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H2, fixed architecture, control design for large scale systems

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Mercadal, Mathieu↗

CRICKET: Cryogenic Reservoir Inventory by Cost-Effective Kinetically Enhanced Technology

NASA PROGRAMMATIC CHALLENGE: Locate hidden water ice in the darkest, coldest places on the moon using dozens of simple, autonomous robots. CONCEPTUAL SOLUTION: Use multiple small, autonomous bots to search for hidden water ice in permanently shadowed regions of the surface of the moon. Bots will locate and tag hidden water ice for follow up missions.Technical Basis for proposed solution: use of emerging and maturing technologies - MEMS, Cubesats, Sensor nets, integrated devices – will minimize cost risk and maximize return. Benefits: Cricket will enable human exploration through in-situ resource utilization: Cricket will demonstrate a distributed constellation to achieve a key NASA goal of novel uses of commercially available technologies. Cricket will reignite public interest in lunar exploration through a sustained human, and robotic, presence on the moon. Technical Approach: The cricket constellation has three members: the "queen"; the "hive" and the "cricket" foragers. The queen transports the hive an its crickets to the moon. The hive lands on the surface and disperses the crickets (there may be more than one species of cricket). The crickets then use the hive as a communications and recharging hub. Each cricket hosts algorithms that allow it to explore its surroundings and monitor its power state - something like a lunar Roomba - and return for recharging. If they are lost due to power or surface condition problems, replacements can carry out the hive tasks. The two most successful types of bio-inspired algorithms (BIAs) are evolutionary algorithms and swarm-based algorithms which are inspired by the natural evolution and collective behavior in animals.The evolution of the idea is summarized in Table 1 and Figure 1. NIAC context: This system integrates key elements from other NIAC efforts; it uses them and extends them into a meaningful whole

Cryogenics↗

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗

OGLE-2018-BLG-1011Lb,c: Microlensing Planetary System with Two Giant Planets Orbiting a Low-mass Star

We report a multiplanetary system found from the analysis of microlensing event OGLE-2018-BLG-1011, for which the light curve exhibits a double-bump anomaly around the peak. We find that the anomaly cannot be fully explained by the binary-lens or binary-source interpretations and its description requires the introduction of an additional lens component. The 3L1S (three lens components and a single source) modeling yields three sets of solutions, in which one set of solutions indicates that the lens is a planetary system in a binary, while the other two sets imply that the lens is a multiplanetary system. By investigating the fits of the individual models to the detailed light curve structure, we find that the multiple-planet solution with planet-to-host mass ratios ∼9.5 X 10(exp −3) and ∼15 X 10(eap −3) are favored over the other solutions. From the Bayesian analysis, we find that the lens is composed of two planets with masses 1.8 (sup +3.4, sub -1.1) M(J) and 2.8 (sup +5.8, sub -1.7) M(J) around a host with a mass 0.18 (sup +0.33,sub - 0.10) M(ʘ) and located at a distance 7.1(sup +1.1, sub -1.5) kpc. The estimated distance indicates that the lens is the farthest system among the known multiplanetary systems. The projected planet–host separations are a(⊥,2) = 1.8 (sup +2.1, sub -1.5)au (0.8 (sup +0.9,sub -0.6 au) and a(⊥,3) = 0.8 (sup +0.9, sub -0.6)au , where the values of a(⊥,2) inside and outside the parenthesis are the separations corresponding to the two degenerate solutions, indicating that both planets are located beyond the snow line of the host, as with the other four multiplanetary systems previously found by microlensing.

Cheongho Han↗

Improved Coupled Z-R and k-R Relations and the Resulting Ambiguities in the Determination of the Vertical Distribution of Rain from the Radar Backscatter and the Integrated Attenuation

Several algorithms to calculate a rain-rate profile from a single-frequency air-or spaceborne radar backscatter profile and a given path-integrated attenuation have been proposed. The accuracy of any such algorithm is limited by the ambiguities between the (multiple) exact solutions, which depend on the variability of the parameters in the Z-R and k-R relations used. In this study, coupled Z-R and k-R relations are derived based on the drop size distribution. It is then shown that, because of the coupling, the relative difference between the multiple mutually ambiguous rain-rate profiles solving the problem must remain acceptably low, provided the available path-integrated attenuation value is known to within 0.5 dB.

