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3,188 records · Page 78

The critical role of intrinsic defects and many-body interactions on the stability of MnBi2Te4

Intrinsic antisite defects pose a major challenge to understanding and predicting the exotic properties of the layered topological magnetic insulator MnBi2Te4 (MBT). In this work, we study the origin of the abundance of intrinsic defects in MBT, including many-body defect–defect interactions and many-body electronic correlations. Until now, ab initio methods have struggled to explain thermodynamic stability and properties influenced by defect behavior in MBT. We model native Mn–Bi antisite defects in MBT at finite temperatures using a cluster expansion that includes defect–defect interactions. To overcome the limitations of conventional density functional theory (DFT), we introduce a hybrid approach that incorporates high-accuracy quantum Monte Carlo (QMC) calculations, introducing missing correlations. This strategy allows for accurate estimation of defect energetics and finite-temperature properties. We compute the configurational free energy, defect concentration, and configurational heat capacity, revealing a second-order order–disorder phase transition near the experimental synthesis temperature. Our study provides the first theoretical insight into the thermodynamics of intrinsic defects in MBT. The negative free energy relative to pristine MBT at synthesis temperatures indicates that Mn–Bi antisite formation is thermodynamically spontaneous. We also present a broadly applicable general framework for correcting low-level theoretical theories using highly accurate many-body corrections from QMC.

Ghaffar, Abdul [ORNL] (ORCID:0000000241190168)

Λ polarization from vortex rings as the medium response for jet thermalization

We performed a systematic study on the formation of vorticity rings as the process for jet thermalization in the medium created in high-energy nuclear collisions. In this work, we expanded our previous analysis to a more realistic framework by considering noncentral events and fluctuations in the initial condition. We simulate the formation and evolution of the flow vortex structure in a relativistic viscous hydrodynamic model and study the sensitivity of the proposed “ring observable” (ℛ$^{𝑡}_{Λ}$) that can be measured experimentally through the polarization of Λ hyperons. We show that this observable is robust with respect to fluctuating initial conditions to capture the jet-induced vortex flow signal and further study its dependence on different model parameters, such as the jet's velocity, position, the fluid's shear viscosity, and the collision centrality. The proposed observable is associated with the formation of vorticity in a quark-gluon plasma, showing that the measurement of particle polarization can be a powerful tool to probe different properties of jet-medium interactions and to understand better the polarization induced by the transverse and longitudinal expansions of the medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

The gas-phase mass–metallicity relation of dwarf galaxies across large-scale environments using the CAVITY parent sample

Context. The gas-phase mass–metallicity relation (MZR) of galaxies shows a noticeable break in slope and an increased scatter at low stellar masses, suggesting that the physical processes governing chemical enrichment differ between dwarf and high-mass systems. Dwarf galaxies, in particular, are highly susceptible to both internal and environmental mechanisms due to their shallow potential wells. Aims. The primary aim of this work is to assess whether a single, universal MZR can describe dwarf galaxies across diverse large-scale environments, or whether systematic environmental variations emerge. To probe these, we examine the MZR and star formation rate (SFR) of dwarf galaxies with stellar masses in the range of 8.9 < log(M ★ /M ⊙ ) < 9.5. Methods. Using optical spectra from the Sloan Digital Sky Survey, we measured the fluxes of key emission lines via the pyPipe3D full spectral fitting pipeline. Aperture-corrected fluxes, along with multiple metallicity indicators and calibrations, were used to derive the MZR and the SFR for 353, 311, and 22 dwarf galaxies located in voids, filaments, and clusters, respectively. Results. We find a systematic variation in the MZR slope, steeper in voids (0.28 ± 0.03) and progressively flatter in clusters (0.17 ± 0.08), indicating a dependence of the MZR on the large-scale environment in this mass regime. When galaxies are separated by local density, no significant differences are observed between isolated and non-isolated dwarfs in voids. Isolated dwarf galaxies in filaments also exhibit properties similar to those of their counterparts in voids. However, non-isolated filament galaxies exhibit similar MZR slopes comparable to those of cluster dwarfs and flatter slopes than their counterparts in voids. Conclusions. We report both large- and local-scale environmental dependencies in the gas-phase metallicity and in the slope of the MZR for dwarf galaxies. Consistent with the general consensus on the pre-processing of galaxies in filaments, our results indicate that the influence of the local environment becomes increasingly significant within the filamentary regions of the cosmic web, affecting the chemical enrichment and star formation activity of low-mass systems. These findings further suggest that a portion of the scatter commonly observed in the MZR of dwarf galaxies arises from environmental effects.

