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DOE OSTI2014

Coupled cluster channels in the homogeneous electron gas

We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner one-body Hamiltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladder-only CCD, ring-only CCD, and crossed-ring-only CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Wind Regimes in Complex Terrain of the Great Valley of Eastern Tennessee

This research was designed to provide an understanding of physical wind mechanisms within the complex terrain of the Great Valley of Eastern Tennessee to assess the impacts of regional air flow with regard to synoptic and mesoscale weather changes, wind direction shifts, and air quality. Meteorological data from 2008 2009 were analyzed from 13 meteorological sites along with associated upper level data. Up to 15 ancillary sites were used for reference. Two-step complete linkage and K-means cluster analyses, synoptic weather studies, and ambient meteorological comparisons were performed to generate hourly wind classifications. These wind regimes revealed seasonal variations of underlying physical wind mechanisms (forced channeled, vertically coupled, pressure-driven, and thermally-driven winds). Synoptic and ambient meteorological analysis (mixing depth, pressure gradient, pressure gradient ratio, atmospheric and surface stability) suggested up to 93% accuracy for the clustered results. Probabilistic prediction schemes of wind flow and wind class change were developed through characterization of flow change data and wind class succession. Data analysis revealed that wind flow in the Great Valley was dominated by forced channeled winds (45 67%) and vertically coupled flow (22 38%). Down-valley pressure-driven and thermally-driven winds also played significant roles (0 17% and 2 20%, respectively), usually accompanied by convergent wind patterns (15 20%) and large wind direction shifts, especially in the Central/Upper Great Valley. The behavior of most wind regimes was associated with detectable pressure differences between the Lower and Upper Great Valley. Mixing depth and synoptic pressure gradients were significant contributors to wind pattern behavior. Up to 15 wind classes and 10 sub-classes were identified in the Central Great Valley with 67 joined classes for the Great Valley at-large. Two-thirds of Great Valley at-large flow was defined by 12 classes. Winds flowed on-axis only 40% of the time. The Great Smoky Mountains helped create down-valley pressure-driven winds, downslope mountain breezes, and divergent air flow. The Cumberland Mountains and Plateau were associated with wind speed reductions in the Central Great Valley, Emory Gap Flow, weak thermally-driven winds, and northwesterly down sloping. Ridge-and-valley terrain enhanced wind direction reversals, pressure-driven winds, as well as locally and regionally produced thermally-driven flow.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1990

Tailoring explicit time-marching schemes to improve convergence characteristics

Multi-stage time-stepping schemes, tailored to chosen spatial-differencing operators, are derived and tested. The schemes are constructed to give optimal damping of the high-frequency waves. They are ideal for use with multi-grid acceleration. The concept of characteristic time-stepping, necessary for the extension of the scalar analysis to systems of equations, is presented. The schemes show a marked improvement over Runge-Kutta schemes.

Powell, Kenneth G.↗

NASA NTRS2023

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using turbulence modeling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been achieved to realize similar performance with two-equation models of the k-w type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k-w type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically renewed mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus, numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the turbulence model. Additionally, in this paper, analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Turbulence↗

NASA NTRS2013

Aqua-planet simulations of the formation of the South Atlantic convergence zone

The impact of Amazon Basin convection and cold fronts on the formation and maintenance of the South Atlantic convergence zone (SACZ) is studied using aqua-planet simulations with a general circulation model. In the model, a circular patch of warm sea-surface temperature (SST) is used to mimic the effect of the Amazon Basin on South American monsoon convection. The aqua-planet simulations were designed to study the effect of the strength and latitude of Amazon Basin convection on the formation of the SACZ. The simulations indicate that the strength of the SACZ increases as the Amazon convection intensifies and is moved away from the equator. Of the two controls studied here, the latitude of the Amazon convection exerts the strongest effect on the strength of the SACZ. An analysis of the synoptic-scale variability in the simulations shows the importance of frontal systems in the formation of the aqua-planet SACZ. Composite time series of frontal systems that occurred in the simulations show that a robust SACZ occurs when fronts penetrate into the subtropics and become stationary there as they cross eastward of the longitude of the Amazon Basin. Moisture convergence associated with these frontal systems produces rainfall not along the model SACZ region and along a large portion of the northern model Amazon Basin. Simulations in which the warm SST patch was too weak or too close to the equator did not produce frontal systems that extended into the tropics and became stationary, and did not form a SACZ. In the model, the SACZ forms as Amazon Basin convection strengthens and migrates far enough southward to allow frontal systems to penetrate into the tropics and stall over South America. This result is in agreement with observations that the SACZ tends to form after the onset of the monsoon season in the Amazon Basin.

