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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Distributed Data-Driven Power Iteration for Strongly Connected Networks

Here, this paper presents data-driven power iteration to distributively estimate the dominant eigenvalues of an unknown linear time-invariant system. The proposed strategy only requires a single trajectory data or measurements. Furthermore, in order to perform the distributed estimation, the communication network topology can be chosen to be any strongly connected directed graphs. The proposed data-driven power iteration is demonstrated using several numerical examples and is then applied to estimate the generalized algebraic connectivity of cooperative systems and to control the epidemic spreading.

Gusrialdi, Azwirman↗
DOE OSTI2021

Genomic Metrics Applied to Rhizobiales ( Hyphomicrobiales ): Species Reclassification, Identification of Unauthentic Genomes and False Type Strains

Taxonomic decisions within the order Rhizobiales have relied heavily on the interpretations of highly conserved 16S rRNA sequences and DNA–DNA hybridizations (DDH). Currently, bacterial species are defined as including strains that present 95–96% of average nucleotide identity (ANI) and 70% of digital DDH (dDDH). Thus, ANI values from 520 genome sequences of type strains from species of Rhizobiales order were computed. From the resulting 270,400 comparisons, a ≥95% cut-off was used to extract high identity genome clusters through enumerating maximal cliques. Coupling this graph-based approach with dDDH from clusters of interest, it was found that: (i) there are synonymy between Aminobacter lissarensis and Aminobacter carboxidus, Aurantimonas manganoxydans and Aurantimonas coralicida, “Bartonella mastomydis,” and Bartonella elizabethae, Chelativorans oligotrophicus, and Chelativorans multitrophicus, Rhizobium azibense, and Rhizobium gallicum, Rhizobium fabae, and Rhizobium pisi, and Rhodoplanes piscinae and Rhodoplanes serenus; (ii) Chelatobacter heintzii is not a synonym of Aminobacter aminovorans; (iii) “Bartonella vinsonii” subsp. arupensis and “B. vinsonii” subsp. berkhoffii represent members of different species; (iv) the genome accessions GCF_003024615.1 (“Mesorhizobium loti LMG 6125T”), GCF_003024595.1 (“Mesorhizobium plurifarium LMG 11892T”), GCF_003096615.1 (“Methylobacterium organophilum DSM 760T”), and GCF_000373025.1 (“R. gallicum R-602 spT”) are not from the genuine type strains used for the respective species descriptions; and v) “Xanthobacter autotrophicus” Py2 and “Aminobacter aminovorans” KCTC 2477T represent cases of misuse of the term “type strain”. Aminobacter heintzii comb. nov. and the reclassification of Aminobacter ciceronei as A. heintzii is also proposed. To facilitate the downstream analysis of large ANI matrices, we introduce here ProKlust (“Prokaryotic Clusters”), an R package that uses a graph-based approach to obtain, filter, and visualize clusters on identity/similarity matrices, with settable cut-off points and the possibility of multiple matrices entries.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Threat Reduction Research Networks: Fostering Sustainable Collaborations Through Trainings for Genomics for Biosurveillance

Scientific research communities can be represented as heterogeneous or multidimensional networks encompassing multiple types of entities and relationships. These networks might include researchers, institutions, meetings, and publications, connected by relationships like authorship, employment, and attendance. We describe a method for efficiently and flexibly capturing, storing, and extracting information from multidimensional scientific networks using a graph database. The database structure is based on an ontology that captures allowable types of entities and relationships. This allows us to construct a variety of projections of the underlying multidimensional graph through database queries to answer specific research questions. We demonstrate this process through a study of the U.S. Biological Threat Reduction Program (BTRP), which seeks to develop Threat Reduction Networks to build and strengthen a sustainable international community of biosecurity, biosafety, and biosurveillance experts to address shared biological threat reduction challenges. Networks like these create connectional intelligence among researchers and institutions around the world, and are central to the concept of cooperative threat reduction. Our analysis focuses on a series of seven BTRP genome sequencing training workshops, showing how they created a growing network of participants and countries over time, which is also reflected in coauthorship relationships among attendees. By capturing concept and relationship hierarchies, our ontology-based approach allows us to pose general or specific questions about networks within the same framework. This approach can be applied to other research communities or multidimensional social networks to capture, analyze, and visualize different types of interactions and how they change over time.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Assessing electrogenetic activation via a network model of biological signal propagation

