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NASA NTRS2017

Water-Leaving Contribution to Polarized Radiation Field Over Ocean

The top-of-atmosphere (TOA) radiation field from a coupled atmosphere-ocean system (CAOS) includes contributions from the atmosphere, surface, and water body. Atmo-spheric correction of ocean color imagery is to retrieve water-leaving radiance from the TOA measurement, from which ocean bio-optical properties can be obtained. Knowledge of the ab-solute and relative magnitudes of water-leaving signal in the TOA radiation field is important for designing new atmospheric correction algorithms and developing retrieval algorithms for new ocean biogeochemical parameters. In this paper we present a systematic sensitivity study of water-leaving contribution to the TOA radiation field, from 340 nm to 865 nm, with polarization included. Ocean water inherent optical properties are derived from bio-optical models for two kinds of waters, one dominated by phytoplankton (PDW) and the other by non-algae particles (NDW). In addition to elastic scattering, Raman scattering and fluorescence from dissolved organic matter in ocean waters are included. Our sensitivity study shows that the polarized reflectance is minimized for both CAOS and ocean signals in the backscattering half plane, which leads to numerical instability when calculating water leaving relative contribution, the ratio between polarized water leaving and CAOS signals. If the backscattering plane is excluded, the water-leaving polarized signal contributes less than 9% to the TOA polarized reflectance for PDW in the whole spectra. For NDW, the polarized water leaving contribution can be as much as 20% in the wavelength range from 470 to 670 nm. For wavelengths shorter than 452 nm or longer than 865 nm, the water leaving contribution to the TOA polarized reflectance is in general smaller than 5% for NDW. For the TOA total reflectance, the water-leaving contribution has maximum values ranging from 7% to 16% at variable wavelengths from 400 nm to 550 nm from PDW. The water leaving contribution to the TOA total reflectance can be as large as 35%for NDW, which is in general peaked at 550 nm. Both the total and polarized reflectances from water-leaving contributions approach zero in the ultraviolet and near infrared bands. These facts can be used as constraints or guidelines when estimating the water leaving contribution to the TOA reflectance for new atmospheric correction algorithms for ocean color imagery.

inelastic scatterin↗

NASA NTRS1995

Theoretical overview and modeling of the sodium and potassium atmospheres of mercury

A general theoretical overview for the sources, sinks, gas-surface interactions, and transport dynamics of sodium and potassium in the exospheric atmsophere of Mercury is given. Information for these four factors, which control the spatial distribution of these two alkali-group gases about the planet, is incorporated in numerical models. The spatial nature and relative importance of the initial source atom atmosphere and the ambient (ballistic hopping) atom atmosphere are then examined and are shown to be controlled and coupled to a great extent by the extremely large and variable solar radiation acceleration experienced by sodium and potassium as they resonantly scatter solar photons. The lateral (antisunward) transport rate of thermally accommodated sodium and potassium ambient atoms is shown to be driven by the solar radiation acceleration and, over a significant portion of Mercury's orbit about the Sun, is sufficiently rapid to be competitive with the short photoionization lifetimes for these atoms when they are located on the summit surface near or within about 30 deg of the terminator. The lateral transport rate is characterized by a migration time determined by model calculations for an ensemble of atoms initially starting at a point source on the surface (i.e., a numerical spacetime dependent Green's function). Four animations for the spacetime evolution of the sodium (or potassium) atmosphere produced by a point source on the surface are presented on a videotape format. For extended surface sources for sodium and potassium, the local column density is determined by competition between the photoionization lifetimes and the lateral transport times of atoms originating from different surface source locations. Sodium surface source fluxes (referenced to Mercury at perihelion) that are required on the sunlit hemisphere to reproduce the typically observed several megarayleighs of D2 emission-line brightness and the inferred column densities of 1-2 x 10(exp 11) atoms per sq cm range from approximately 2-5 x 10(exp 7) atoms/sq cm/sec. The sodium model is applied to study observational data that document an anticorrelation in the average sodium column density and solar radiation acceleration. Lateral transport driven by the solar radiation acceleration is shown to produce this behavior for combinations of different sources and surface accomodation coefficients. The best fit model fits to the observational data require a significant degree of thermal accommodation of the ambient sodium atoms to the surface and a source rate that decreases as an inverse power of 1.5 to 2 in heliocentric distance.