Bidaran, Bahar [Dpto. de Física Teórica y del Cosm

Dynamic Analysis of the STARC-ABL Propulsion System

In the pursuit of Electrified Aircraft Propulsion (EAP), much of the attention is on the development of hybrid electric concept vehicles and their propulsion systems from a steady state performance perspective. While it is steady-state performance that largely determines the efficiency of civil air transports, engine operability and transient performance define constraints for the steady state design that impact efficiency and system viability. Neglecting dynamics and control technologies can result in an over-designed, sub optimal propulsion system or a concept that is not feasible. Thus, dynamic system studies were conducted on the propulsion system of the conceptual aircraft design known as the Single-aisle Turboelectric AiRCraft with Aft Boundary Layer propulsor (STARC-ABL). This paper describes the development of a controller to verify the baseline concept's feasibility from an operability perspective. Further, studies were conducted to identify excessive stability margin in the baseline design that could be traded for potential benefits in efficiency through an engine re design. This study revealed the potential to reduce the high pressure compressor (HPC) stall margin by 3%. Finally, a study was conducted to investigate the potential benefit of adding energy storage to the STARC-ABL concept that further improves operability and enables more gains in engine efficiency and performance. The energy storage provided an additional 0.5% stall margin can be removed from the HPC.

hybrid electric propulsion

NASA Interests in Superconducting and Cryogenic Technology

NASA develops and operates technology for a wide range of applications and environments across its aeronautics and space portfolios. This presentation will summarize the applications and environments where superconducting technology and associated cryogenics are contributing to NASA’s missions and areas where there is an opportunity to expand the contribution. Important characteristics of high priority space environments will be discussed. An emphasis will be placed on aircraft propulsion and NASA’s Artemis mission (a Moon to Mars initiative). The discussion of space applications will include takeaways from NASA’s recent rankings of 187 space technology “shortfalls”. The aircraft propulsion application will be described in detail and existing NASA investments will be summarized.

Electrified Aircraft Propulsion

Gauge theory of giant phonon magnetic moment in doped Dirac semimetals

Here, we develop a quantitative theory of phonon magnetic moment in doped Dirac semimetals. Our theory is based on an emergent gauge field approach to the electron-phonon coupling, applicable to gapless systems. We find that the magnetic moment is directly proportional to the electrical Hall conductivity through the phonon Hall viscosity. Our theory is combined with the first-principles calculations, allowing us to quantitatively implement it to realistic materials. Magnetic moments are found to be of the order of a Bohr magneton for Raman-active phonon modes in graphene and Cd 3 ⁢As 2 . Our results provide practical guidance for the dynamical generation of large magnetization in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Synthesis‐Related Nanoscale Defects in Mo‐Based Janus Monolayers Revealed by Cross‐Correlated AFM and TERS Imaging

2D Janus transition metal dichalcogenides (TMDs) are promising candidates for various applications including non-linear optics, energy harvesting, and catalysis. These materials are usually synthesized via chemical conversion of pristine TMDs. Nanometer-scale characterization of the obtained Janus materials’ morphology and local composition is crucial for both the synthesis optimization and the future device applications. In this work, we present the results of cross-correlated atomic force microscopy (AFM) and tip-enhanced Raman spectroscopy (TERS) study of Janus monolayers synthesized by the hydrogen plasma-assisted chemical conversion of MoSe 2 and MoS 2 . We demonstrate that the choice of both the growth substrate and the starting TMD influences the residual strain, thereby shaping the nanoscale morphology of the resulting Janus material. Furthermore, by employing TERS imaging, we show the presence of nanoscale islands (≈20 nm across) of MoSe 2 - ${\mathrm{Mo}}_{{\mathrm{Se}}}^{\mathrm{S}}$ (MoS 2 -${\mathrm{Mo}}_{\mathrm{S}}^{{\mathrm{Se}}}$) vertical heterostructures originating from the bilayer nanoislands in the precursor monolayer crystals. The understanding of the origins of nanoscale defects in Janus TMDs revealed in this study can help with further optimization of the Janus conversion process towards uniform and wrinkle-/crack-free Janus materials. Moreover, this work shows that cross-correlated AFM and TERS imaging is a powerful and accessible method for studying nanoscale composition and defects in Janus TMD monolayers.