Introduction: Molecular communication is the transfer of information encoded by molecular structure and activity. We examine molecular communication within bacterial consortia as cells with diverse biosynthetic capabilities can be assembled for enhanced function. Their coordination, both in terms of engineered genetic circuits within individual cells as well as their population-scale functions, is needed to ensure robust performance. We have suggested that “electrogenetics,” the use of electronics to activate specific genetic circuits, is a means by which electronic devices can mediate molecular communication, ultimately enabling programmable control. Methods: Here, we have developed a graphical network model for dynamically assessing electronic and molecular signal propagation schemes wherein nodes represent individual cells, and their edges represent communication channels by which signaling molecules are transferred. We utilize graph properties such as edge dynamics and graph topology to interrogate the signaling dynamics of specific engineered bacterial consortia. Results: We were able to recapitulate previous experimental systems with our model. In addition, we found that networks with more distinct subpopulations (high network modularity) propagated signals more slowly than randomized networks, while strategic arrangement of subpopulations with respect to the inducer source (an electrode) can increase signal output and outperform otherwise homogeneous networks. Discussion: We developed this model to better understand our previous experimental results, but also to enable future designs wherein subpopulation composition, genetic circuits, and spatial configurations can be varied to tune performance. We suggest that this work may provide insight into the signaling which occurs in synthetically assembled systems as well as native microbial communities.

Chun, Kayla↗
DOE OSTI2019

Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization

This article presents a resilient Integrated Resource Planning (IRP) framework designed for transmission systems, with a specific focus on analyzing and optimizing responses to High-Impact Low-Probability (HILP) events. The framework aims to improve the resilience of transmission networks in the face of extreme events by prioritizing the assessment of events with significant consequences. Unlike traditional reliability-based planning methods that average the impact of various outage durations, this work adopts a metric based on the proximity of outage lines to generators to select HILP events. The system’s baseline resilience is evaluated by calculating load curtailment in different parts of the network resulting from HILP outage events. The transmission network is represented as an undirected graph. Graph-theoretic techniques are used to identify islands with or without generators, potentially forming segmented grids or microgrids. This article introduces Expected Load Curtailment (ELC) as a metric to quantify the system’s resilience. The framework allows for the re-evaluation of system resilience by integrating additional generating resources to achieve desired resilience levels. Optimization is performed in the re-evaluation stage to determine the optimal placement of distributed energy resources (DERs) for enhancing resilience, i.e., minimizing ELC. Case studies on the IEEE 24-bus system illustrate the effectiveness of the proposed framework. In the broader context, this resilient IRP framework aligns with energy sustainability goals by promoting robust and resilient transmission networks, as the optimal placement of DERs for resilience enhancement not only strengthens the system’s ability to withstand and recover from disruptions but also contributes to efficient resource utilization, advancing the overarching goal of energy sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕ ). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕ ), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕ ) and larger planets (>2 × R ⊕ ) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕ ), when viewed from the perspective of planet equilibrium temperature (T eq ), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

FUN-BioCROP model with litter decomposition parameters derived from the LIDET dataset

