simulate the interactions between the manager and participants, and a rainfall simulation model to evaluate the effectiveness of various reward allocation policies. We simulate six reward allocation policies of varying levels of administrative cost, and consideration of participant and rainfall spatial heterogeneities. The findings indicate the performance of each policy to improve with the reward budget and their spatial uniformity. Among the six policies tested, we discover that the participant density weighted maximum participation policy yields the most accurate estimation of rainfall intensity due to its more explicit consideration of the spatial distribution of participants; however, this policy associates with a high administrative cost. This highlights the trade-off between performance and cost in designing effective reward allocation policies. This paper provides a physical and behavior simulation modeling tool to study the feasibility and complexity of reward-based participant management for crowdsourcing rainfall monitoring. The proposed crowdsourcing method is beneficial for a wide range of applications that require rainfall data with fine resolution, such as storm water management and water availability and biomass assessment for food and energy crops.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Imaging perturbed shock propagation in powders

A novel experimental methodology is presented to study the deviatoric response of powders in shock regimes. The powders are confined to a cylindrical wedge volume, and a projectile-driven shock wave with a sinusoidally varying front propagates through the powder. The perturbed shock wave exhibits a damping behavior due to irreversible processes of viscosity and strength (deviatoric) of the powder with propagation through increasing powder thicknesses. The inclined surface of the wedge is polished and coated to establish a diffuse surface suitable for reflecting incident laser light into a high-speed camera imaging at 5 MHz. Images of the contrast loss upon shock wave arrival at the observation surface are post-processed for qualitative and quantitative information. New data of shock damping behavior with parameters of perturbation wavelength and initial shock strength are presented for powders of copper, tantalum, and tungsten carbide as well as their mixtures. We present the first full-field images showing additional spatial disturbances on the perturbed shock front that appear dependent on particle material and morphology.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Nucleation kinetics model for primary crystallization in Al–Y–Fe metallic glass

The high density of aluminum nanocrystals (>10 21 m -3 ) that develop during the primary crystallization in Al-based metallic glasses indicates a high nucleation rate (~10 18 m -3 s -1 ). Several studies have been advanced to account for the primary crystallization behavior, but none have been developed to completely describe the reaction kinetics. Recently, structural analysis by fluctuation electron microscopy has demonstrated the presence of the Al-like medium range order (MRO) regions as a spatial heterogeneity in as-spun Al 88 Y 7 Fe 5 metallic glass that is representative for the class of Al-based amorphous alloys that develop Al nanocrystals during primary crystallization. From the structural characterization, an MRO seeded nucleation configuration is established, whereby the Al nanocrystals are catalyzed by the MRO core to decrease the nucleation barrier. The MRO seeded nucleation model and the kinetic data from the delay time (τ) measurement provide a full accounting of the evolution of the Al nanocrystal density (N v ) during the primary crystallization under isothermal annealing treatments. Moreover, the calculated values of the steady state nucleation rates (J ss ) predicted by the nucleation model agree with the experimental results. Moreover, the model satisfies constraints on the structural, thermodynamic, and kinetic parameters, such as the critical nucleus size, the interface energy, and the volume-free energy driving force that are essential for a fully self-consistent nucleation kinetics analysis. In conclusion, the nucleation kinetics model can be applied more broadly to materials that are characterized by the presence of spatial heterogeneities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Magnetic probe diagnostics of nonlinear standing waves and bulk ohmic electron power absorption in capacitive discharges

It is recognized that standing wave effects appearing in large-area, very-high-frequency capacitively coupled plasma (CCP) reactors cause center-high plasma non-uniformity. Using a high-frequency magnetic probe, we present a direct experimental diagnostic of the nonlinear standing waves and bulk ohmic electron power absorption dynamics in low pressure CCP discharges for different driving frequencies of 13.56, 30, and 60 MHz. The design, principle, calibration, and validation of the probe are described in detail. Spatial structures of the harmonics of the magnetic field, determined by the magnetic probe, were used to calculate the distributions of the harmonic current and the corresponding ohmic electron power deposition, providing insights into the behavior of nonlinear harmonics. At a low driving frequency, i.e. 13.56 MHz, no remarkable nonlinear standing waves were identified and the bulk ohmic electron power absorption was observed to be negligible. Here, the harmonic magnetic field/current was found to increase dramatically with the driving frequency, due to decreased sheath reactance and more remarkable nonlinear standing waves at a higher driving frequency, leading to the enhancements of the ohmic heating and the plasma density in the bulk, specifically at the electrode center. At a high driving frequency, i.e. 60 MHz, the high-order harmonic current density and the corresponding ohmic electron power absorption exhibited a similar node structure, with the main peak on axis, and one or more minor peaks between the electrode center and the edge, contributing to the center-high profile of the plasma density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Precision Measurements of Electron-Proton Elastic Scattering Cross Sections at Large Q2