2D materials

Massive red spiral galaxies in SDSS-IV MaNGA survey

ABSTRACT Massive red spiral galaxies (MRSGs) are supposed to be the possible progenitors of lenticular galaxies (S0s). We select a large sample of MRSGs ($M_*\gt 10^{10.5}\rm {\rm M}_{\odot }$) from Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) DR17 using the g − r colour versus stellar mass diagram, along with control samples of blue spirals and S0s. Our main results are as follows: (1) After comparing the Sérsic index, concentration parameter, asymmetry parameter distribution, size–mass relation, and Σ1 (stellar mass surface density within the central 1 kpc)−mass relation, we find MRSGs are similar to S0s and have more compact and symmetric structures than blue spirals. MRSGs also resemble S0s in Dn4000, metallicity, Mgb/$\rm \left\langle Fe \right\rangle$, and V/σ radial profile. (2) By using MaNGA 2D spectra data, we separate the spatial regions into inner (R < 0.8Re) and outer (0.8 < R < 1.5Re) regions, and detect residual star formation in the outer regions of MRSGs. (3) When we select a sub-sample of MRSGs with NUV − r > 5, we find that they are completely star formation quenched in both inner and outer regions. Compared to optically selected MRSGs, NUV − r selected MRSGs appear to be more concentrated and have more massive dark matter haloes. The similarities between S0s and MRSGs suggest the possible evolutionary trend between MRSGs and S0s.

Astronomy & Astrophysics

The NASA OSIRIS-REx Sample Catalog: Samples Returned from Investigators

OSIRIS-REx is a sample return mission that collected carbon-rich material from B-type asteroid Bennu. After landing on September 24th, 2023, the science canister was transported to NASA Johnson Space Center (JSC) in Houston, Texas where it was opened and samples were processed by the curation team in pristine sample nitrogen gloveboxes. As the sample analysis phase of the OSIRIS-REx mission concludes, the Sample Analysis Team (SAT) has returned the majority of mission samples to NASA JSC curation and will return the remaining samples on a defined timetable. The curation team processed and documented as many of these samples as possible to include in the spring 2026 catalog update and are steadily working to process hundreds of more samples to include in the fall 2026 catalog update.

OSIRIS-REx

Future Projection of Tropical Upper-Tropospheric Troughs and Implications for Tropical Cyclone Activity

Summertime tropical upper-tropospheric troughs (TUTTs) provide a unified framework to better understand how extratropical and tropical forcings jointly modulate basin-scale tropical cyclone (TC) activity. In this study, we examine future changes in TUTTs and their implications for TC activity. Multimodel ensemble-mean projections from 45 Coupled Model Intercomparison Project phase 6 (CMIP6) models suggest a contraction of the Pacific TUTT and an expansion of the Atlantic TUTT as the climate warms. Consistently, future changes in environment-based TC indices indicate that the large-scale conditions will become more favorable for TC genesis and intensification over the central North Pacific but less favorable over the tropical North Atlantic and Gulf of Mexico. Utilizing a TC-permitting large-ensemble dataset [i.e., the Database for Policy Decision-Making for Future Climate Change (d4PDF)] that adequately captures the observed interannual TUTT–TC relationships, we further confirm the impacts of projected TUTT changes on the TC activity in a warmer climate. In contrast, the TUTT–TC relationship is poorly represented in most CMIP6 High-Resolution Model Intercomparison Project (HighResMIP) models; such deficiencies call for caution when assessing future TC risk based on explicitly tracked TCs in these models. Additionally, CMIP6 projections show large intermodel spread in TUTT changes, implying uncertainty in projected TC activity, especially over the central-to-eastern Pacific and the North Atlantic. This intermodel spread is associated with interhemispheric sea surface temperature warming asymmetry, which leads to a meridional shift of the intertropical convergence zone (ITCZ) and the simultaneous weakening or strengthening of TUTTs in the North Pacific and North Atlantic. The potential contributions of anthropogenic aerosol forcing and oceanic circulation to this interhemispheric warming asymmetry are briefly examined.

