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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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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The distribution of dust in edge-on galaxies: I. The global structure

ABSTRACT In this first paper in a series we present a study of the global dust emission distribution in nearby edge-on spiral galaxies. Our sample consists of 16 angularly large and 13 less spatially resolved galaxies selected from the DustPedia sample. To explore the dust emission distribution, we exploit the Herschel photometry in the range 100–500 $\mu $m. We employ Sérsic and 3D disc models to fit the observed 2D profiles of the galaxies. Both approaches give similar results. Our analysis unequivocally states the case for the presence of extraplanar dust in between 6 and 10 large galaxies. The results reveal that both the disc scale length and height increase as a function of wavelength between 100 and 500 $\mu $m. The dust disc scale height positively correlates with the dust disc scale length, similar to what is observed for the stellar discs. We also find correlations between the scale lengths and scale heights in the near- and far-infrared which suggest that the stellar discs and their dust counterparts are tightly connected. Furthermore, the intrinsic flattening of the dust disc is inversely proportional to the maximum rotation velocity and the dust mass of the galaxy: more massive spiral galaxies host, on average, relatively thinner dust discs. Also, there is a tendency for the dust-to-stellar scale height ratio to decrease with the dust mass and rotation velocity. We conclude that low-mass spiral galaxies host a diffuse, puffed-up dust disc with a thickness similar to that of the stellar disc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Analytical Study and Experimental Verification of Shear-Thinning Ink Flow in Direct Ink Writing Process

Abstract Direct ink writing (DIW) process is a facile additive manufacturing technology to fabricate three-dimensional (3D) objects with various materials. Its versatility has attracted considerable interest in academia and industry in recent years. As such, upsurging endeavors are invested in advancing the ink flow behaviors in order to optimize the process resolution and the printing quality. However, so far, the physical phenomena during the DIW process are not revealed in detail, leaving a research gap between the physical experiments and its underlying theories. Here, we present a comprehensive analytical study of non-Newtonian ink flow behavior during the DIW process. Different syringe-nozzle geometries are modeled for the comparative case studies. By using the computational fluid dynamics (CFD) simulation method, we reveal the shear-thinning property during the ink extrusion process. Besides, we study the viscosity, shear stress, and velocity fields, and analyze the advantages and drawbacks of each syringe-nozzle model. On the basis of these investigations and analyses, we propose an improved syringe-nozzle geometry for stable extrusion and high printing quality. A set of DIW printing experiments and rheological characterizations are carried out to verify the simulation studies. The results developed in this work offer an in-depth understanding of the ink flow behavior in the DIW process, providing valuable guidelines for optimizing the physical DIW configuration toward high-resolution printing and, consequently, improving the performance of DIW-printed objects.

Engineering↗
DOE OSTI2023

Numerical Simulations of High Prandtl Number Liquid Jets Impinging on a Flat Plate

In this work, 3D simulations of oil jets impinging on a flat, heated wall are presented. The numerical setup uses the Volume of Fluid (VoF) method to model the two-phase flow. A careful grid definition across the liquid film, along with the use of the Conjugate Heat Transfer (CHT) approach allowed local heat transfer to be solved with fine resolution at the wall. Variations of liquid flow rate, liquid temperature and surface temperature allow to cover a wide range of local Reynolds and Prandtl numbers (226 < Re < 2850, 77 < Pr < 161). Resulting surface-averaged heat transfer compares very well with experimental measurements conducted in a previous study. In-depth analysis of the flow has identified expected features from the literature. In particular, the impact of jet axial velocity profiles on the heat transfer distribution in the stagnation zone was clearly stated. The increase in heat transfer when warming the liquid film was also reproduced and explained by a decrease in oil viscosity and an increase in film velocity. All those effects were taken into account in correlations for stagnation and local values of Nusselt number. A grid sensitivity study was also conducted, showing that if the grid solving the thermal boundary layer in the stagnation zone can be coarsened without impacting local and surface-averaged predictions of heat transfer, a minimum resolution (2 to 3 cells) within the thermal boundary layer is however required for an accurate prediction of heat transfer.

conjugate heat transfer↗
DOE OSTI2026

Benchmarking of massively parallel phase-field codes for directional solidification

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.