This repository contains the code and data necessary to run the FUN-BioCROP (Fixation and Uptake of Nitrogen-Bioenergy Carbon, Rhizosphere, Organisms, and Protection) model with litter decomposition parameters derived from a modified Monte Carlo simulation that used the Long-term Intersite Decomposition Experiment Team dataset. Related publication:Juice, S.M., Ridgeway, J.R., Hartman, M.D., Parton, W.J., Berardi, D.M., Sulman, B.N., Allen, K.E., & Brzostek, E.R. Reparameterizing litter decomposition using a simplified Monte Carlo method improves litter decay simulated by a microbial model and alters bioenergy soil carbon estimates. Description of Files: FUNBioCROP_LIDET Study.Rmd R code with FUN-BioCROP model that can be run with 10 different sets of parameters for litter decomposition (Baseline, LIDET, or eight other best parameter sets identified in the modified Monte Carlo simulation. CORPSE Functions_Bioenergy_V2.R Code with CORPSE model functions, called by FUNBioCROP_LIDET Study.Rmd Model Input Data: bulk.csv, bulk_till.csv, rhizo.csv, rhizo_till.csv, litter.csv Initial C and N (kg C or N/m2) pool values for each soil compartment, final values from spin up. All five files have the same columns: (Column - Description - Units) uFastC - Unprotected fast decomposing carbon - kg carbon/m2 uSlowC - Unprotected slow decomposing carbon - kg carbon/m2 uNecroC - Unprotected necromass carbon - kg carbon/m2 pFastC - Protected fast decomposing carbon - kg carbon/m2 pSlowC - Protected slow decomposing carbon - kg carbon/m2 pNecroC - Protected necromass carbon - kg carbon/m2 livingMicrobeC - Carbon in living microbial biomass - kg carbon/m2 uFastN - Unprotected fast decomposing nitrogen - kg nitrogen/m2 uSlowN - Unprotected slow decomposing nitrogen - kg nitrogen/m2 uNecroN - Unprotected necromass nitrogen - kg nitrogen/m2 pFastN - Protected fast decomposing nitrogen - kg nitrogen/m2 pSlowN - Protected slow decomposing nitrogen - kg nitrogen/m2 pNecroN - Protected necromass nitrogen - kg nitrogen/m2 inorganicN - Inorganic nitrogen - kg nitrogen/m2 CO2 - Carbon in carbon dioxide - kg carbon/m2 livingMicrobeN - Nitrogen in living microbial biomass - kg nitrogen/m2 Model Input Data: FluxTower_AvgSoilT.csv: Average daily soil temperature (oC) at 10 cm depth at University of Illinois Urbana-Champaign (UIUC) Energy Farm flux tower from 7/2008-3/2016. (One year of averaged data) Model Input Data: FluxTower_AvgSoilVWC.csv: Average daily soil volumetric water content (VWC) at 10 cm depth at UIUC Energy Farm flux tower from 7/2008-3/2016. (One year of averaged data) Model Input Data: input_CCS_LIDET Study.csv: This file has daily data to run FUN-BioCROP (Column - Description - Units): yr - calendar year - year doy - day of year (1 to 365) (no leap year) - day anpp - aboveground NPP (DayCent) - kg C/m2/day bnpp - belowground NPP (DayCent) - kg C/m2/day aglivc - live aboveground biomass carbon (DayCent) - kg C/m2 bglivcj - live juvenile fine root biomass carbon (DayCent) - kg C/m2 bglivcm - live mature fine root biomass carbon (DayCent) - kg C/m2 aglivn - live aboveground biomass nitrogen (DayCent) - kg N/m2 bglivnj - live juvenile fine root biomass nitrogen (DayCent) - kg N/m2 bglivnm - live mature fine root biomass nitrogen (DayCent) - kg N/m2 nyr - simulation year - year cult - indicates a cultivation event (0 or 1) crop - indicates a new crop (0 or 1) fert - indicates a fertilizer event (0 or 1) frst - indicates the first day of the growing season (0 or 1) harv - indicates a harvest event (0 or 1) last - indicates the end of the growing season (0 or 1) croptype - crop type (0=none; 1=alfalfa; 2=corn; 3=grass clover pasture; 4=soybean; 5=wheat) cropsrl - crop specific root length - mm/g root cultrhizmix - fraction of rhizosphere mixed with bulk soil during cultivation (0.0-1.0) - fraction cultlitmix - fraction of litter mixed with bulk soil during cultivation (0.0-1.0) - fraction harvremov - fraction of above ground biomass removed during harvest (0.0-1.0) - fraction fertamt - fertilization amount - g N/m2 lifehist - plant life history (0 = annual, 1 = perennial) froot_turnover_c - amount of C in fine root turnover - kg C/m2 froot_turnover_n - amount of N in fine root turnover - kg N/m2 agrd_turnover_c - amount of C in aboveground biomass turnover - kg C/m2 agrd_turnover_n - amount of N in aboveground biomass turnover - kg N/m2 leaf_litter_fastfrac - Fast decomposing fraction of leaf litter (0.0-1.0) - fraction root_litter_fastfrac - Fast decomposing fraction of root litter (0.0-1.0) - fraction root_diameter - root diameter - mm root_length - root length - mm root/m2 rhizo_frac - fraction of total soil volume that is rhizosphere (0.0 - 1.0) - fraction date - date in format YYYY-MM-DD Instructions: Save the model code ("FUN-BioCROP_LIDET Study.Rmd") and accompanything files (data streams and CORPSE function code) in the same folder. In model code "Chunk 3: Load CORPSE Data Streams" set the working directory (setwd) to the folder with the files saved in step #1. In "Chunk 5: Define LIDET parameter sets" select the litter decomposition parameter set to be used in the run, and comment out all other sets. If changing any parameter values, edit them in "Chunk 6: Load parameters." Run all chunks up to and including "Chunk 10: Prepare Data for Export." In "Chunk 11: Export Output Data" edit data frames for export and filenames, as necessary. "Chunk 12: Graph Total Soil C" makes a figure of C remaining over the model run period. Description of each model chunk (in file FUN-BioCROP_LIDET Study.Rmd): Chunk 1: Remove all functions, clear memory. Removes all functions from R environment, clears the memory. Chunk 2: Load Packages. Loads packages necessary to run the code. Chunk 3: Load CORPSE Data Streams. Sets the working directory and loads the data files necessary to run CORPSE. Chunk 4: Load CORPSE Functions. Loads the R script with CORPSE functions from the working directory, "CORPSE Functions_Bioenergy_V2.R". Chunk 5: Define LIDET parameter sets. Has ten different parameter sets for litter decomposition tested in this study: Baseline parameters, LIDET parameters, and the other 8 best performing parameter sets identified in the modified Monte Carlo. To run the model, all but one parameter set must be commented out. Chunk 6: Load Parameters. Loads all fixed parameters to run the model. Data frame with definitions of parameters is in the CORPSE function script "CORPSE Functions_Bioenergy_V2.R" Chunk 7: Prepare Data Streams. Takes data streams loaded in Chunk 3 and puts them in the format necessary to run the model. The model is coded to run at least two sites at a time, so if only one site is being run it must be run in duplicate. Individual data tables of daily values are created in this chunk from the input data file. Chunk 8: Set Initial Conditions. Creates data tables of soil C and N pools for each soil compartment (rhizo_till, rhizo, bulk_till, bulk, litter) and loads initial values into the data tables. Creates lists for each soil compartment to hold model output. Chunk 9: Load FUN Data and Set Up Matrices. Uses DayCent data to calculate FUN input data: root and leaf N demand, total N demand, plant CN, leaf N available for retranslocation, and litter production. Creates matrices for FUN model outputs. Chunk 10: Run Model. Runs the model. Chunk 11: Prepare Data for Export. Combines data from each day saved as lists into data frames for each soil compartment. Adds values from all soil compartments together to calculate total soil values, creates separate data frames for each soil C and N pool (e.g., protected slow C) for the total soil value. Adds different C and N pools together to calculate total soil C and N for all layers. Creates data frame of ratio of protected to unprotected SOC. Organizes FUN data for export. Chunk 12: Export Results. Exports CSV files of model results to the working directory. Chunk 13: Graph Total Soil C. Makes figure of C remaining over time. Related Links: Original FUN-BioCROP model: https://github.com/BrzostekEcologyLab/FUN-BioCROP LIDET dataset: https://andlter.forestry.oregonstate.edu/data/abstract.aspx?dbcode=TD023