The electromagnetic form factors are fundamental quantities characterizing the internal structure of the nucleon. Their measurements have provided significant insight into the spatial distribution and interaction of quarks inside the proton. The knowledge of high Q2 form factors proves essential in understanding the properties of quantum chromodynamics in the transition region from non-perturbative to perturbative behavior. It also provides important links to generalized parton distributions, which describe the three-dimensional structure of hadrons at the parton level. In view of the significant theoretical research activities in this field, high quality experimental data are crucial for providing stringent tests and benchmarks to guide and test different models. The form factors can be accessed in experiments by measuring elastic scattering of electrons off a hydrogen target. Experiment E12-07-108, which took place at the Thomas Jefferson National Accelerator Facility, conducted precise measurements of the unpolarized e-p elastic scattering cross section over a Q2 range of 0.6-16.5 GeV2 . This thesis presents the results for 7 kinematic settings with total uncertainties that are 1.5 times smaller than those of the existing data at large Q2 . The proton magnetic form factors were extracted using a parameterization of the form factor ratio obtained from recent polarized e-p scattering experiments. Comparisons to existing global and phenomenological fits are presented.

Ou, Longwu↗
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

High temperature thick film sensor development based on doped lanthanum chromites refractory semiconductors materials

High temperature advanced sensing materials have generated high demand due the high accuracy temperature measurements requirements for process optimization, controlling and sensing. Some technological applications of harsh conditions sensing include monitoring tiles of space shuttles, rotating bearings in aircraft engines, turbines, jet engines dynamics and chemical reactors. High temperature conditions limit the sensing strategies, where typically traditional metal thermocouples are unstable, and the sensing options are limited to optical spectroscopy methods. Recently, refractory semiconductors thick- and thin-film thermocouples have been developed and, in many cases, preferred over conventional metallic thermocouples due their spatial resolution, and capability of direct deposition on any surface. Rare earth chromites ceramics materials, exhibit some properties of interest for high temperature sensing technologies development, such as: high microstructure and sintering stability, excellent conductive behavior at high temperatures, and matching thermal expansion coefficients relative to other conductors and refractory ceramics. In this work, high performance ultra-high temperature thermocouples using p-type and n-type doped lanthanum chromites materials were fabricated and tested at temperatures up to 1500 o C. Thermoelectric voltage, Seebeck Coefficients were established for all devices, evidencing high stability and performance in prolongated operational time and harsh conditions.

20 FOSSIL-FUELED POWER PLANTS↗
NASA NTRS1984

3-D inelastic analysis methods for hot section components (base program)

A 3-D inelastic analysis methods program consists of a series of computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of combustor liners, turbine blades, and turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. These models are used to solve 3-D inelastic problems using linear approximations in the sense that stresses/strains and temperatures in generic modeling regions are linear functions of the spatial coordinates, and solution increments for load, temperature and/or time are extrapolated linearly from previous information. Three linear formulation computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), were developed and are described.

Wilson, R. B.↗
NASA NTRS1989

A finite element method for nonlinear panel flutter

Panel flutter is the self excited oscillations of a plate in supersonic flow. Linear theory gives no information about the panel's deflections and stresses. Hence, the service life of the panel cannot be predicted by linear methods. Nonlinear structural theory determines the limit cycle oscillating frequency, and also panel deflections and stresses. Panel fatigue life, therefore, can be predicted. For a more thorough understanding of panel flutter behavior, the geometric nonlinearity effects due to large deflections must be considered in the formulation. The Galerkin's method was used in the investigation of limit cycle oscillations of panels in supersonic flow in the spatial domain, and the panel deflections. All nonlinear flutter methods and results presently available were limited to a linear or linearized aerodynamic theory. Extension of the finite element flutter formulation to include nonlinear hypersonic aerodynamic loading and finite element nonlinear panel flutter results are presented.

Mei, Chuh↗