Smyth, William H.↗

DOE OSTI2022

Symmetry relation database and its application to ferroelectric materials discovery

To investigate the displacive phase transition at the atomic scale, we have implemented a numerical algorithm to automate the detection of the symmetry relations between any two candidate crystal structures. Using this algorithm, here we systematically screen all possible polar–nonpolar structure pairs from the Materials Project database and establish a library of ~4500 pairs that can be connected through a continuous phase transition with small atomic displacements. From this database, we identify several new ferroelectric materials. In addition, the database may also be used in other areas, such as material structure prediction and new materials discovery.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Ice-Over-Water Cloud Properties in an Artificial Neural Network Approach

Clouds are a crucial component of the atmospheric energy system, particularly the radiative balance within, above, and below the troposphere. The vertical distribution of cloud mass and phase determines layer heating rates, the loss of radiation to space, and the amount of radiative heating at the surface. Thus, it is important to know how clouds are distributed both vertically and horizontally at all times of day. Satellite remote sensing is the only approach available to monitor clouds day and night around the globe. In this paper several artificial neural network (ANN) algorithms, employing several Aqua MODIS infrared channels, profiles of relative humidity and temperature from GMAO numerical weather analyses, and the retrieved total cloud visible optical depth, are trained to detect multilayer ice-over-water cloud systems and to retrieve some of their properties as identified by a year of 2008 Aqua MODIS data matched with CloudSat and CALIPSO (CC) cloud profiles. The CC lidar and radar profiles provide the vertical structure that serves as output truth for the multilayer algorithm. The neural networks were trained using one year (2008) of cloud top height data from the CC dataset, with correlation around 0.94 (0.95) and MAE as low as 0.82 (0.81) km for nonpolar regions during the day (night). Applying the trained ANN to independent year 2009 MODIS data resulted in a combined ML and single layer hit rate of 86.4% (85.1%) for nonpolar regions during the day (night). Since the ANN is trained using near-nadir MODIS pixels, infrared radiance corrections were developed as a function of view zenith angle from MODIS and applied to off-nadir pixels when processing MODIS swath data. The multilayer amount derived with the ANN is relatively invariant with increasing view zenith angle compared to the multilayer amount without the corrections.

MODIS↗

NASA NTRS2003

A Numerical Climate Observing Network Design Study

This project was concerned with three related questions of an optimal design of a climate observing system: 1. The spatial sampling characteristics required from an ARGO system. 2. The degree to which surface observations from ARGO can be used to calibrate and test satellite remote sensing observations of sea surface salinity (SSS) as it is anticipated now. 3. The more general design of an climate observing system as it is required in the near future for CLIVAR in the Atlantic. An important question in implementing an observing system is that of the sampling density required to observe climate-related variations in the ocean. For that purpose this project was concerned with the sampling requirements for the ARGO float system, but investigated also other elements of a climate observing system. As part of this project we studied the horizontal and vertical sampling characteristics of a global ARGO system which is required to make it fully complementary to altimeter data with the goal to capture climate related variations on large spatial scales (less thanAttachment: 1000 km). We addressed this question in the framework of a numerical model study in the North Atlantic with an 1/6 horizontal resolution. The advantage of a numerical design study is the knowledge of the full model state. Sampled by a synthetic float array, model results will therefore allow to test and improve existing deployment strategies with the goal to make the system as optimal and cost-efficient as possible. Attachment: "Optimal observations for variational data assimilation".

Stammer, Detlef↗

NASA NTRS1980

Stability analysis for laminar flow control, part 2

Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows.

