Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “loss functions”

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 1,531 records · Page 85

Probing Active-Site Relocation in Cu/SSZ-13 SCR Catalysts during Hydrothermal Aging by in situ EPR Spectroscopy, Kinetic Studies, and DFT Calculations

Cu/SSZ-13 selective catalytic reduction catalysts display activity loss after mild hydrothermal aging without support degradation or loss of isolated Cu ion content. By applying electron paramagnetic resonance spectroscopy to compare hydrated, dehydrated and NH3-saturated catalysts before and after hydrothermal aging, as well as density functional theory calculations, it is found that hydrothermal aging induces Cu relocation, leading to stronger Cu-support interactions. This is particularly evidenced by ZCuOH conversion to Z2Cu, which leads to the generation of a unique structure with two Cu(II) ions positioned in a double 6-membered ring prism. The Cu(II) ions that do not undergo such dramatic changes also appear to stay closer to framework windows as evidenced by the overall increased anisotropy during EPR measurements. In situ EPR measurements under SCR conditions demonstrate that, in comparison to the fresh catalyst, higher percentages of Cu species stay as Cu(II) in the aged catalyst. This suggests that the reduction half-cycle of the SCR redox, i.e., Cu(II) ? Cu(I), becomes slower for the hydrothermally aged catalyst.

42 ENGINEERING↗

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

Here we propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of constructing a very wide network while keeping the number of parameters low. Our theoretical analysis reveals that under suitable conditions, KNNs induce a faster decay of the loss than that by the feed-forward networks. This is also empirically verified through a set of computational examples. Furthermore, under certain technical assumptions, we establish global convergence of gradient descent for KNNs. As a specific case, we propose the Rowdy activation function that is designed to get rid of any saturation region by injecting sinusoidal fluctuations, which include trainable parameters. The proposed Rowdy activation function can be employed in any neural network architecture like feed-forward neural networks, Recurrent neural networks, Convolutional neural networks etc. The effectiveness of KNNs with Rowdy activation is demonstrated through various computational experiments including function approximation using feed-forward neural networks, solution inference of partial differential equations using the physics-informed neural networks, and standard deep learning benchmark problems using convolutional and fully-connected neural networks.

97 MATHEMATICS AND COMPUTING↗

Communication Limits Due to Photon-Detector Jitter

A theoretical and experimental study was conducted of the limit imposed by photon-detector jitter on the capacity of a pulse-position-modulated optical communication system in which the receiver operates in a photon-counting (weak-signal) regime. Photon-detector jitter is a random delay between impingement of a photon and generation of an electrical pulse by the detector. In the study, jitter statistics were computed from jitter measurements made on several photon detectors. The probability density of jitter was mathematically modeled by use of a weighted sum of Gaussian functions. Parameters of the model were adjusted to fit histograms representing the measured-jitter statistics. Likelihoods of assigning detector-output pulses to correct pulse time slots in the presence of jitter were derived and used to compute channel capacities and corresponding losses due to jitter. It was found that the loss, expressed as the ratio between the signal power needed to achieve a specified capacity in the presence of jitter and that needed to obtain the same capacity in the absence of jitter, is well approximated as a quadratic function of the standard deviation of the jitter in units of pulse-time-slot duration.

Moision, Bruce E.↗

The Effects of Spaceflight and Microgravity Exposure on Female Astronaut Health and Performance

Over the past half century, our understanding of the physiological effects of space exploration and microgravity exposure have improved immensely. Microgravity causes incredible changes to the human body that increase risk of injury upon return to Earth and lunar/planetary egress scenarios. This is due to deconditioning of the cardiovascular and skeletal muscle systems that reduce aerobic capacity and muscular strength. With upcoming exploration class missions, such as NASA’s Artemis lunar exploration program which aims to send the first female astronaut to the lunar surface by 2030, as well as a long-term goal of Martian exploration, maintaining astronaut health during extended-duration space flight is critical for achieving mission objectives. However, our understanding of these physiological implications due to microgravity are based primarily on flight studies of male astronauts and 1g bedrest analog study participants, with few investigations focusing specifically on females. Innate physiologic differences in endocrine signaling and reproductive function impact sex-dependent responses to various health conditions, treatments, and environmental factors in nearly every system in the body. Therefore, to assume comparable alterations in females in response to microgravity exposure may be inappropriate and consequentially, could lead to lasting impacts on female astronaut health and impact mission success. Moreover, differences in sex hormones may also influence the regulation of cardiovascular control during egress activity after space flight-induced deconditioning and blood volume loss (i.e., risk for orthostatic intolerance). Other potential physiological systems and factors related to musculoskeletal health and aerobic capacity that warrant investigation with respect to microgravity include endocrine/reproductive function, vascular control, bone mineral density/microarchitecture, and soft-tissue health. The purpose of this investigation is two-fold: 1) to summarize the data available from space flight and simulated bedrest analog exposures to begin addressing these gaps in knowledge regarding impacts to female astronaut health, and 2) to describe differences in demographic health characteristics, injury prevalence, and aerobic capacity and muscular strength in NASA female and male astronauts. Female astronauts make up 50% of Artemis-specific astronaut corps and the extent to which microgravity exposure impacts female cardiovascular and musculoskeletal health, and whether these alterations are consistent with their male counterparts, is inconclusive. With the growing inclusion of female astronauts in the NASA space program and the increased duration of missions beyond low Earth orbit, a greater understanding of the sex-specific adaptation to space travel will help determine the development of appropriate countermeasures for minimizing risk and maintaining health of all astronauts.

