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At least 1,441 records · Page 80

Ice Accretion Measurements on an Airfoil and Wedge in Mixed-Phase Conditions

This paper describes ice accretion measurements from experiments conducted at the National Research Council (NRC) of Canada's Research Altitude Test Facility during 2012. Due to numerous engine power loss events associated with high altitude convective weather, potential ice accretion within an engine due to ice crystal ingestion is being investigated collaboratively by NASA and NRC. These investigations examine the physical mechanisms of ice accretion on surfaces exposed to ice crystal and mixed phase conditions, similar to those believed to exist in core compressor regions of jet engines. A further objective of these tests is to examine scaling effects since altitude appears to play a key role in this icing process.

ice crystals↗

System Assessment of a High Power 3-U CubeSat

The Advanced eLectrical Bus (ALBus) CubeSat project is a technology demonstration mission of a 3-UCubeSat with an advanced, digitally controlled electrical power system capability and novel use of Shape Memory Alloy (SMA) technology for reliable deployable solar array mechanisms. The objective of the project is to, through an on orbit demonstration, advance the state of power management and distribution (PMAD) capabilities to enable future missions requiring higher power, flexible and reliable power systems. The goals of the mission include demonstration of: 100 Watt distribution to a target electrical load, efficient battery charging in the orbital environment, flexible power system distribution interfaces, adaptation of power system control on orbit, and reliable deployment of solar arrays and antennas utilizing re-settable SMA mechanisms. The power distribution function of the ALBus PMAD system is unique in the total power to target load capability of 100 W, the flexibility to support centralized or point-to-load regulation and ability to respond to fast transient power requirements. Power will be distributed from batteries at 14.8 V, 6.5 A to provide 100 W of power directly to a load. The deployable solar arrays utilize NASA Glenn Research Center superelastic and activated Nitinol(Nickel-Titanium alloy) Shape Memory Alloy (SMA) technology for hinges and a retention and release mechanism. The deployable solar array hinge design features utilization of the SMA material properties for dual purpose. The hinge uses the shape memory properties of the SMA to provide the spring force to deploy the arrays. The electrical conductivity properties of the SMA also enables the design to provide clean conduits for power transfer from the deployable arrays to the power management system. This eliminates the need for electrical harnesses between the arrays and the PMAD system in the ALBus system design. The uniqueness of the SMA retention and release mechanism design is the ability to reset the mechanism, allowing functional tests of the mechanisms prior to flight with no degradation of performance. The project is currently in preparation at the NASA Glenn Research Center for a launch in late calendar year of 2017. The 100 Watt power distribution and dual purpose, re-settable SMA mechanisms introduced several system level challenges due to the physical constraints in volume, mass and surface area of 3-U CubeSats. Several trade studies and design cycles have been completed to develop a system which supports the project objectives. This paper is a report on the results of the system level trade studies and assessments. The results include assessment of options for thermal control of 100 Watts of power dissipation, data from system analyses and engineering development tests, limitations of the 3-U system and extensibility to larger scale CubeSat missions.

CubeSat↗

What it Takes to Compute Highly Accurate Rovibrational Line Lists for Use in Astrochemistry