Orszag, S. A.↗

NASA NTRS1992

Structural tailoring/analysis for hypersonic components - Executive system development

No direct analytical or integrated numerical tool exists today for the optimal design of a generic class of built-up actively cooled composite structure for applications in hypersonic propulsion ducts. The need exists for a numerical tool to perform the comprehensive design/analysis of a panel on the inlet wall under hypersonic flight conditions. Such a tool requires relatively complex multi-disciplinary analysis. One such numerical tool controlled by an executive system has been developed and is named as STAHYC (Structural Tailoring/Analysis for HYpersonic Components). A detailed account of the executive system development of STAHYC along with the results of one example inlet panel design problem is given in this paper.

Narayanan, G. V.↗

DOE OSTI2025

Data from TropiRoot 1.0 database: tropical root characteristics across environments

TropiRoot 1.0 is a new tropical root database with root characteristics across environment gradients. It has data extracted from 104 new sources, resulting in more than 8000 rows of data (either species or community data). Most of the data in TropiRoot 1.0 includes root characteristics such as root biomass, morphology, root dynamics, mass fraction, architecture, anatomy, physiology and root chemistry. This initiative represents an approximately 30% increase in the currently available data for tropical roots in the Fine Root Ecology Database (FRED). TropiRoot 1.0, contains root characteristics from 25 different countries where seven are located in Asia, six in South America, five in Central America and the Caribbean, four in Africa, two in North America, and 1 in Oceania. Due to the volume of data, when ancillary data was available, including soil data, these data was either extracted and included in the database or their availability was recorded in an additional column. Multiple contributors checked the entries for outliers during the collation process to ensure data quality. For text-based observations, we examined all cells to ensure that their content relates to their specific categories. For numerical observations, we ordered each numerical value from least to greatest and plotted the values, checking apparent outliers against the data in their respective sources and correcting or removing incorrect or impossible values. Some data (soil and aboveground) have different columns for the same variable presented in different units, including originally published units, but root characteristics data had units converted to match the ones reported in FRED. By filling a gap from global databases, TropiRoot 1.0 expands our knowledge of otherwise so far underrepresented regions, and our ability to assess global trends. This advancement can be used to improve tropical forest representation in vegetation models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates

The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.

Shu, Chi-Wang↗

DOE OSTI2024

How Does Vertical Wind Shear Influence Updraft Characteristics and Hydrometeor Distributions in Supercell Thunderstorms?

Abstract Vertical wind shear is known to affect supercell thunderstorms by displacing updraft hydrometeor mass downshear, thereby facilitating the storms’ longevity. Shear also impacts the size of supercell updrafts, with stronger shear leading to wider, less dilute, and stronger updrafts with likely greater hydrometeor production. To more clearly define the role of shear across different vertical layers on hydrometeor concentrations and displacements relative to supercell updrafts, a suite of idealized numerical model simulations of supercells was conducted. Shear magnitudes were systematically varied across the 0–1, 1–6, and 6–12 km AGL layers, while the thermodynamic environment was held fixed. Simulations show that as shear magnitude increases, especially from 1 to 6 km, updrafts become wider and less dilute with an increase in hydrometeor loading, along with an increase in the low-level precipitation area/rate and total precipitation accumulation. Even with greater updraft hydrometeor loading amid stronger shear, updrafts are more intense in stronger shear simulations due to larger thermal buoyancy owing to wider, less dilute updraft cores. Furthermore, downshear hydrometeor displacements are larger in environments with stronger 1–6-km shear. In contrast, there is relatively less sensitivity of hydrometeor concentrations and displacements to variations in either 0–1- or 6–12-km shear. Results are consistent across free tropospheric relative humidity sensitivity simulations, which show an increase in updraft size and hydrometeor mass with increasing free tropospheric relative humidity owing to a reduction in entrainment-driven dilution for wider updrafts in moister environments. Significance Statement Rotating thunderstorms, known as supercells, are able to persist for multiple hours. One common explanation is that large changes in wind speed and/or direction with height, or shear, transport rain/hail away from supercell updrafts, supporting their maintenance. The strong shear within supercell environments, however, may also lead to greater rail/hail amounts, thereby leading to weaker storms due to this extra mass of water/ice within updrafts. Furthermore, the impact of shear across different height layers on supercell rain/hail characteristics has not been thoroughly investigated. In this study, computer simulations of supercells were conducted to determine that shear occurring between 1 and 6 km above ground level has a large impact on rain/hail distribution in supercells and that stronger shear in this layer leads to wider/stronger supercells with greater rain/hail accumulations at the surface. Additionally, some of the extra mass of water/ice is transported farther away from updrafts due to the stronger environmental storm-relative winds.