Climate Change

Reduced fast-ion transport calculations of m = n = 1 fishbone-like instabilities in MAST-U

Fast-ion transport associated with an m = n = 1 fishbone-like burst in MAST-U discharge 47128 is investigated using a reduced guiding-center-based transport model (ORBIT-Kick) constrained by multi-diagnostic measurements. The two-dimensional beam-emission spectroscopy system provides measurements of the core poloidal mode structure and fluctuation amplitude, while EFIT++ reconstructions constrained by the motional Stark effect diagnostic indicate a flat q-profile with q 0 > 1⁠, indicating the absence of a resonant q = 1 surface and supporting a pressure-driven infernal-mode interpretation. Analytic m = n = 1 displacement profiles consistent with the measured core mode structure and equilibrium constraints are used as the mode structure inputs to ORBIT-Kick. The calculations show that the dominant resonances occur between the mode and co-passing fast ions, producing redistribution localized near the magnetic axis. Synthetic neutron camera signals from TRANSP-Kick recover up to 90% of the experimentally observed neutron deficit at the time of peak mode amplitude, indicating that the measured m = n = 1 mode is a dominant contributor to core fast-ion transport. However, the synthetic neutron signals recover rapidly, whereas the measured neutron emission continues to decrease after the peak amplitude. In conclusion, the remaining discrepancy may arise from contributions not included in the present single-harmonic model, including higher-m and higher-n harmonics, multi-harmonic interactions, and additional transport mechanisms, motivating future diagnostic development and modeling efforts to resolve and incorporate these additional contributions.

Wong, Henry H. [University of California, Los Ange

The ABCs of phase retrieval: Connecting the acronyms of scanning transmission electron microscopy

High-resolution scanning transmission electron microscopy (S/TEM) is an indispensable tool for characterizing the structure and properties of materials down to the atomic scale. Conventional S/TEM imaging, however, is limited by the phase problem, whereby the phase of the electron exit wave is lost upon detection. Recent advances in diffractive imaging and 4D-STEM have enabled a range of phase-retrieval techniques that computationally reconstruct the missing information encoded in the phase of the transmission function. These approaches offer improved dose efficiency and enhanced sensitivity to weakly scattering signals, extending quantitative imaging to beam-sensitive materials composed of light elements. In this work, we introduce the phase problem in electron microscopy and survey the diverse landscape of phase-retrieval techniques used in the field. Despite their many acronyms and algorithmic variations, these techniques share a common physical and mathematical foundation. We present a unified framework that connects these seemingly distinct methods, from parallax imaging and tilt-corrected bright-field (tcBF-STEM), to aberration-corrected bright-field (acBF-STEM), optimum bright-field (OBF-STEM) and single-sideband (SSB) ptychography, as well as first-moment integrated center of mass techniques (iCOM) and iterative ptychographic algorithms. Based on these insights, we discuss the opportunities and practical limitations of applying these methods across different materials systems, detector designs, and microscope configurations.Graphical abstractRepresentative electron microscopy configurations used for phase retrieval and diffractive imaging in S/TEM: (a) Zernike phase-contrast transmission electron microscopy (TEM), (b) small-convergence-angle four-dimensional scanning transmission electron microscopy (4D-STEM) for nanobeam-based phase reconstruction methods, and (c) large-convergence-angle 4D-STEM for ptychographic and related diffractive imaging techniques reviewed in this work.

36 MATERIALS SCIENCE

An Overview of CMIP5 and CMIP6 Simulated Cloud Ice, Radiation Fields, Surface Wind Stress, Sea Surface Temperatures and Precipitation over Tropical and Subtropical Oceans