Juice, Stephanie↗
DOE OSTI2021

Algebraic Algorithms for Betweenness and Percolation Centrality

Abstract In this paper, we explored different ways to write the algebraic version of betweenness centrality algorithm. Particularly, we focused on Brandes' algorithm. We aimed for algebraic betweenness centrality that can be parallelized easily. We proposed 3-tuple geodetic semiring as an extension to the usual geodetic semiring with 2-tuples. Using the 3-tuple geodetic semiring, Dijkstra's and Brandes' algorithm, we wrote more concise and general algebraic betweenness centrality (ABC) algorithm which is valid for weighted and directed graphs. We also proposed an alternative version of ABC using the usual geodetic semiring with 2-tuple where we used a simple way to construct shortest path tree after computing shortest path distances in the usual geodetic semiring. This allows us to avoid computational complexity of ABC implementation using 3-tuple geodetic semiring. We used numba to optimize and parallelize ABC. We evaluated the performance of ABC using 2-tuple geodetic semiring as compared to NetworkX, a common python package for graph algorithms. We did scalability experiments on parallel ABC and showed its total speedup. We also showed that with small modification, ABC can be adapted to algebraicly compute other centrality measures such as percolation centrality.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

Lunar orbital photogaphic planning charts for candidate Apollo J-missions

A technique is presented for minimizing Mapping Camera film usage by reducing redundant coverage while meeting the desired sidelap of greater than or equal to 55%. The technique uses the normal groundtrack separation determined as a function of the number of revolutions between the respective tracks, of the initial and final nodal azimuths (or orbital inclination), and of the lunar latitude. The technique is also applicable for planning Panoramic Camera photography such that photographic contiguity is attained but redundant coverage is minimized. Graphs are included for planning mapping camera (MC) and panoramic camera (PC) photographic passes for a specific mission (i.e., specific groundtracks) to Descartes (Apollo 16), for specific missions to potential Apollo 17 sites such as Alphonsus, Proclus, Gassendi, Davy, and Tycho, and for a potential Apollo orbit-only mission with a nodal azimuth of 85 deg. Graphs are also included for determining the maximum number of revolutions which can elapse between successive MC and PC passes, for greater than or equal 55% sidelap and rectified contiguity respectively, for nodal azimuths between 5 deg and 85 deg.