Haddad, Z. S.↗

GPU acceleration of hybrid functional calculations in the SPARC electronic structure code

We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing hybrid functional calculations in generalized Kohn–Sham density functional theory. In particular, we develop a batch variant of the recently formulated Kronecker product-based linear solver for the simultaneous solution of multiple linear systems. We then develop a modular, math kernel based implementation for hybrid functionals on NVIDIA architectures, where computationally intensive operations are offloaded to the GPUs, while the remaining workload is handled by the central processing units (CPUs). Considering bulk and slab examples, we demonstrate that GPUs enable up to 8× speedup in node-hours and 80× in core-hours compared to CPU-only execution, reducing the time to solution on V100 GPUs to around 300 s for a metallic system with over 6000 electrons, and significantly reducing the computational resources required for a given wall time.

Kohn-Sham density functional theory↗

Generalized Reference Targeting for Spaceflight

For spaceflight programs to achieve some of the aggressive exploration initiatives such as visiting and landing on other celestial bodies, rendezvousing with other orbiting vehicles, and ultimately returning crew safely to Earth, an assortment of targeting algorithms to compute the necessary burns to strategically maneuver a spacecraft to a variety of destinations are required. Numerous examples exist, but rather than creating and implementing multiple targeting solutions, is it possible to have a general targeting model that can accommodate a variety of applications? Originally motivated for mission design and analysis purposes, this paper outlines a generalized reference targeting algorithm for spaceflight that may also have applications in on-orbit flight software. It accommodates arbitrary flight dynamics and both impulsive and finite burns for either absolute or relative targeting applications. It also allows for an arbitrary number of targeting design parameters such as multiple discrete correction burns or finite thrust parameters to satisfy numerous combinations of targeting constraints that can have fixed or variable time epochs. Given a reference trajectory, this targeting technique provides a general framework to quickly solve an assortment of targeting problems that may be well-defined, over-determined, or under-determined while naturally producing metrics providing insight into the controllability for a given problem formulation. Due to the derivation, speed, and accuracy of the algorithm, it lends to supporting rapid linear covariance analysis and robust trajectory design applications for a variety of flight phases such as rendezvous and docking, cislunar transfer, interplanetary flight, orbit maintenance, de-orbit, and powered descent and landing.

Targeting↗

Lunar Node – 1: Initial Flight Results and the Role of Surface Psuedolites in Lunar Navigation