South American Monsoon↗

DOE OSTI2016

Implications of Grain-Scale Mineralogical Heterogeneity for Radionuclide Transport in Fractured Media

The geological disposal of nuclear waste is based on the multi-barrier concept, comprising various engineered and natural barriers, to confine the radioactive waste and isolate it from the biosphere. Some of the planned repositories for high-level nuclear waste will be hosted in fractured crystalline rock formations. The potential of these formations to act as natural transport barriers is related to two coupled processes: diffusion into the rock matrix and sorption onto the mineral surfaces available in the rock matrix. Different in situ and laboratory experiments have pointed out the ubiquitous heterogeneous nature of the rock matrix: mineral surfaces and pore space are distributed in complex microstructures and their distribution is far from being homogeneous (as typically assumed by Darcy-scale coarse reactive transport models). We use a synthetically generated fracture–matrix system to assess the implications of grain-scale physical and mineralogical heterogeneity on cesium transport and retention. The resulting grain-scale reactive transport model is solved using high-performance computing technologies, and the results are compared with those derived from two alternative models, denoted as upscaled models, where mineral abundance is averaged over the matrix volume. In the grain-scale model, the penetration of cesium into the matrix is faster and the penetration front is uneven and finger-shaped. The analysis of the cesium breakthrough curves computed at two different points in the fracture shows that the upscaled models provide later first-arrival time estimates compared to the grain-scale model. The breakthrough curves computed with the three models converge at late times. These results suggest that spatially averaged upscaled parameters of sorption site distribution can be used to predict the late-time behavior of breakthrough curves but could be inadequate to simulate the early behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

The hazard components of representative key risks. The physical climate perspective

The framework of Representative Key Risks (RKRs) has been adopted by the Intergovernmental Panel on Climate Change Working Group II in order to categorize, assess and communicate a wide range of regional and sectoral key risks, expected to become severe as a consequence of the potentially detrimental convergence of changing climate conditions, exposure and vulnerability of human and natural systems, and responses through (mal)adaptation measures. Other papers in this special issue treat each of eight RKRs by holistically assessing their current status and future evolution as a result of this convergence. However, their treatment cannot always organize such assessment according to a systematic gradation of climatic changes, often times having to extrapolate the big-picture evolution of risk from either qualitative effects of “low” medium” and “high” warming, or limited/focused analysis of the consequences of particular mitigation choices (e.g., benefits of limiting warming to 1.5 or 2C). In this study we offer as systematic a representation as possible – given current literature and assessments – of the future evolution of the hazard components of RKRs. We draw on the assessment of changes in climatic impact-drivers relevant to RKRs described in the 6th Assessment Report by Working Group 1 (WGI) supplemented when needed by more recent literature. We identify the relevant hazards for each RKR, based upon the WGII authors’ assessment, and we report on their current state and expected future changes in magnitude, intensity and/or frequency, linking these changes to Global Warming Levels to the extent possible. For some of these quantities - like regional trends in oceanic and atmospheric temperature and precipitation, some heat and precipitation extremes, permafrost thaw and Northern Hemisphere snow cover - a strong and quantitative relationship with global average temperature change has been assessed. For others - like frequency and intensity of tropical cyclones and extra-tropical storms, and fire weather - the link to increasing global temperatures can only be described qualitatively. For some processes - like the behavior of ice-sheets, or changes in circulation dynamics - large uncertainties about the effects of different levels of warming remain, and for a few others - like ocean pH and air pollution - the composition of the scenario of anthropogenic emissions is most relevant, rather than the warming reached. In almost all cases, however, the basic message remains that every small increment in CO2 concentration in the atmosphere and associated warming will bring changes in climate phenomena that will contribute to increasing risk of impacts on human and natural systems when these changes happen in conjunction with these systems’ conditions of exposure and vulnerability, and in lack of effective adaptation. Our picture of the evolution of RKR-relevant climatic impact-drivers complements and enriches the treatment of RKRs in the other papers in at least two ways: by filling in an often only cursory or limited representation of the physical climate aspects driving impacts, and by providing a fuller representation of their future possible evolution which represents an important component – if never the only one – of the potential future evolution of risk severity.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