Meteorology & Atmospheric Sciences↗

DOE OSTI2025

TropiRoot 1.0: Database of tropical root characteristics across environments

Tropical ecosystems contain the world's largest biodiversity of vascular plants. Yet, our understanding of tropical functional diversity and its contribution to global diversity patterns is constrained by data availability. This discrepancy underscores an urgent need to bridge data gaps by incorporating comprehensive tropical root data into global datasets. Here, we provide a database of tropical root characteristics. This new database, TropiRoot 1.0, will be instrumental in evaluating an array of hypotheses pertaining to root functional ecology and plant biogeography, both within the tropics and relative to other global biomes. The data compilation was conducted by the TropiRoot Initiative, in partnership with the Fine-Root Ecology Database (FRED) and the Global Root Trait (GRooT) database, Colorado State University (CSU) and the Smithsonian Tropical Research Institute (STRI). Literature search and data extraction were conducted between 2020 and 2024. Literature was identified using Web of Science, Scopus, and complemented using the expert knowledge of members of TropiRoot. To provide broad environmental and geographical distributions, literature searches included root characteristics (traits) across global change drivers, natural gradients, and from different continents. We adopted FRED standardized data columns and streamlined the format to enhance accessibility for data extraction across various user groups. This optimized framework resulted in a smaller, yet comprehensive datasheet. To make the database compatible with other global root trait initiatives, column identification was standardized following the codes provided by FRED. These efforts culminated in data extracted from 104 new sources, resulting in more than 8000 rows of data (either species or community data). Most of the data in TropiRoot 1.0 include root characteristics such as root biomass, morphology, root dynamics, mass fraction, architecture, anatomy, physiology, and root chemistry. This initiative represents a 30% increase in the currently available data for tropical roots in FRED. TropiRoot 1.0 contains root characteristics from 25 different countries, where seven are located in Asia, six in South America, five in Central America and the Caribbean, four in Africa, two in North America, and 1 in Oceania. Due to the volume of data, when ancillary data were available, including soil data, these data were either extracted and included in the database or its availability was recorded in an additional column. Multiple contributors checked the entries for outliers during the collation process to ensure data quality. For text-based observations, we examined all cells to ensure that their content relates to their specific categories. For numerical observations, we ordered each numerical value from least to greatest and plotted the values, checking apparent outliers against the data in their respective sources and correcting or removing incorrect or impossible values. Some data (soil and aboveground) have different columns for the same variable presented in different units, including originally published units, but root characteristics data had units converted to match those reported in FRED. By filling a gap from global databases, TropiRoot 1.0 expands our knowledge of otherwise so far underrepresented regions and our ability to assess global trends. This advancement can be used to improve tropical forest representation in vegetation models. The data are freely available and should be cited when used.

FRED↗

DOE OSTI2018

Casimir recursion relations for general conformal blocks

We study the structure of series expansions of general spinning conformal blocks. We find that the terms in these expansions are naturally expressed by means of special functions related to matrix elements of Spin(d) representations in Gelfand-Tsetlin basis, of which the Gegenbauer polynomials are a special case. We study the properties of these functions and explain how they can be computed in practice. We show how the Casimir equation in Dolan-Osborn coordinates leads to a simple one-step recursion relation for the coefficients of the series expansion of general spinning conformal block. The form of this recursion relation is determined by 6j symbols of Spin(d – 1). In particular, it can be written down in closed form in d = 3, d = 4, for seed blocks in general dimensions, or in any other situation when the required 6j symbols can be computed. As a result, we work out several explicit examples and briefly discuss how our recursion relation can be used for efficient numerical computation of general conformal blocks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Resurgence, conformal blocks, and the sum over geometries in quantum gravity