Nicole Christine Strock↗

The Effects of Space Flight and Microgravity Exposure on Female Astronaut Health and Performance

Over the past half century, our understanding of the physiological effects of space exploration and microgravity exposure have improved immensely. Microgravity causes incredible changes to the human body that increase risk of injury upon return to Earth and lunar/planetary egress scenarios. This is due to deconditioning of the cardiovascular and skeletal muscle systems that reduce aerobic capacity and muscular strength. With upcoming exploration class missions, such as NASA’s Artemis lunar exploration program which aims to send the first female astronaut to the lunar surface by 2030, as well as a long-term goal of Martian exploration, maintaining astronaut health during extended-duration space flight is critical for achieving mission objectives. However, our understanding of these physiological implications due to microgravity are based primarily on flight studies of male astronauts and 1g bed rest analog study participants, with few investigations focusing specifically on females. Innate physiologic differences in endocrine signaling and reproductive function impact sex-dependent responses to various health conditions, treatments, and environmental factors in nearly every system in the body. Therefore, to assume comparable alterations in females in response to microgravity exposure may be inappropriate and consequentially, could lead to lasting impacts on female astronaut health and impact mission success. Moreover, differences in sex hormones may also influence the regulation of cardiovascular control during egress activity after space flight-induced deconditioning and blood volume loss (i.e., risk for orthostatic intolerance). Other potential physiological systems and factors related to musculoskeletal health and aerobic capacity that warrant investigation with respect to microgravity include endocrine/reproductive function, vascular control, bone mineral density/microarchitecture, and soft-tissue health. The purpose of this investigation is two-fold: 1) to summarize the data available from space flight and simulated bed rest analog exposures to begin addressing these gaps in knowledge regarding impacts to female astronaut health, and 2) to describe differences in demographic health characteristics, injury prevalence, and aerobic capacity and muscular strength in NASA female and male astronauts. Female astronauts make up 50% of Artemis-specific astronaut corps and the extent to which microgravity exposure impacts female cardiovascular and musculoskeletal health, and whether these alterations are consistent with their male counterparts, is inconclusive. With the growing inclusion of female astronauts in the NASA space program and the increased duration of missions beyond low Earth orbit, a greater understanding of the sex-specific adaptation to space travel will help determine the development of appropriate countermeasures for minimizing risk and maintaining health of all astronauts.

Female Astronaut↗

The Effects of Space Flight and Microgravity Exposure on Female Astronaut Health and Performance