We review the Best Theory + Reliable High-resolution Experiment (BTRHE) strategy for obtaining highly accurate molecular rovibrational line lists with InfraRed (IR) intensities. The need for highly accurate molecular rovibrational line lists is two-fold: a) assignment of the many rovibrational lines for common stable molecules especially those that exhibit a large amplitude motion, such as NH3, or have a high density of states such as SO2; and b) characterization of the atmospheres of exoplanets which will be one of the main areas of research in astronomy in the coming decades. The first motivation arises due to the need to eliminate lines due to common molecules in an astronomical observation in order to identify lines from new molecules, while the second motivation arises due to the need to obtain accurate molecular opacities in order to characterize the atmosphere of an exoplanet. The BTRHE strategy first consists of using high quality ab initio quantum chemical methods to obtain a global potential energy surface (PES) and dipole moment surface (DMS) that contains the proper physics. The global PES is then refined using a subset of the reliable high-resolution experimental data. The refined PES then gives energy level predictions to an accuracy similar to the reproduction accuracy of the experimental data used in the refinement step in the interpolation region (i.e., within the range of the experimental data used in the refinement step). The accuracy of the energy levels will slowly degrade as they are extrapolated to spectral regions beyond the high-resolution experimental data used in the refinement step. However, because the degradation is slow, the predicted energy levels can be used to assign new high-resolution experiments, and the data from these can then be used in a subsequent refinement step. In this way, the global PES eventually can yield highly accurate energy levels for all desired spectral regions including to very high energies and high J values. We show that IR intensities computed with the BTRHE rovibrational wavefunctions and the DMS can be very accurate provided one has minimized the fitting error of the DMS and tested the completeness of the DMS. Some examples of our work on NH3, CO2, and SO2 are given to highlight the usefulness of the BTRHE strategy and to provide ideas on how to further improve its predictive power in the future. In particular, it is shown how successive refinement steps, once new high-resolution data is available, can lead to PESs that yield highly accurate transition energies to larger spectral regions. The importance of including non-adiabatic corrections to reduce the J-dependence of errors for H-containing molecules is shown with work on NH3. Another very important aspect of the BTRHE approach is the consistency across isotopologues, which allows for highly accurate line lists for any isotopologue once one is obtained for the main isotopologue (which has more high-resolution data available for refinement).

Xinchuan Huang↗

The Porous Microstructure Analysis (PuMA) software

The open-source Porous Microstructure Analysis (PuMA) software was implemented to offer an efficient framework for determining material characteristics from 3D microstructures. Its development was inspired by progress in X-ray microtomography, an imaging technology that captures the internal structure of materials in 3D, and even in a 4D temporal context. Over recent years, this method has transformed the domain of materials science due to its capability to non-destructively examine material microstructures while presenting digital data about their geometrical details. It has provided insights into materials relevant to several NASA missions, including heatshields, parachute fabrics, meteorites, and other advanced composites. PuMA, in its current version 3, delivers an array of features, spanning from basic geometric insights of a microstructure to intricate anisotropic thermo-elastic and chemical behavior. Specifically, the software evaluates morphological attributes (specific surface area, volume fractions, mean intercept lengths, orientation) and physical characteristics (conductivity, elasticity, permeability, and tortuosity). Additionally, it can model material degradation processes, such as oxidation and surface chemistry interactions. The software can generate synthetic microstructures, from straightforward geometrical designs to intricate woven and non-woven geometries. Coupling material generation and characterization enable parametric studies and sensitivity analysis to optimize the microstructural performance and inform design decisions and reliability assessment based on uncertainty quantification. A recent addition to PuMA includes the TomoSAM plugin, devised to incorporate the cutting-edge Segment Anything Model (SAM). SAM is a promptable deep learning model that can identify objects and create image masks in a zero-shot manner, based only on a few user clicks. The synergy between these tools aids in the segmentation of complex 3D datasets from tomography or other imaging techniques, which would otherwise require a laborious manual segmentation process.

Tomography↗

The Porous Microstructure Analysis (PuMA) software

The open-source Porous Microstructure Analysis (PuMA) software was created to offer an efficient framework for determining material properties from 3D microstructures. Its development was inspired by progress in X-ray microtomography, an imaging technology that captures the internal structure of materials in 3D, and even in a 4D temporal context. Over recent years, this method has transformed the domain of materials science due to its capability to non-destructively examine material microstructures while presenting digital data about their geometrical details. It has provided insights into materials relevant to several NASA missions, including heatshields, parachute fabrics, meteorites, and other advanced composites. PuMA, in its current version 3, delivers an array of features, spanning from basic geometric insights of a microstructure to intricate anisotropic thermo-elastic and chemical behavior. Specifically, the software evaluates morphological attributes (specific surface area, volume fractions, mean intercept lengths, orientation) and physical characteristics (conductivity, elasticity, permeability, and tortuosity). Additionally, it can model material degradation processes, such as oxidation and surface chemistry interactions. The software can generate synthetic microstructures, from straightforward geometrical designs to intricate woven and non-woven geometries. Coupling material generation and characterization enables parametric studies and sensitivity analysis to optimize the microstructural performance and inform design decisions and reliability assessment based on uncertainty quantification. A recent addition to PuMA includes the TomoSAM plugin, devised to incorporate the cutting-edge Segment Anything Model (SAM) into our image segmentation workflow. SAM is a promptable deep learning model that can identify objects and create image masks in a zero-shot manner, based only on a few user clicks. The synergy between these tools aids in the segmentation of complex 3D datasets from tomography and other imaging techniques, which would otherwise require a laborious manual segmentation process.