In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the central charge c. This expansion is an asymptotic series, so — via the same resurgence analysis familiar from quantum mechanics — necessitates the existence of non-perturbative effects. In the case of identity conformal blocks, these new effects have a simple interpretation: the CFT must possess new primary operators with dimension of order the central charge. This constrains the data of CFTs with large central charge in a way that is similar to (but distinct from) the conformal bootstrap. We study this phenomenon in three ways: numerically, analytically using Zamolodchikov’s recursion relations, and by considering non-unitary minimal models with large (negative) central charge. In the holographic dual to a CFT2, the expansion in powers of c is the perturbative loop expansion in powers of ћ. So our results imply that the graviton loop expansion is an asymptotic series, whose cure requires the inclusion of new saddle points in the gravitational path integral. In certain cases these saddle points have a simple interpretation: they are conical excesses, particle-like states with negative mass which are not in the physical spectrum but nevertheless appear as non-manifold saddle points that control the asymptotic behaviour of the loop expansion. This phenomenon also has an interpretation in SL(2, R) Chern-Simons theory, where the non-perturbative effects are associated with the non-Teichmüller component of the moduli space of flat connections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Analysis and prediction of reaction kinetics using the degree of rate control

“Degree of rate control” (DRC) analysis provides a quantitative approach for analysing the kinetics of multi-step reaction mechanisms that has been widely applied to both heterogeneous and homogeneous catalysis research, as well as electrocatalysis. The DRC of any given transition state or intermediate is defined as a partial derivative such that it approximately equals the fractional increase in net rate to the product of interest per differential decrease in its standard-state free energy for that species (÷RT), holding constant the standard-state free energies of all other transition states and intermediates. Even very complex mechanisms usually have only a few species with non-zero DRCs and are thus the species whose interactions with the catalyst most strongly affect the net rate. These key DRC values thus offer a simple and intuitive route to optimize catalyst materials, especially with the assistance of computational methods like density functional theory (DFT). These high-DRC species are also the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. In simple cases with a single “rate-determining step”, the DRC for its transition state (TS) is + 1. Catalyst-bound intermediates, on the other hand, often have negative DRCs equal to a small integer times their fractional occupancy of catalyst sites. The apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all the species (intermediates, transition states and products) in the reaction mechanism, each weighted by its DRC (+RT). It has been shown that the apparent transfer coefficient in electrocatalysis, an inverted form of the Tafel slope, is a weighted average of the number of electrons transferred to generate each intermediate or product species in the mechanism, weighted again by the DRC. Quantitative analysis of kinetic isotope effects (KIEs, or the ratio of net rates for different reactant isotopes) in complex mechanisms has shown that the logarithm of the KIE equals the weighted average over all species in the mechanism of the difference between the two isotopes in their standard-state free energies (÷RT), again weighted by the DRC. The reaction orders with respect to fluid-phase concentrations of reactants, products and intermediates have also been proven to be directly related to DRCs. Thus, there are numerous experimental observables which equate to short linear combinations of DRCs, so that combinations of experimental measurements might provide access to DRC values. Since its invention for transition states in 1994 and its generalization to include intermediates in 2009, the DRC has thus far mainly been calculated for microkinetic models based either entirely on DFT or on DFT with the key energies (i.e., those for high-DRC species) being fine-tuned to match experiments. The relationships summarized in this work provide new opportunities for using experiments earlier in the development and optimization of microkinetic models that require input from computational catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Ion mobility spectrometry and the omics: Distinguishing isomers, molecular classes and contaminant ions in complex samples

Ion mobility spectrometry (IMS) is a widely used analytical technique providing rapid gas phase separations. IMS alone is useful, but its coupling with mass spectrometry (IMS-MS) and various front-end separation techniques has greatly increased the molecular information achievable from omic analyses, including the sensitivity and peak capacity extracted from complex biological and environmental sample analyses. Due to these characteristics, IMS-MS is rapidly gaining attention for improving metabolomic, lipidomic, glycomic, proteomic and exposomic analyses. Numerous studies including national security-related analyses, disease screenings and environmental evaluations are illustrating that IMS-MS is able to extract information not possible with MS alone. Furthermore, IMS-MS has shown great utility in salvaging molecular information for low abundance molecules of interest when high concentration contaminant ions are present in the sample. This review highlights how IMS-MS is currently being used in omic analyses to distinguish structurally similar molecules, isomers, molecular classes and contaminant ions.