Over the past half century, our understanding of the physiological effects of space exploration and microgravity exposure have improved immensely. Microgravity causes incredible changes to the human body that increase risk of injury upon return to Earth and lunar/planetary egress scenarios. This is due to deconditioning of the cardiovascular and skeletal muscle systems that reduce aerobic capacity and muscular strength. With upcoming exploration class missions, such as NASA’s Artemis lunar exploration program which aims to send the first female astronaut to the lunar surface by 2030, as well as a long-term goal of Martian exploration, maintaining astronaut health during extended-duration space flight is critical for achieving mission objectives. However, our understanding of these physiological implications due to microgravity are based primarily on flight studies of male astronauts and 1g bed rest analog study participants, with few investigations focusing specifically on females. Innate physiologic differences in endocrine signaling and reproductive function impact sex-dependent responses to various health conditions, treatments, and environmental factors in nearly every system in the body. Therefore, to assume comparable alterations in females in response to microgravity exposure may be inappropriate and consequentially, could lead to lasting impacts on female astronaut health and impact mission success. Moreover, differences in sex hormones may also influence the regulation of cardiovascular control during egress activity after space flight-induced deconditioning and blood volume loss (i.e., risk for orthostatic intolerance). Other potential physiological systems and factors related to musculoskeletal health and aerobic capacity that warrant investigation with respect to microgravity include endocrine/reproductive function, vascular control, bone mineral density/microarchitecture, and soft-tissue health. The purpose of this investigation is two-fold: 1) to summarize the data available from space flight and simulated bed rest analog exposures to begin addressing these gaps in knowledge regarding impacts to female astronaut health, and 2) to describe differences in demographic health characteristics, injury prevalence, and aerobic capacity and muscular strength in NASA female and male astronauts. Female astronauts make up 50% of Artemis-specific astronaut corps and the extent to which microgravity exposure impacts female cardiovascular and musculoskeletal health, and whether these alterations are consistent with their male counterparts, is inconclusive. With the growing inclusion of female astronauts in the NASA space program and the increased duration of missions beyond low Earth orbit, a greater understanding of the sex-specific adaptation to space travel will help determine the development of appropriate countermeasures for minimizing risk and maintaining health of all astronauts.

Female Astronaut↗

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon

Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. In this study, we have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗

Armstrong Laboratory Space Visual Function Tester Program

Viewgraphs on space visual function tester program are presented. Many astronauts and cosmonauts have commented on apparent changes in their vision while on-orbit. Comments have included descriptions of earth features and objects that would suggest enhanced distance visual acuity. In contrast, some cosmonaut observations suggest a slight loss in their object discrimination during initial space flight. Astronauts have also mentioned a decreased near vision capability that did not recover to normal until return to earth. Duntley space vision experiment, USSR space vision experiments, and visual function testers are described.

Oneal, Melvin R.↗

Cooling Properties of the Shuttle Advanced Crew Escape Spacesuit: Results of an Environmental Chamber Experiment

The shuttle crew wears the Advanced Crew Escape Spacesuit (ACES) to protect themselves from cabin decompression and to support bail out during landing. ACES is cooled by a liquid-cooled garment (LCG) that interfaces to a heat exchanger that dumps heat into the cabin. The ACES outer layer is made of Gore-Tex(Registered TradeMark), permitting water vapor to escape while containing oxygen. The crew can only lose heat via insensible water losses and the LCG. Under nominal landing operations, the average cabin temperature rarely exceeds 75 F, which is adequate for the ACES to function. Problem A rescue shuttle will need to return 11 crew members if the previous mission suffers a thermal protection system failure, preventing it from returning safely to Earth. Initial analysis revealed that 11 crew members in the shuttle will increase cabin temperature at wheel stop above 80 F, which decreases the ACES ability to keep crew members cool. Air flow in the middeck of the shuttle is inhomogeneous and some ACES may experience much higher temperatures that could cause excessive thermal stress to crew members. Methods A ground study was conducted to measure the cooling efficiency of the ACES at 75 F, 85 F, and 95 F at 50% relative humidity. Test subjects representing 5, 50, and 95 percentile body habitus of the astronaut corps performed hand ergometry keeping their metabolic rate at 400, 600, and 800 BTU/hr for one hour. Core temperature was measured by rectal probe and skin, while inside and outside the suit. Environmental chamber wall and cooling unit inlet and outlet temperatures were measured using high-resolution thermistors ( 0.2 C). Conclusions Under these test conditions, the ACES was able to protect the core temperature of all test subjects, however thermal stress due to high insensible losses and skin temperature and skin heat flow may impact crew performance. Further research should be performed to understand the impact on cognitive performance.

Hamilton, Douglas↗

Boric acid removal with polyol-functionalized polyether membranes

Poor selectivity of conventional desalination membranes for boron often necessitates multi-stage treatment trains to achieve desired boron removal for end uses such as irrigation. One approach to membrane design for improved single-pass boric acid removal is via incorporation of chelating ligands that selectively sorb boron. In this study, membranes based on epoxy-amine cross-linked poly(glycidyl glycidyl ether) (PGGE) were synthesized and functionalized with N-methyl-d-glucamine (NMDG), a polyol known to interact selectively with boron. PGGE and PGGE-NMDG membranes exhibited boron sorption isotherms that were well-described by dual mode isotherms. PGGE-NMDG sorbed 2.5 mmol B/g dry polymer from a neutral aqueous solution containing 100 mmol B/L, which was almost three times the adsorption density of a commercial boron selective resin, Amberlite IRA743. Further, the membranes were regenerated in acid without a significant loss of boron sorption capacity over four cycles. Interactions between boron and NMDG and PGGE sites (e.g., epoxides) impacted boron diffusion in both membranes. The use of ligand functionalized membranes to capture target solutes such as boron requires high loading of interacting sites to maximize uptake capacity. Establishing fundamental structure/property rules for boron selectivity could lead to new material designs with improved boron separation properties for water purification.