Tomography↗

Wall-Jet Evolution During Plume-Surface Interaction Using PLIF Imaging

Planar laser-induced fluorescence (PLIF) flow visualization was used to examine the spatial evolution for the wall-jet formed by an impinging supersonic jet in a large-scale vacuum environment. This canonical configuration is representative of the plume-surface interaction induced by a rocket exhaust plume impinging on the planetary surface at lunar-relevant and Martian-relevant environments. PLIF flow visualization of the very low-density environment (as low as ~0.006% of standard atmospheric density) was performed using seeded nitric oxide in a nitrogen flow at three test conditions. Two conditions are representative of the lunar environment, and one is representative of the Martian environment. The combined images from two simultaneous PLIF views were used to construct a 2D slice of the flowfield spanning approximately 150 mm in height (determined by the laser sheet) and 500 mm in width (determined by the camera views). The three test conditions showed different behavior for the wall-jet, largely due to the different levels of lifting above the surface and the appearance of a physical process similar to a Kelvin–Helmholtz instability for the Martian-relevant case, which appeared to create a dramatic expansion of the wall-jet height with increased radial distance.

PSI↗

Wall-Jet Evolution During Plume-Surface Interaction Using PLIF Imaging

Planar laser-induced fluorescence (PLIF) flow visualization was used to examine the spatial evolution for the wall-jet formed by an impinging supersonic jet in a large-scale vacuum environment. This canonical configuration is representative of the plume-surface interaction induced by a rocket exhaust plume impinging on the planetary surface at lunar-relevant and Martian-relevant environments. PLIF flow visualization of the very low-density environment (as low as ~0.006% of standard atmospheric density) was performed using seeded nitric oxide in a nitrogen flow at three test conditions. Two conditions are representative of the lunar environment, and one is representative of the Martian environment. The combined images from two simultaneous PLIF views were used to construct a 2D slice of the flowfield spanning approximately 150 mm in height (determined by the laser sheet) and 500 mm in width (determined by the camera views). The three test conditions showed different behavior for the wall-jet, largely due to the different levels of lifting above the surface and the appearance of a physical process similar to a Kelvin–Helmholtz instability for the Martian-relevant case, which appeared to create a dramatic expansion of the wall-jet height with increased radial distance.

PSI↗

Spaceborne Lidar Retrievals of PM2.5 for Air Quality Studies and Applications

Fine particulate matter (PM2.5) substantially contributes to air pollution and negatively affects human health. While many studies have investigated the use of passive column-integrated aerosol optical depth to infer surface PM2.5, the use of lidar observations for air quality characterization is not nearly as extensive. Lidar measurements are critical, however, due to the vertical aerosol information they provide, including near the surface. In this presentation, we first provide an overview of various lidar-based approaches for estimating PM2.5 concentrations and then discuss how lidar measurements can assist other air quality applications. For example, estimates of PM2.5 have been obtained in a physics-based approach through CALIOP near-surface aerosol extinction retrievals, assumptions on the mass extinction efficiency, and incorporating other parameters (an aerosol hygroscopic growth factor and PM2.5/PM10 ratio). Application of this algorithm over the contiguous United States (CONUS) from 2006 to 2018 yielded larger PM2.5 values over the eastern and western CONUS (~10-15 μg/m³) and lower PM2.5 levels in the central CONUS (~5 μg/m³). These spatial patterns were similar to those from gridded PM2.5 concentrations obtained through in situ measurements at ground stations operated by the US Environmental Protection Agency. In another approach, the Cloud Aerosol Transport System (CATS) lidar was used with the Goddard Earth Observing System (GEOS) model in a 1D ensemble-based variational technique to obtain PM2.5 over the US and Europe, and the spatial patterns of the CATS/GEOS based PM2.5 concentrations generally captured those from surface stations (with corresponding hourly EPA PM2.5 vs CATS PM2.5 statistics of R=0.4 and bias=1.5 μg/m³). In our recent work, as part of the Models, In situ, and Remote sensing of Aerosols (MIRA) Working Group, we have applied both the CALIOP and CATS/GEOS based approaches over the highly polluted country of India during the post-monsoon season (September-October 2016). We derived elevated levels of two-month mean PM2.5 (~100 μg/m³) in northern India, especially near New Delhi. These high PM2.5 concentrations in the Indo-Gangetic plain are driven in large part from the seasonal burning of crop residue and meteorological conditions typical at this time of the year, such as low wind speeds and a shallow boundary layer. While the satellite-derived PM2.5 moderately replicates (R = ~0.7-0.9) the spatial variability in the two-month mean of surface in situ PM2.5 from monitoring sites operated by the Central and State Pollution Control Boards, we show results from specific scenes for which there are large deviations between the satellite-derived PM2.5 and in situ measurements. Other current work on this topic focuses on developing PM2.5 estimates using airborne high spectral resolution lidar measurements through machine learning regression algorithms and involves several parameters (e.g., aerosol extinction, color ratio, lidar ratio). Application of this method over major metropolitan areas in the US and Asia have resulted in high correlations (R = 0.93) with surface measurements. This airborne lidar approach can be adapted to spaceborne lidar measurements, and all three of these approaches can be applied to ESA’s EarthCARE Atmospheric Lidar instrument, setting the stage for the future Cloud Aerosol Lidar for Global Scale Observations of the Ocean-Land Atmosphere System (CALIGOLA) mission. Ultimately, beyond estimates of PM2.5, the aerosol vertical distribution from lidars can benefit studies involving passive sensor approaches for PM2.5 proxies (including from geostationary satellites), wildfire smoke plume injection heights, volcanic emissions (e.g., ash height retrievals), and aerosol/air quality model assimilation, evaluation, and forecasts.