Hickson, P. J.↗
NASA NTRS1971

Thermal contact resistance in a non-ideal joint

The contact of two rough, wavy surfaces; the contact of two rough but nominally flat plates pressed together over a concentrated area; and the contact of two rough but nominally flat plates bolted together are considered. In each case the pressure distribution is calculated as a function of the surface properties. In the case of wavy surfaces it is found that all necessary information for any combination of parameters can be reduced to one master graph. In the other two cases one such graph is needed for each geometry used. The resulting pressure distributions are used in a specific heat transfer example and the total joint resistance versus roughness is presented. A method for decreasing the resistance by increasing the roughness is shown.

Roca, R. T.↗
NASA NTRS1970

Optimum outgassing cycles for aluminum and stainless steel

Outgassing rates were measured for a modified 7075T6 aluminum and 304L stainless steel, for two degrees of finish, at temperatures of 285 deg F to 392 deg F, for times of 0.5 to 72 hours. The results were analyzed to determine optimum time and temperature cycles for outgassing. Optimum cycles were determined with and without the limitations of a graph. The graph related allowable time at temperature to a 5 percent or less reduction in room temperature properties of 7075T6 aluminum. For aluminum, within the limits set by reduction in mechanical properties, the optimum cycle tested was 40 hours at 285 deg F. Disregarding the limits, optimum outgassing was achieved at the highest temperatures and longest times tested, for both aluminum and stainless steel.

Garrison, R. L.↗
NASA NTRS1972

Kinematic distributions for electron pair production by muons

Cross sections and kinematic distributions for the trident production process plus or negative muon plus charge yields plus or minus muon plus electron plus positron plus charge (with charge = dipion moment and Fe) are given for beam energies of 100 to 300 GeV at fixed (electron positron) masses from 5 to 15 GeV. This process is interesting as a test of quantum electrodynamics at high energies, and in particular as a test of the form of the photon propagator at large timelike (four-momentum) squared. For this purpose, it is desirable to impose kinematic cuts that favor those Bethe-Heitler graphs which contain a timelike photon propagator. It is found that there are substantial differences between the kinematic distributions for the full Bethe-Heitler matrix element and the distributions for the two timelike-photon graphs alone; these differences can be exploited in the selection of appropriate kinematic cuts.

Linsker, R.↗
NASA NTRS1972

The Nasa earth resources spectral information system: A data compilation, first supplement

The NASA Earth Resources Spectral Information System and the information contained therein are described. It is intended to be used as a supplement to the NASA Earth Resources Spectral Information System: A Data Compilation, N72-28366. This supplement includes approximately 500 rock and mineral, 100 soil, and 30 vegetation bidirectional and directional reflectance, transmittance, emittance, and degree-of-polarization curves in the optical region from 0.2 to 22.0 microns. The data have been categorized by subject and each curve plotted on a single graph. For some rocks and minerals, all curves of the same type, differing only in particle size, have been plotted on one grid as a composite plot. Each graph, composite or single, is fully titled to indicate curve source and is indexed by subject to facilitate user retrieval.

Leeman, V.↗
NASA NTRS1971

Variability of radiation from circumstellar grains surrounding R Coronae Borealis.

Radiation at IR wavelengths from circumstellar grains surrounding R CrB has been observed for approximately three years. Variations of flux with time have been larger at a wavelength of 3.5 microns than at 11 microns. Observations at IR and visual wavelengths of R CrB are presented in a graph. Another graph shows the change in the shape of the excess radiaton between two observations spaced by a period of about one year.

Forrest, W. J.↗
NASA NTRS1972

FGRAAL: Technical documentation

Implementation of FGRAAL, a FORTRAN-extended graph algorithmic language for the Univac 1108 is described. The report contains the description of the implemented data structures for sets, lists and graphs. It summarizes the changes made for the RALPH compiler to accommodate the special statements of FGRAAL; gives the calling sequences generated by the changed compiler; and describes the object time subroutine package.

Mesztenyi, C. K.↗
NASA NTRS1973

Path-length distributions of photons diffusely reflected from a semi-infinite atmosphere.

Knowledge of the probability distribution of photon path lengths for diffuse reflection in the continuum from a planetary atmosphere greatly simplifies computation of the shape and strength of absorption lines formed under conditions of multiple scattering. Graphs of this probability distribution are presented for diffuse reflection from a semiinfinite conservative atmosphere for both isotropic and forward-directed scattering, and for several angles of incidence and reflection. Graphs showing distributions for the case of absorption in the continuum are also discussed. The distributions are obtained from an analytic expression for the path-length distribution for nth-order scattering and a tabulation of nth-order intensities. It is found that te shape of the probability distribution depends markedly on the degree of forward scattering due to the phase function. The results are compared with those obtained by a Monte Carlo computation of the sort which might be used if tabulated nth-order intensities were not available.

Appleby, J. F.↗