36 MATERIALS SCIENCE↗

Calculation of the Thermodynamic Voltage Limit of CdSeTe Solar Cells

The first step to understand the origin of losses in any photovoltaic solar cell is to determine the fundamental thermodynamic efficiency and voltage limits of such a device. In this contribution, we detail techniques to calculate the voltage limit in the case of cadmium selenium telluride (CdSeTe) solar cells, and how approaches based on bandgap alone—i.e., the Shockley-Queisser approach with step-function absorptance—can overestimate the thermodynamic open-circuit voltage limit Voc,ideal . This is particularly true for arsenic-doped samples, which tend to exhibit below-bandgap absorptance.

absorptance↗

Functional fiber-optic sensors embedded in stainless steel components using ultrasonic additive manufacturing for distributed temperature and strain measurements

The nuclear industry is progressing toward microreactors that can be factory assembled and deployed to remote regions for reliable, scalable power generation. However, the reduced power output requires enhanced monitoring capabilities to reduce staffing and eventually move toward autonomous control to improve the economics of microreactors. The ability to embed sensors such as fiber-optics, which can provide spatially distributed temperature and strain measurements, within microreactor components for real-time health monitoring would be particularly advantageous. Recent advances in ultrasonic additive manufacturing (UAM) have demonstrated the successful embedding of fiber-optics in soft materials such as Al and Cu by placing the sensors in machined cavities and ultrasonically welding over the top with thin foils. This article reports the first successful embedment of fiber-optic sensors and thermocouples within a common nuclear reactor material, SS304, via UAM. UAM parameters were first explored with simple plate geometries before moving to more complex geometries, such as pipes and other test articles for heat pipe–based microreactors. Select samples were sectioned for microscopy to evaluate the sensor/foil and foil/foil interfaces from samples fabricated by using 100% SS304 foils vs. foils plated with a Ni coating to improve UAM bonding. Furthermore, embedding metal-coated, low-bend loss fibers resulted in greatly reduced signal attenuation and adequate compressive residual strain in the embedded region to ensure successful strain coupling. Pipe specimen functional testing was performed by monitoring temperature and strain during transient and steady-state thermal testing.

36 MATERIALS SCIENCE↗

High temperature elastic properties of sub-stoichiometric yttrium dihydrides

Yttrium hydrides are considered as candidate materials for neutron moderation applied in microreactors (akin transportable tiny nuclear reactors) owing to their superior thermal stability and hydrogen retention. The evolution of elastic properties of these materials at elevated temperatures, needed for predicting the thermomechanical response and performance of the moderator during in-service reactor conditions, however, is lacking. Here, we report the Young’s and shear elastic moduli of three stoichiometries of bulk yttrium hydride (YH x , x = 1.61, 1.82, and 1.84) from room temperature to 1000°C. In situ temperature-dependent measurements of the longitudinal and shear wave velocities were performed using a laser ultrasonic technique while heating the sample in a vacuum-pumped heating stage. The elastic moduli increased linearly with increasing hydrogen content and decreased by ~10% during heating from room temperature to 1000°C in the three YH x compositions. The linear relationship between the elastic moduli and the hydrogen content in yttrium hydride was verified by atomistic calculations based on density functional theory (DFT). The absence of abrupt changes in the temperature-dependent measurements of elastic modulus of the YH x samples suggested negligible loss of hydrogen at elevated temperatures. Excellent agreement was found between the measured and calculated dependence of the elastic moduli on the stoichiometry, thereby providing a new approach for investigating the effects of fabrication-induced parameters (such as porosity) on the elastic moduli. Furthermore, this study demonstrates the utility of the combined approach involving DFT-based atomistic calculations and measurements of the elastic moduli for the informative development of metal hydrides and can be used as a metric for novel moderator materials investigations for emerging microreactors and beyond.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Revealing the Origin and Nature of the Buried Metal‐Substrate Interface Layer in Ta/Sapphire Superconducting Films