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

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

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Structural insights into the polyphyletic origins of glycyl tRNA synthetases

Glycyl tRNA synthetase (GlyRS) provides a unique case among class II aminoacyl tRNA synthetases, with two clearly widespread types of enzymes: a dimeric (α 2 ) species present in some bacteria, archaea, and eukaryotes; and a heterotetrameric form (α 2 β 2 ) present in most bacteria. Although the differences between both types of GlyRS at the anticodon binding domain level are evident, the extent and implications of the variations in the catalytic domain have not been described, and it is unclear whether the mechanism of amino acid recognition is also dissimilar. Here, we show that the α-subunit of the α 2 β 2 GlyRS from the bacterium Aquifex aeolicus is able to perform the first step of the aminoacylation reaction, which involves the activation of the amino acid with ATP. The crystal structure of the α-subunit in the complex with an analog of glycyl adenylate at 2.8 Å resolution presents a conformational arrangement that properly positions the cognate amino acid. This work shows that glycine is recognized by a subset of different residues in the two types of GlyRS. Furthermore, a structural and sequence analysis of class II catalytic domains shows that bacterial GlyRS is closely related to alanyl tRNA synthetase, which led us to define a new subclassification of these ancient enzymes and to propose an evolutionary path of α 2 β 2 GlyRS, convergent with α 2 GlyRS and divergent from AlaRS, thus providing a possible explanation for the puzzling existence of two proteins sharing the same fold and function but not a common ancestor.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2013

Low Concentrations of Silver Nanoparticles in Biosolids Cause Adverse Ecosystem Responses under Realistic Field Scenario

A large fraction of engineered nanomaterials in consumer and commercial products will reach natural ecosystems. To date, research on the biological impacts of environmental nanomaterial exposures has largely focused on high-concentration exposures in mechanistic lab studies with single strains of model organisms. These results are difficult to extrapolate to ecosystems, where exposures will likely be at low-concentrations and which are inhabited by a diversity of organisms. Here we show adverse responses of plants and microorganisms in a replicated long-term terrestrial mesocosm field experiment following a single low dose of silver nanoparticles (0.14 mg Ag kg −1 soil) applied via a likely route of exposure, sewage biosolid application. While total aboveground plant biomass did not differ between treatments receiving biosolids, one plant species, Microstegium vimeneum, had 32 % less biomass in the Slurry+AgNP treatment relative to the Slurry only treatment. Microorganisms were also affected by AgNP treatment, which gave a significantly different community composition of bacteria in the Slurry+AgNPs as opposed to the Slurry treatment one day after addition as analyzed by T-RFLP analysis of 16S-rRNA genes. After eight days, N 2 O flux was 4.5 fold higher in the Slurry+AgNPs treatment than the Slurry treatment. After fifty days, community composition and N 2 O flux of the Slurry+AgNPs treatment converged with the Slurry. However, the soil microbial extracellular enzymes leucine amino peptidase and phosphatase had 52 and 27% lower activities, respectively, while microbial biomass was 35% lower than the Slurry. We also show that the magnitude of these responses was in all cases as large as or larger than the positive control, AgNO 3 , added at 4-fold the Ag concentration of the silver nanoparticles.

biomass↗

DOE OSTI2023

Application of prophage sequence analysis to investigate a disease outbreak involving Salmonella Adjame, a rare serovar and implications for the population structure