On February 22, 2024, the Intuitive Machines IM-1 NOVA-C lander, nick-named Odysseus, landed on the lunar surface, carrying with it a cadre of NASA scientific and technology demonstration payloads. These payloads and missions marked the first delivery of NASA instruments to operate from the lunar surface since the Apollo landings. One of these payloads is Lunar Node -1 (LN-1), a navigation beacon demonstration mission. The payload was designed and built by NASA’s Marshall Space Flight Center. The payload’s main goal was to demonstrate and provide insight into the use of lunar surface-based radio navigation aids. As part of the mission, LN-1 successfully conducted multiple one-way transmissions from the NOVA-C vehicle to Deep Space Network ground receivers using its onboard S-band transmitter, while being disciplined by an onboard Space Chip Scale Atomic Clock. LN-1 transmitted to DSN on an almost daily basis during transit to the moon, including two surface passes. The payload was originally plan to conduct 7-10 days of surface operation as an always-on beacon. These passes focused on evaluating two main navigation approaches: performance and stability of ranging using time-based transfer techniques on a cubesat size and grade platform, as well as one-way psuedonoise ranging approaches. To assess performance, the measurements were compared to independent navigation solutions using multiple approaches including: one-way Doppler tracking, two-way Doppler Tracking, and visual verification of the landing location provided by visual observations from orbital platforms. While the mission only conducted limited surface operations, the data provides some initial insight to performance form the lunar surface. These results are compared with initial ground-based testing as well as continued evaluation of the flight-space platform using multiple grades of oscillators for maintaining clock and frequency stability. These focus on the timing stability of platform in a deep-space environment as well variations in state determination. Given these insights, this paper provides additional description and evaluation of how this approach can be utilized as part of a broader lunar navigation architecture, such as being developed and deployed across multiple international space agencies. Analysis is provided to develop overall timing requirements and assessment of operational scenarios, such as orbit and surface location determination. In addition, the results support discussion as to how surface pseudolites could best be used within existing standard signal definitions, such as defined in the LunaNet Interoperability Specifications. This will consider concerns such as the near-/far- problem as well as operational considerations, including whether a beacon is better suited as two- or one-way ranging platform. The use cases are focused on how these psuedolites can provide additional coverage to augment and support planned operational coverage. For example, this analysis provides analysis of mid-latitude surface missions, where there may be limited geometry and availability of orbital relays. The results will show how these navigation psuedolites can fit within the developing architecture to provide additional robustness, capability, and support multiple use cases. Lastly, the paper will discuss challenges and next steps to be addressed in the implementation and testing of a follow-on payload and a continued path towards demonstration and integration of this capability into Lunar PNT architectures.

Evan Anzalone↗

Lunar Node – 1: Initial Flight Results and the Role of Surface Psuedolites in Lunar Navigation

On February 22, 2024, Intuitive Machines NOVA-C lander, nick-named Odysseus, landed on the lunar surface, carrying with it a cadre of NASA scientific and technology demonstration payloads. These payloads and missions marked the first delivery of NASA instruments to operate from the lunar surface since the Apollo landings. One of these payloads is Lunar Node -1 (LN-1), a navigation beacon demonstration mission. The payload was designed and built by NASA’s Marshall Space Flight Center. The payload’s main goal was to demonstrate and provide insight into the use of lunar surface-based radio navigation aids. As part of the mission, LN-1 successfully conducted multiple one-way transmissions from the NOVA-C vehicle to Deep Space Network ground receivers using its onboard S-band transmitter, while being disciplined by an onboard Space Chip Scale Atomic Clock. LN-1 transmitted to DSN on an almost daily basis during transit to the moon, including two surface passes. The payload was originally plan to conduct 7-10 days of surface operation as an always-on beacon. These passes focused on evaluating two main navigation approaches: performance and stability of ranging using time-based transfer techniques on a cubesat size and grade platform, as well as one-way psuedonoise ranging approaches. To assess performance, the measurements were compared to independent navigation solutions using multiple approaches including: one-way Doppler tracking, two-way Doppler Tracking, and visual verification of the landing location provided by visual observations from orbital platforms. While the mission only conducted limited surface operations, the data provides some initial insight to performance form the lunar surface. These results are compared with initial ground-based testing as well as continued evaluation of the flight-space platform using multiple grades of oscillators for maintaining clock and frequency stability. These focus on the timing stability of platform in a deep-space environment as well variations in state determination. Given these insights, this paper provides additional description and evaluation of how this approach can be utilized as part of a broader lunar navigation architecture, such as being developed and deployed across multiple international space agencies. Analysis is provided to develop overall timing requirements and assessment of operational scenarios, such as orbit and surface location determination. In addition, the results support discussion as to how surface pseudolites could best be used within existing standard signal definitions, such as defined in the LunaNet Interoperability Specifications. This will consider concerns such as the near-/far- problem as well as operational considerations, including whether a beacon is better suited as two- or one-way ranging platform. The use cases are focused on how these psuedolites can provide additional coverage to augment and support planned operational coverage. For example, this analysis provides analysis of mid-latitude surface missions, where there may be limited geometry and availability of orbital relays. The results will show how these navigation psuedolites can fit within the developing architecture to provide additional robustness, capability, and support multiple use cases. Lastly, the paper will discuss challenges and next steps to be addressed in the implementation and testing of a follow-on payload and a continued path towards demonstration and integration of this capability into Lunar PNT architectures.