The potential links between ice water path (IWP), radiation, circulation, sea surface temperature (SST) and precipitation over the Pacific and Atlantic Oceans resulting from the falling ice radiative effects (FIREs) are examined from present day model outputs of CMIP5 and CMIP6. The latter is divided into two subsets with (SON6) and without FIREs (NOS6) as more models with FIREs are included in CMIP6 than in CMIP5. Improvement in floating cloud ice (~20 g m-2) is noticeable over convective regions in CMIP6 relative to CMIP5. The inclusion of FIREs in SON6 subset may contribute to reduce biases of overestimated outgoing longwave radiation and downward surface shortwave and overestimated reflected shortwave at the top of the atmosphere (TOA) by magnitudes of 4?8 W m-2 over convective regions against CERES, compared to NOS6 subset. The reduced biases in radiative fluxes in convective regions stabilize the atmosphere and lead to circulation, SST, cloud and precipitation changes over the trade-wind regions, as seen from improved radiative fluxes (4?15 W m-2), surface wind stress biases, SST (0.2?0.8 K) and precipitation (1 mm day-1) biases. The significant improvement from NOS6 to SON6 leads to improved multi-model means for CMIP6 relative to CMIP5 for radiation fields over the trade wind regions but the degradation over convective zones is attributed to NOS6 subset. The results suggest that other sources of uncertainty and deficiencies in climate models may play significant roles for reducing discrepancies although FIREs, via radiation-circulation coupling, may be one of the factors that help to reduce regional biases.

Jui-Lin F Li

Microstructure prediction for Ti-22Al-25Nb in laser powder bed fusion

This work presents a physics-informed framework for predicting solidification morphology and defect susceptibility in additively manufactured Ti–22Al–25Nb across a broad processing space. The framework integrates solidification microstructure selection (SMS) analysis with a single-track defect-based printability map to establish a unified methodology linking processing parameters to both interfacial morphology and manufacturability. Thermal gradients G and solidification rates R are first computed using the Thermo-Calc Additive Manufacturing (TC-AM) module, a finite-interface-dissipation (FID) phase-field (PF) model coupled with CALPHAD method is then employed to systematically distinguish planar and dendritic regimes as functions of $G$ and $R$. By superimposing the printability map onto the morphology projections, a comprehensive process–structure framework is obtained. Across most processing conditions, the predicted microstructure is predominantly dendritic, while planar growth emerges only under selected laser power $P$ and scan speed $v$ combinations. In addition to morphology classification, the framework quantifies the dendritic area fraction and introduces a width-based morphology descriptor to characterize the spatial extent of planar/dendritic regions within the melt pool. It provides mechanistic insight into the interplay between solidification physics and defect formation, offering practical guidance for parameter selection and microstructural control in Ti–22Al–25Nb additive manufacturing (AM).

36 MATERIALS SCIENCE

In Situ Tracking of Nonthermal Plasma Etching of ZIF-8 Films

Surface characterization is critical for understanding the processes used for preparing catalysts, sorbents, and membranes. Nonthermal plasma (NTP) is a process that achieves high reactivity at low temperatures and is used to tailor the surface properties of materials. In this work, we combine the capabilities of infrared reflection absorption spectroscopy (IRRAS) with NTP for the in situ interrogation of zeolitic imidazolate framework-8 (ZIF-8) thin films to probe modifications in the material induced by oxygen and nitrogen plasmas. The IRRAS measurements in oxygen plasma reveal etching of organic ligands with sequential removal of the methyl group and imidazole ring and with the formation of carbonyl moieties (C═O). In contrast, nitrogen plasma induces mild etching and grafting of nitrile groups (−C≡N). Scanning electron microscopy imaging shows that oxygen plasma, at prolonged times, significantly degrades the ZIF-8 film at the grain boundaries. Treatment of ZIF-8 membranes using mild plasma conditions yields a fivefold enhancement for H 2 /N 2 and CO 2 /CH 4 ideal selectivities and an eightfold enhancement for CO 2 /N 2 ideal selectivity. Additionally, the new tools described here can be used for spectroscopic in situ tracking of plasma-induced chemistry on thin films in general.

IRRAS

First Principles Study of Aluminum Doped Polycrystalline Silicon as a Potential Anode Candidate in Li‐ion Batteries

Addressing sustainable energy storage remains crucial for transitioning to renewable sources. While Li‐ion batteries have made significant contributions, enhancing their capacity through alternative materials remains a key challenge. Micro‐sized silicon is a promising anode material due to its tenfold higher theoretical capacity compared to conventional graphite. However, its substantial volumetric expansion during cycling impedes practical application due to mechanical failure and rapid capacity fading. A novel approach is proposed to mitigate this issue by incorporating trace amounts of aluminum into the micro‐sized silicon electrode using ball milling. Density functional theory (DFT) is employed to establish a theoretical framework elucidating how grain boundary sliding, a key mechanism involved in preventing mechanical failure is facilitated by the presence of trace aluminum at grain boundaries. This, in turn, reduces stress accumulation within the material, reducing the likelihood of failure. To validate the theoretical predictions, capacity retention experiments are conducted on undoped and Al‐doped micro‐sized silicon samples. In conclusion, the results demonstrate significantly reduced capacity fading in the doped sample, corroborating the theoretical framework and showcasing the potential of aluminum doping for improved Li‐ion battery performance.