Introduction Outbreak investigation of foodborne salmonellosis is hindered when the food source is contaminated by multiple strains of Salmonella , creating difficulties matching an incriminated organism recovered from patients with the specific strain in the suspect food. An outbreak of the rare Salmonella Adjame was caused by multiple strains of the organism as revealed by single-nucleotide polymorphism (SNP) variation. The use of highly discriminatory prophage analysis to characterize strains of Salmonella should enable a more precise strain characterization and aid the investigation of foodborne salmonellosis. Methods We have carried out genomic analysis of S. Adjame strains recovered during the course of a recent outbreak and compared them with other strains of the organism ( n = 38 strains), using SNPs to evaluate strain differences present in the core genome, and prophage sequence typing (PST) to evaluate the accessory genome. Phylogenetic analyses were performed using both total prophage content and conserved prophages. Results The PST analysis of the S. Adjame isolates showed a high degree of strain heterogeneity. We observed small clusters made up of 2-6 isolates ( n = 27) and singletons ( n = 11) in stark contrast with the three clusters observed by SNP analysis. In total, we detected 24 prophages of which only four were highly prevalent, namely: Entero_p88 (36/38 strains), Salmon_SEN34 (35/38 strains), Burkho_phiE255 (33/38 strains) and Edward_GF (28/38 strains). Despite the marked strain diversity seen with prophage analysis, the distribution of the four most common prophages matched the clustering observed using core genome. Discussion Mutations in the core and accessory genomes of S. Adjame have shed light on the evolutionary relationships among the Adjame strains and demonstrated a convergence of the variations observed in both fractions of the genome. We conclude that core and accessory genomes analyses should be adopted in foodborne bacteria outbreak investigations to provide a more accurate strain description and facilitate reliable matching of isolates from patients and incriminated food sources. The outcomes should translate to a better understanding of the microbial population structure and an 46 improved source attribution in foodborne illnesses.

Gao, Ruimin↗

DOE OSTI2016

ARCADE IMPLOSION CAUSED BY A FILAMENT ERUPTION IN A FLARE

Coronal implosions—the convergence motion of plasmas and entrained magnetic field in the corona due to a reduction in magnetic pressure—can help to locate and track sites of magnetic energy release or redistribution during solar flares and eruptions. We report here on the analysis of a well-observed implosion in the form of an arcade contraction associated with a filament eruption, during the C3.5 flare SOL2013-06-19T07:29. A sequence of events including the magnetic flux-rope instability and distortion, followed by a filament eruption and arcade implosion, lead us to conclude that the implosion arises from the transfer of magnetic energy from beneath the arcade as part of the global magnetic instability, rather than due to local magnetic energy dissipation in the flare. The observed net contraction of the imploding loops, which is found also in nonlinear force-free field extrapolations, reflects a permanent reduction of magnetic energy underneath the arcade. This event shows that, in addition to resulting in the expansion or eruption of an overlying field, flux-rope instability can also simultaneously implode an unopened field due to magnetic energy transfer. It demonstrates the “partial opening of the field” scenario, which is one of the ways in 3D to produce a magnetic eruption without violating the Aly–Sturrock hypothesis. In the framework of this observation, we also propose a unification of three main concepts for active region magnetic evolution, namely the metastable eruption model, the implosion conjecture, and the standard “CSHKP” flare model.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1990

Innovative design of composite structures: The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes

The gains in buckling performance are explored that can be achieved by deviating from the conventional straightline fiber format and considering the situation whereby the fiber orientation in a layer, or a group of layers, can vary from point to point. The particular situation studied is a simply supported square plate with a centrally located hole loaded in compression. By using both a sensitivity analysis and a gradient-search technique, fiber orientation in a number of regions of the plate are selected so as to increase the buckling load relative to baseline straightline designs. The sensitivity analysis is used to determine which regions of the plate have the most influence on buckling load, and the gradient search is used to find the design that is believed to represent the absolute maximum buckling load for the conditions prescribed. Convergence studies and sensitivity of the final design are discussed. By examining the stress resultant contours, it is shown how the curvilinear fibers move the load away from the unsupported hole region of the plate to the supported edges, thus increasing the buckling capacity. The tensile capacity of the improved buckling design is investigated, and it is shown that both tensile capacity and buckling capacity can be improved with the curvilinear fiber concept.

Hyer, M. W.↗

NASA NTRS1990

Fully elliptic incompressible flow calculations on regular grid by a new pressure substitution method

A new method is presented for the solution of incompressible flow in generalized coordinates. This method is based on the substitution of the pressure weighted form of the momentum equations into the continuity equation. The algorithm is rigorously derived and a Fourier analysis is used to assess its suitability to act as an error smoother. Linear stability analysis results indicate that the performance of the new pressure substitution method (PSM) and the pressure correction method (PCM) is about the same at low Reynolds numbers, with no significant pressure gradient. At high Reynolds numbers the PSM shows much faster convergence. Likewise prediction of various flows indicate that the PSM has better accuracy for high Reynolds number flows with significant pressure gradients. Since most practical aerodynamic flows have significant pressure gradients, the PSM seems to be attractive for such flows. Solutions for both laminar and turbulent flow are compared with the experimental data. A two-equation low Reynolds number turbulence model is used to resolve the turbulent flowfield.