Evan J Anzalone↗

Geometry-aware framework for deep energy method: An application to structural mechanics with hyperelastic materials

Here, in this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) for solving structural mechanics problems on different geometries. As the weak form of the physical system equation (or the energy-based approach) has demonstrated clear advantages compared to the strong form for solving solid mechanics problems, GADEM employs the weak form and aims to infer the solution on multiple shapes of geometries. Integrating a geometry-aware framework into an energy-based method results in an effective physics-informed deep learning model in terms of accuracy and computational cost. Different ways to represent the geometric information and to encode the geometric latent vectors are investigated in this work. We introduce a loss function of GADEM which is minimized based on the potential energy of all considered geometries. An adaptive learning method is also employed for the sampling of collocation points to enhance the performance of GADEM. We present some applications of GADEM to solve solid mechanics problems, including a loading simulation of a toy tire involving contact mechanics and large deformation hyperelasticity. The numerical results of this work demonstrate the remarkable capability of GADEM to infer the solution on various and new shapes of geometries using only one trained model.

97 MATHEMATICS AND COMPUTING↗

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗

Moon Base Transportation - Deliveries to the Lunar Surface

Development of the Moon Base will enable a home away from home for astronauts who will live and work at humanity’s first lunar outpost. In this effort, NASA’s Moon Transportation Office is responsible for enabling the transformational missions required to deliver habitats, supplies, science payloads, and all other elements needed to cultivate a permanent presence on the Lunar Surface. The Mission Concept (MC) is characterized through evaluation of an end-to-end architecture that can successfully deliver a generalized heavy large-volume payload, in excess of 4000 kg, to a precision landing and touchdown on the lunar surface. The mission architecture utilizes a single launch configuration of a Lunar Lander (LL) with a unique propellant system. The LL has an integral orbital transfer capability and features jettisonable elements. The design circumvents the need for prop transfer on orbit and multiple launch configurations. The launch vehicle (LV) for this work will assume the capability to deliver a payload in excess of 40,000 kg to orbit, affording multiple LV solutions. Considerations for the LL and payload deployment from the fairing are assumed to be handled through compliance with a launch providers’ Interface Requirements Document (IRD). The MC will span from launch at Kennedy Space Center (KSC) to terminal descent and touchdown on the lunar surface, requiring a total ΔV on the order of 6 km/s beyond what is required to get the vehicle stack to a 200 km circular Low Earth Orbit (LEO). Major mission phases include: launch and launch vehicle separation, transfer operations, pre-landing navigation, and lunar descent and touchdown. A Concept of Operations (ConOps) is used as the primary design driver for defining architecture of the vehicles necessary to achieve final payload delivery. Numerous ground rules and assumptions will be provided for each phase of the mission. Concept designs for the LL is presented. An emphasis of the design maximizes a feasible path for maturation, manufacturing, and operation. A self-imposed practical consideration for this effort is the incorporation of legacy designed hardware to minimize expensive, time-intensive, and high-risk hardware development cycles. The propulsion system of the LL adopts a conventional storable bipropellant configuration of monomethyl hydrazine (MMH) and mixed oxides of nitrogen (MON3). This effort will showcase a unique propellant delivery system to minimize the reliance on propellant management devices (PMDs) during descent. Numerous key constraints have been considered, across the multiple segments of the mission. These include the unique aspects of center of gravity (CG) management, thruster plume effects including self-impingement, propulsion system hardware limitations, navigation during multiple mission phases, and landing gear geometry for uneven terrain. These constraints shape the trades necessary for precision landing of heavy cargo and ensure compatibility with broader Moon Base Transportation concepts. The resulting insights inform future transportation strategies for the Moon and beyond; directly contributing to the development of cargo‑delivery standards that will support the long‑term buildup of a sustainable, continuously inhabited Moon Base.