Ion mobility spectrometry,, Mass Spectometry, Omic↗

DOE OSTI2024

Tensor Hypercontraction of Cluster Perturbation Theory: Quartic Scaling Perturbation Series for the Coupled Cluster Singles and Doubles Ground-State Energies

Even though Cluster Perturbation has been shown to be a robust non-iterative alternative to Coupled Cluster Theory, it is still plagued by high order polynomial computational scaling and the storage of higher order tensors. Here we present a proof-of-concept strategy for implementing Cluster Perturbation Theory ground state energy series for the coupled cluster singles and doubles energy with N 4 computational scaling using Tensor Hypercontraction (THC). The reduction in computational scaling by two orders is achieved by decomposing two electron repulsion integrals, doubles amplitudes and multipliers, as well as selected doubles intermediates to Tensor Hypercontraction format. Using the outlined strategy, we showcase that the Tensor Hypercontraction pilot implementations retain numerical accuracy to within 1 kcal/mol relative to corresponding conventional and density fitting implementations and we empirically verify the N 4 scaling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Beyond the Debye–Hückel limit: Toward a general theory for concentrated electrolytes

The phenomenon of underscreening in concentrated electrolyte solutions leads to a larger decay length of the charge–charge correlation than the prediction of Debye–Hückel (DH) theory and has found a resurgence of both theoretical and experimental interest in the chemical physics community. To systematically understand and investigate this phenomenon in electrolytes requires a theory of concentrated electrolytes to describe charge–charge correlations beyond the DH theory. We review the theories of electrolytes that can transition from the DH limit to concentrations where charge correlations dominate, giving rise to underscreening and the associated Kirkwood Transitions (KTs). In this perspective, we provide a conceptual approach to a theoretical formulation of electrolyte solutions that exploits the competition between molecular-informed short-range (SR) and long-range interactions. We demonstrate that all deviations from the DH limit for real electrolyte solutions can be expressed through a single function ΣQ that can be determined both theoretically and numerically. Importantly, ΣQ can be directly related to the details of SR interactions and, therefore, can be used as a tool to understand how differences in representations of interaction can influence collective effects. The precise function form of ΣQ can be inferred through a Gaussian field theory of both the number and charge densities. The resulting formulation is validated by experiment and can accurately describe the collective phenomenon of screening in concentrated bulk electrolytes. Importantly, the Gaussian field theory predictions of the screening lengths appear to be less than ∼1 nm at concentrations above KTs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Dynamical friction in a Fuzzy Dark Matter universe

We present an in-depth exploration of the phenomenon of dynamical friction in a universe where the dark matter is composed entirely of so-called Fuzzy Dark Matter (FDM), ultralight bosons of mass m ~ O(10 -22 ) eV. We review the classical treatment of dynamical friction before presenting analytic results in the case of FDM for point masses, extended mass distributions, and FDM backgrounds with finite velocity dispersion. We then test these results against a large suite of fully non-linear simulations that allow us to assess the regime of applicability of the analytic results. We apply these results to a variety of astrophysical problems of interest, including infalling satellites in a galactic dark matter background, and determine that (1) for FDM masses m & 10 -21 eV c -2 , the timing problem of the Fornax dwarf spheroidal’s globular clusters is no longer solved and (2) the effects of FDM on the process of dynamical friction for satellites of total mass M and relative velocity vrel should require detailed numerical simulations for M/109 M m/10 -22 eV 100 km s -1 /vrel ~ 1, parameters which would lie outside the validated range of applicability of any currently developed analytic theory, due to transient wave structures in the time-dependent regi

79 ASTRONOMY AND ASTROPHYSICS↗