Travis D Toth↗

Porous electrodes for spectroelectrochemistry and x-ray structure analyses

An electrochemical cell that allows for in-situ structural characterization of amorphous thin film materials during the course of electrolysis using high-energy X-ray scattering (>50 keV). The compact and versatile cell employs a three-electrode configuration and minimizes X-ray scattering contributions from the cell, reference and counter electrodes, as well as the working electrode support. A large surface area working electrode has a physically robust support and is largely transparent to X-rays. This design, which utilizes a three-dimensional working electrode, also greatly improves the intensity and quality of the scattered signal compared to a two-dimensional working electrode. The in-situ cell can be used not only to investigate structural evolution during electrolysis using X-ray scattering (e.g. pair distribution function), but also to perform electrochemical potential-dependent structural analysis by extended X-ray absorption fine structure.

Kwon, Gihan↗

Characterization of Lanthanum Monazite Surface Chemistry and Crystal Morphology through Density Functional Theory and Experimental Approaches

Monazite is a rare earth element (REE)-containing mineral that consists of (REE)PO 4 formal units and is one of the most important sources of these critical materials. The concentration of REEs from mined monazite ore often involves froth flotation, which is a beneficiation process that enhances the efficiency of downstream processing. The effectiveness of froth flotation is largely governed by the ability of collector agents to selectively bind to monazite particles. Thus, a molecular-level understanding of monazite interfacial chemistry is integral to the design of effective collector agents. To address this need, we performed density functional theory (DFT) calculations and a variety of experimental techniques to characterize La-monazite and elucidate its crystal morphology. Interestingly, we find minimal differences in the predicted morphologies of La-monazite for hydrous and anhydrous environments, which are largely dominated by low-index facets (e.g., {110}, {100}, and {010}). Indexing of synthesized La-monazite crystals via X-ray diffraction also uncovers {110} and {100} as the predominant facets. The average surface energies of 0% and 100% water coverage La-monazite crystals were predicted to be 0.87 and 0.76 J/m 2 , respectively, while calorimetry suggests values of 1.30 and 1.15 J/m 2 , respectively. The apparent discrepancies between the theoretical and experimental values are expected and attributed to defects present in physical crystals, in contrast to the perfect mineral surfaces in simulations. The difference in surface energy between the 0% and 100% water coverage morphologies predicted by theory is consistent with the value measured via calorimetry. DFT reveals a wide range of adsorption energies for water across the studied facets, but in all cases, water is predicted to strongly bind to monazite surfaces with an average adsorption energy of -92.7 kJ/mol for a La-monazite single crystal. Finally, this study provides the groundwork necessary for the rational design of froth flotation collector agents by granting molecular-level insight into the predominant facets of monazite.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon dioxide-enhanced metal release from kerogen