Abstract Despite constituting a smaller fraction of the qubit's electromagnetic mode, surfaces and interfaces can exert significant influence as sources of high‐loss tangents, which brings forward the need to reveal properties of these extended defects and identify routes to their control. Here, we examine the structure and composition of the metal‐substrate interfacial layer that exists in Ta/sapphire‐based superconducting films. Synchrotron‐based X‐ray reflectivity measurements of Ta films, commonly used in these qubits, reveal an unexplored interface layer at the metal‐substrate interface. Scanning transmission electron microscopy and core‐level electron energy loss spectroscopy identified an intermixing layer (≈0.65 ± 0.05 nm) at the metal‐substrate interface containing Al, O, and Ta atoms. Density functional theory modeling reveals that the structure and properties of the Ta/sapphire heterojunctions are determined by the oxygen content on the sapphire surface prior to Ta deposition for two atomic terminations of sapphire. Using a multimodal approach, we gained deeper insights into the interface layer between the metal and substrate, which suggests that the orientation of deposited Ta films depend on the surface termination of sapphire. The observed elemental intermixing at the metal‐substrate interface influences the thermodynamic stability and electronic behavior of the film, which may also affect qubit performance.

36 MATERIALS SCIENCE↗

Microbial drought resistance may destabilize soil carbon

Droughts are becoming more frequent and intense with climate change. As plants and microbes respond to drought, there may be consequences for the vast stocks of organic carbon stored in soils. If microbes sustain their activity under drought, soils could lose carbon, especially if inputs from plants decline. Empirical and theoretical studies reveal multiple mechanisms of microbial drought resistance, including tolerance and avoidance. Physiological responses allow microbes to acclimate to drought within minutes to days. Along with dispersal, shifts in community composition could allow microbiomes to maintain functioning despite drought. Microbes might also adapt to drier conditions through evolutionary processes. Together, these mechanisms could result in soil carbon losses larger than currently anticipated under climate change.

54 ENVIRONMENTAL SCIENCES↗

Focused Electron Beam Induced Deposition Synthesis of 3D Photonic and Magnetic Nanoresonators

While many plasmonic phenomena have been realized by using standard nanoscale synthesis in a single 2-dimensional plane, enhanced functionality should be possible by extending into the third dimension. Several nanoscale synthesis approaches have been explored to achieve 3-dimensional (3d) geometries; however, a robust strategy for synthesizing complex 3d plasmonic architectures is lacking. In this study, we utilize a hybrid of direct-write 3d nanoprinting and thin film deposition to fabricate 3d plasmonic structures. Focused electron beam induced deposition (FEBID) is used to deposit nonplasmonic 3d scaffolds, which are subsequently isolated with a conformal SiO 2 layer and coated with a gold layer to create functional 3d plasmonic nanostructures. A variety of rod antennae, split-ring nanoresonators, and ring resonators are synthesized, and low-loss electron energy loss spectroscopy (EELS) is utilized to characterize their full plasmonic spectra with nanoscale resolution. Complementary EELS simulations are performed to interpret the spectra and elucidate the associated electric and magnetic field distributions of the infrared and near optical modes. This work demonstrates the flexibility that FEBID scaffolds offer for the advancement of 3d plasmonic devices and future advanced optical and magnetic metamaterials.

3d printing↗

Quantifying the Effect of Magnetic Field Line Curvature Scattering on the Loss of Ring Current Ions

During geomagnetic storms, the ring current ions sometimes exhibit rapid loss as suggested by the fast recovery of the Dst index on a time scale of a few hours. Here, the effects of magnetic field line curvature (FLC) scattering on the loss of ring current ions, which have not been well quantified, are studied here by test particle simulations under the T89c magnetic field model. Our simulation results show that the prediction of ion loss based on a single–value cutoff of the κ parameter or maximum of δμ/μ of a single FLC scattering is not accurate. Instead, the e–folding lifetime (τ) for the loss of ring current ions due to cumulative FLC scattering has been calculated for different initial ion energies, equatorial pitch angles, and L shells under different geomagnetic conditions. The results show that in general the FLC scattering loss is faster for ions of higher energy, higher mass, smaller pitch angle, higher L, and at high Kp level. Specifically, we find that at Kp = 6 the lifetime can be <10 h at L > 5 for 100 s keV protons and at L > 4 for 100 s keV O + , which demonstrates that FLC scattering can be an important mechanism for the observed fast loss (τ < 10 h) of ring current ions during geomagnetic storms. Furthermore, we formulate an empirical formula for τ as a function of ion energy, pitch angle, position, species, and Kp. The empirical formula can be directly included in ring current models to account for the FLC scattering effects.

79 ASTRONOMY AND ASTROPHYSICS↗