25 ENERGY STORAGE

Lunar Electrical Conductivity, Permeability and Temperature From Apollo Magnetometer Experiments

Magnetometers have been deployed at four Apollo sites on the Moon to measure remanent and induced lunar magnetic fields. Measurements from this network of instruments have been used to calculate the electrical conductivity, temperature, magnetic permeability, and iron abundance of the lunar interior. The measured lunar remanent fields range from 3 gammas (γ) minimum at the Apollo 15 site to 327 γ maximum at the Apollo 16 site. Simultaneous magnetic field and solar plasma pressure measurements show that the remanent fields at the Apollo 12 and 16 sites interact with, and are compressed by, the solar wind. Remanent fields at Apollo 12 and Apollo 16 are increased 16 γ and 32 γ, respectively, by a solar plasma bulk pressure increase of 1.5 x 10 -7 dynes/cm 2 . Global lunar fields due to eddy currents, induced in the lunar interior by magnetic transients, have been analyzed to calculate an electrical conductivity profile for the Moon. From nightside magnetometer data in the solar wind it has been found that deeper than 170 km into the Moon the conductivity rises from 3 x 10 -4 mhos/m to 10 -2 mhos/m at 1000-km depth. Recent analysis of data obtained in the geomagnetic tail, in regions free of complicating plasma effects, yields results consistent with nightside values. Conductivity profiles have been used to calculate the lunar temperature for an assumed lunar material of olivine. In the outer layer (~ 170 km thick) the temperature rises to 110° C, after which it gradually increases with depth to 1500° C at a depth of ~ 1000 km. Simultaneous measurements by magnetometers on the lunar surface and in orbit around the moon are used to construct a whole-moon hysteresis curve, from which the global lunar magnetic permeability is determined to be μ = 1.012 ± 0.006. The corresponding global induced dipole moment is 2 x 10 18 gauss-cm 3 for typical inducing fields of 10 -4 gauss in the lunar environment. Lunar free iron abundance corresponding to the global permeability is determined to be 2.5 ± 2.0 wt. %. Total iron abundance (sum of iron in the ferromagnetic and paramagnetic states) is calculated for two assumed compositional models of the lunar interior. For a free iron/orthopyroxene lunar composition the total iron content is calculated to be 12.8 ± 1.0 wt. %; for a free iron/olivine composition, total iron content is 5.5 ± 1.2 wt. %. Other lunar models with an iron core and with a shallow iron-rich layer are also discussed in light of the measured global lunar permeability. Velocities and thicknesses of the Earth's magnetopause and bow shock have been estimated from simultaneous magnetometer measurements. Average speeds are determined to be about 50 km/s for the magnetopause and 70 km/s for the bow shock, although there are large variations in the measurement for any particular boundary crossing. Corresponding measured boundary thicknesses average about 2300 km for the magnetopause and 1400 km for the bow shock.

P Dyal

Computational Fluid Dynamics at the Lewis Research Center: An Overview

Lewis is a multidisciplinary Center with strong research and development programs in aeronautical and space propulsion, power, space communications, space experiments and materials. Computational fluid dynamics (CFD) is playing an important and growing role in most of these areas. Described here is how CFD is integrated into these programs and highlights elements of the CFD activities. Examples are presented of codes developed to predict flow fields in advanced propulsion systems and several of the code validation experiments are described. The CFD effort at Lewis ranges from basic research on new and improved algorithms through code development to the application of these codes to specific engineering problems. Because of the substantial improvement in CFD's predictive capability, its use at Lewis is on a steep growth path, spreading rapidly into new areas which had not traditionally taken advantage of the techniques of numerical simulation. Multidisciplinary codes and the future direction of CFD at Lewis are discussed.

Robert M Stubbs