Lunar Habitat↗

Simulation of Multiphase Flow and Poromechanical Effects Around Injection Wells in CO 2 Storage Sites

In geological CO 2 storage operations, wellbore deformations and leakage pathways formations can occur around injection and abandoned wells subjected to high rates and long-term CO 2 injection. To guide engineering design and prevent CO 2 leakage risks, a full understanding of the underlying physics and robust numerical models is necessary to evaluate the response of underground formations in the near wellbore region and in the reservoir. In this study, a multi-scale and multi-physics open-source simulator (GEOS) is used to simulate multiphase flow and poromechanical deformations over time in three dimensions. The governing equations for mechanical deformations of the rock body and multiphase compositional fluid flow within the rock matrix are solved with a fully coupled finite element and finite volume approach. The Drucker–Prager model with friction hardening is applied to simulate elastoplastic deformation and a multiphase fluid model with power-law correlations for relative permeability is used to model the migration of CO 2 plume, which are coupled with numerical implicit scheme. Simulation results are verified against multiple analytical solutions for multiphase flow and wellbore problems, thus demonstrating the accuracy of this advanced simulator. In two engineering applications, here we highlight the impact of elastoplastic deformation and coupled modeling for assessing induced displacements and stress perturbations, which are more pronounced in the near wellbore regions. This work focuses on short-term processes in the vicinity of injection wells where stress evolutions, rock deformations and multiphase compositional flow and transport are simulated jointly to ensure wellbore stability and prevent damage. This fully coupled geomechanical model can simulate multiphase flow and any associated poromechanical effects within the CO 2 storage site and in the surrounding formations. Such a large-scale, long-term, multi-physics simulation model is useful in many ways: it can guide operational decisions for CO 2 injection, assess the containment potential and risks of a site, and analyze the wellbore stability and integrity during and after CO 2 injection.

58 GEOSCIENCES↗

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

Quantifying dispersity in size and shape of nanoparticles from small-angle scattering data using machine learning based CREASE

Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Supporting Special Values in ZFP

This white paper outlines potential approaches to supporting special values in the ZFP numerical compressor without breaking backwards compatibility. Other than infinities and NaNs, special values are often used to indicate the absence of data, where no value is defined, for example by designating finite but extreme “fill values” as special. Such fill values are commonly used in earth system science, among other applications, but if left as is during compression lead to artifacts and loss of precision in nearby true values. Multiple candidate solutions that would allow ZFP to recognize special values are here proposed. Until such support is available, we also sketch available workarounds.

97 MATHEMATICS AND COMPUTING↗

Micro-Hydropower and Aquatic Restoration on Lands of the Eastern Band of Cherokee Indians

Rural and Tribal communities in Southern Appalachia face persistent challenges in energy access owing to rugged terrain, dense forest cover, and limited infrastructure. The Eastern Band of Cherokee Indians (EBCI) is a federally recognized Tribe whose ancestral homelands include much of Southern Appalachia. The Tribe’s present-day homeland, termed the Qualla Boundary, lies in the heart of the region, where the extreme ruggedness of the Blue Ridge Mountains exacerbates challenges to energy access. For the EBCI, these challenges also intersect with a deep cultural commitment to stewardship of land and water. The Tribe has explored multiple energy solutions, with hydropower serving as an existing and realized source of energy for the region’s communities. However, the EBCI’s commitment to protecting aquatic systems has led not only to a historical lack of endorsement of new conventional hydropower on Tribal lands but also to ongoing efforts to remove the area’s only existing hydropower facility at Ela Dam.

13 HYDRO ENERGY↗

Multiple scattering calculation of the middle ultraviolet reaching the ground

An investigation is conducted regarding the increase in the UV radiation as a function of wavelength due to changes in the amounts of ozone and various other parameters affecting the radiation in the atmosphere. Attention is given to the methods that can be used to solve the problem of the transfer of radiation through an absorbing and scattering atmosphere which includes aerosols. The multiple channel solution reported by Mudgett and Richards' (1971) is extended to vertically inhomogeneous atmospheres.

Shettle, E. P.↗