Heavy metals released from kerogen to produced water during oil/gas extraction have caused major environmental concerns. To curtail water usage and production in an operation and to use the same process for carbon sequestration, supercritical CO 2 (scCO 2 ) has been suggested as a fracking fluid or an oil/gas recovery agent. It has been shown previously that injection of scCO 2 into a reservoir may cause several chemical and physical changes to the reservoir properties including pore surface wettability, gas sorption capacity, and transport properties. Using molecular dynamics simulations, we here demonstrate that injection of scCO 2 might lead to desorption of physically adsorbed metals from kerogen structures. This process on one hand may impact the quality of produced water. On the other hand, it may enhance metal recovery if this process is used for in-situ extraction of critical metals from shale or other organic carbon-rich formations such as coal.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GW190814's Secondary Component with Mass 2.50–2.67 M ⊙ as a Superfast Pulsar

Using Stergioulas's RNS code for investigating fast pulsars with Equation of States (EOSs) on the causality surface (where the speed of sound equals that of light) of the high-density EOS parameter space satisfying all known constraints from both nuclear physics and astrophysics, we show that one possible explanation for the GW190814's secondary component of mass (2.50-2.67) M ⊙ is that it is a super-fast pulsar spinning faster than 971 Hz about 42% below its Kepler frequency. If confirmed, it would be the fastest pulsar with the highest mass observed presently. There is a large and physically allowed EOS parameter space below the causality surface where pulsars heavier than 2.50 M ⊙ are supported if they can rotate even faster with critical frequencies depending strongly on the high-density behavior of nuclear symmetry energy.

79 ASTRONOMY AND ASTROPHYSICS↗

Global Evaluation of Terrestrial Near-Surface Air Temperature and Specific Humidity Retrievals from the Atmospheric Infrared Sounder (AIRS)

Global observations of near-surface air temperature and specific humidity over land are needed for a variety of applications, including to constrain global estimates of evapotranspiration (ET). Spaceborne hyperspectral observations, such as those from NASA’s Atmospheric Infrared Sounder (AIRS) mission, show promise for meeting this need, yet there are surprisingly few validation studies of AIRS near-surface atmospheric state retrievals. In this study, we use triple collocation to validate AIRS Level 3 retrievals of near-surface atmospheric state over land using twelve years of gridded station observations and two reanalyses. Deseasonalized AIRS retrievals correlate well with deseasonalized ground observations outside the tropics, but correlate less well in the tropics. Lower temporal sensitivity near the surface in the tropics contributes to the lower correlation for near-surface air temperature and is consistent with known physics of the tropical atmosphere, in which temperatures outside the boundary layer (which dominate the AIRS retrieval signal) are poorly correlated with those near the surface. Retrievals in the tropics may also be more susceptible to errors in cloud-clearing algorithms, and to uncertainty in surface emissivity. Since ET is greatest in the tropics, and tropical measurement networks are particularly sparse, this work motivates new approaches for measuring ET in the tropics.

Evapotranspiration↗

Some Theoretical Aspect of Cryosorption

When a gas or vapor is allowed to come to equilibrium with a solid surface, the concentration of gas molecules is always found to be greater in the immediate vicinity of the surface than in the free gas phase, regardless of the nature of the gas or of the surface. The process by which this surface excess is formed is termed adsorption. In any solid, the atoms at the surface are subject to unbalanced forces of attraction normal to the surface plane; the balance of forces is partially restored by the adsorption of gas molecules. If the forces responsible for adsorption are of van der Waals type, the process is called physical adsorption. Furthermore, if the solid (and its surface) are maintained at relatively low temperatures (say 50°K or below), the term cryosorption is used.