Hobson, G. V.↗

NASA NTRS1991

The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes

Hyer, M. W.↗

NASA NTRS1993

On the static stability of forward swept propfans

An hybrid Euler solver coupled with a NASTRAN structural analysis is used to investigate the static stability characteristics of two forward swept propfan blades. The designs, having same geometry but different structural properties - one being statically stable and the other unstable, are analyzed. The stable design takes more iterations to converge than previously designed aft swept blades. The unstable design diverges to an unrealistic shape within five iterations.

Srivastava, R.↗

NASA NTRS1996

Cascade Optimization Strategy for Aircraft and Air-Breathing Propulsion System Concepts

Design optimization for subsonic and supersonic aircraft and for air-breathing propulsion engine concepts has been accomplished by soft-coupling the Flight Optimization System (FLOPS) and the NASA Engine Performance Program analyzer (NEPP), to the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Aircraft and engine design problems, with their associated constraints and design variables, were cast as nonlinear optimization problems with aircraft weight and engine thrust as the respective merit functions. Because of the diversity of constraint types and the overall distortion of the design space, the most reliable single optimization algorithm available in COMETBOARDS could not produce a satisfactory feasible optimum solution. Some of COMETBOARDS' unique features, which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications, successfully optimized the performance of both aircraft and engines. The cascade method has two principal steps: In the first, the solution initiates from a user-specified design and optimizer, in the second, the optimum design obtained in the first step with some random perturbation is used to begin the next specified optimizer. The second step is repeated for a specified sequence of optimizers or until a successful solution of the problem is achieved. A successful solution should satisfy the specified convergence criteria and have several active constraints but no violated constraints. The cascade strategy available in the combined COMETBOARDS, FLOPS, and NEPP design tool converges to the same global optimum solution even when it starts from different design points. This reliable and robust design tool eliminates manual intervention in the design of aircraft and of air-breathing propulsion engines where it eases the cycle analysis procedures. The combined code is also much easier to use, which is an added benefit. This paper describes COMETBOARDS and its cascade strategy and illustrates the capability of the combined design tool through the optimization of a subsonic aircraft and a high-bypass-turbofan wave-rotor-topped engine.

Patnaik, Surya N.↗

NASA NTRS2005

Time-Averaged Velocity, Temperature and Density Surveys of Supersonic Free Jets

A spectrally resolved molecular Rayleigh scattering technique was used to simultaneously measure axial component of velocity U, static temperature T, and density p in unheated free jets at Mach numbers M = 0.6,0.95, 1.4 and 1.8. The latter two conditions were achieved using contoured convergent-divergent nozzles. A narrow line-width continuous wave laser was passed through the jet plumes and molecular scattered light from a small region on the beam was collected and analyzed using a Fabry-Perot interferometer. The optical spectrum analysis air density at the probe volume was determined by monitoring the intensity variation of the scattered light using photo-multiplier tubes. The Fabry-Perot interferometer was operated in the imaging mode, whereby the fringe formed at the image plane was captured by a cooled CCD camera. Special attention was given to remove dust particles from the plume and to provide adequate vibration isolation to the optical components. The velocity profiles from various operating conditions were compared with that measured by a Pitot tube. An excellent comparison within 5m's demonstrated the maturity of the technique. Temperature was measured least accurately, within 10K, while density was measured within 1% uncertainty. The survey data consisted of centerline variations and radial profiles of time-averaged U, T and p. The static temperature and density values were used to determine static pressure variations inside the jet. The data provided a comparative study of jet growth rates with increasing Mach number. The current work is part of a data-base development project for Computational Fluid Dynamics and Aeroacoustics codes that endeavor to predict noise characteristics of high speed jets. A limited amount of far field noise spectra from the same jets are also presented. Finally, a direct experimental validation was obtained for the Crocco-Busemann equation which is commonly used to predict temperature and density profiles from known velocity profiles. Data presented in this paper are available in ASCII format upon request.

Panda, Jayanta↗