ADSORPTION↗

Mars Environmental Chamber for Dynamic Dust Deposition and Statics Analysis

Recent observations of the 2001 dust storms encircling Mars confirm predictions of environmental challenges for exploration. Martian dust has been found to completely mantle the Martian surface over thousands of square kilometers and the opacity of airborne dust has been shown to be capable of modifying atmospheric temperature, radiative transfer and albedo. Planetary dust cycling dynamics are suggested to be a key factor in the evolution of the Martian surface. Long-term robotic and manned exploration of Mars will be confronted by dust deposition in periods of atmospheric calm and violent wind storms. Aeolian dust deposition recorded during the Mars Pathfinder mission was estimated to fall at rates of 20-45 microns per Earth year. Although many tools of exploration will be challenged by coating, adhesion, abrasion and possible chemical reaction of deposited, wind blown and actively disturbed Martian dust, solar cells are thought to be of primary concern. Recent modeling work of power output by gallium arsenide/germanium solar cells was validated by the Pathfinder Lander data and showed power output decreases of 0.1 to 0.5% per Martian day. A major determinant for the optimal positioning angle of solar panels employed in future missions is the angle of repose of the settling dust particles that is dependent on a variety of physical and chemical properties of the particles, the panel surface, and the environmental conditions on the Mars surface. While the effects of many of these factors are well understood qualitatively, quantitative analyses, especially under physical and chemical conditions prevailing on the Mars surface are lacking.

L.E. Moeller↗

Surface Functionalization of Black Phosphorus with Nitrenes: Identification of P=N Bonds Using Isotopic Labeling

Abstract: Surface functionalization of two-dimensional crystals is a key path to tuning their intrinsic physical and chemical properties. However, synthetic protocols and experimental strategies to directly probe chemical bonding in modified surfaces are scarce. Introduced here is a mild, surface-specific protocol for the surface functionalization of few-layer black phosphorus nanosheets using a family of photolytically generated nitrenes (RN) from the corresponding azides. By embedding spectroscopic tags in the organic backbone, a multitude of characterization techniques are employed to investigate in detail the chemical structure of the modified nanosheets, including vibrational (infrared, Raman), Xray (emission, photoelectron), CPMAS NMR, and UV-vis spectroscopy. To directly probe the functional groups introduced on the surface, R fragments were selected such that in conjunction with vibrational spectroscopy, 15N-labeling experiments, and DFT methods, diagnostic P=N vibrational modes indicative of iminophosphorane units on the nanosheet surface could be conclusively identified.

Walz, Kendall↗

Stable Simulation of the Community Atmosphere Model Using Machine‐Learning Physical Parameterization Trained With Experience Replay

In recent years, machine learning (ML) models have been used to improve physical parameterizations of general circulation models (GCMs). A significant challenge of integrating ML models into GCMs is the online instability when they are coupled for long‐term simulation. We present a new strategy that demonstrates robust online stability when the physical parameterization package of an atmospheric GCM is replaced by a deep ML model. The method uses experience replay with a multistep training scheme of the ML model in which the model's own output at the previous time step is used in the training. Predicted physics tendencies in the replay buffer with the most recent errors in the training iterations are reused, making the ML model learn from its own errors. The training method reduces the gap between the offline and online environments of the ML model. The method is used to train the ML model as the physical parameterization of the Community Atmosphere Model (CAM5) with training data from the Multi‐scale Modeling Framework high resolution simulations. Three 6‐year online simulations of the CAM5 are carried out by using the ML physics package. The simulated spatial distributions of precipitation, surface temperature and zonally averaged atmospheric fields demonstrate overall better accuracy than that of the standard CAM5 and benchmark model even without the use of additional physical constraints or tuning. This work is the first to demonstrate a solution to address the online instability problem in climate modeling with ML physics by using experience replay.

54 ENVIRONMENTAL SCIENCES↗

High frequency scattering from corrugated stratified cylinders

Interest in applying radar remote sensing for the study of forested areas led to the development of a model for scattering from corrugated stratified dielectric cylinders. The model is used to investigate the effect of bark and its roughness on scattering from tree trunks and branches. The outer layer of the cylinder (bark) is assumed to be a low-loss dielectric material and to have a regular (periodic) corrugation pattern. The inner layers are treated as lossy dielectrics with smooth boundaries. A hybrid solution based on the moment method and the physical optics approximation is obtained. In the solution, the corrugations are replaced with polarization currents that are identical to those of the local tangential periodic corrugated surface, and the stratified cylinder is replaced with equivalent surface currents. New expressions for the equivalent physical-optics currents are used which are more convenient than the standard ones. It is shown that the bark layer and its roughness both reduce the radar cross-section. It is also demonstrated that the corrugations can be replaced by an equivalent anisotropic layer.

Sarabandi, Kamal↗