36 MATERIALS SCIENCE↗
NASA NTRS2009

Modeling the Strahl in the Solar Wind Using CLUSTER/PEACE Electron Distribution Functions

We present a study of kinetic properties of the strahl electron velocity distribution functions (VDF's) in the solar wind. These are used to investigate the pitch-angle scattering and stability of the population to interactions with electromagnetic (whistler) fluctuations. The study is based on high time resolution data from the Cluster/PEACE electron spectrometer. Our study focuses on the mechanisms that control and regulate the pitch-angle and stability of strahl electrons in the solar wind; mechanisms that are not yet well understood. Various parameters are investigated such as the strahl-electron density, temperature anisotropy, and electron heat-flux. The goal is to check whether the strahl electrons are constrained by some instability (e.g., the whistler instability), or are maintained by other types of processes. The electron heat-flux and temperature anisotropy are determined by modeling the 3D-VDFs to a spectral spherical harmonic model from which the moments are obtained directly from the spectral coefficients.

Vinas, Adolfo F.↗
NASA NTRS1998

The Relationship of Ion Beams and Fast Flows in the Plasma Sheet Boundary Layer

We report new findings on the behavior of plasmas in the vicinity of the plasma sheet boundary layer (PSBL). A large geometrical factor detector on WIND (3D plasma experiment) has discovered a unidirectional ion beam streaming in the tailward direction missed by previous observations. This tailward beam is as intense as the earthward streaming beam and it is found just inside the outer edge of the PSBL where earthward streaming beams are observed. The region where this tailward beam is observed includes an isotropic plasma component which is absent in the outer edge where earthward streaming beams are found. When these different distributions are convolved to calculate the velocity moments, fast flows (greater than 400 km/s) result in the earthward direction and much slower flows (less than 200 km/s) in the tailward direction. These new findings are substantially different from previous observations. Thus, the interpretation of fast flows and earthward and counterstreaming ion beams in terms of a neutral line model must be reexamined.

Parks, G. K.↗
DOE OSTI2022

Constraining the shape of Milky Way satellites with distance gradients

We combine the Dark Energy Camera Legacy Survey DR8 photometry with Gaia photometry to study the 3D structure of Bootes I, Draco, Ursa Minor, Sextans, and Sculptor dwarf galaxies using blue horizontal branch (BHB) stars as distance indicators. We construct a new colour–absolute magnitude of BHB stars that we use to measure the distance gradients within the body of the dwarf galaxies. We detect a statistically significant non-zero gradient only in Sextans and Sculptor. Through modelling of the gradient and 2D density of the systems by triaxial Plummer models, we find that the distance gradients in both dwarf galaxies are inconsistent with prolate shape, but compatible with oblate or triaxial shapes. In order to explain the observed gradients, oblate models of Sextans and Sculptor need to have a significant intrinsic ellipticity larger than 0.47 for Sextans and 0.46 for Sculptor. Furthermore, the flattened oblate shape may imply a significant anisotropy in velocity distribution in order to be consistent with the lack of significant velocity gradients in these systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

PFLOTRAN modeling data and scripts associated with “Refining the Hydrogeologic Framework of a Large River Corridor Model Using Waterborne Transient Electromagnetics”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the publication “Refining the Hydrogeologic Framework of a Large River Corridor Model Using Waterborne Transient Electromagnetics” submitted to Water Resources Research (Terry et al. 2025). The data package contains the groundwater modeling dataset from PFLOTRAN software. It includes the python script for mesh generation, boundary condition setting, PFLOTRAN input deck formation and postprocessing. It couples groundwater flow and species transport for Hanford Reach river corridor and pipelines the model generation and processing. This model can be used to easily generate the model and analysis for Hanford site. It can also be adjusted to other hydrologic area with ease. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. The data package consists of 6 folders: (1) “data” contains all necessary data as input and intermediate data for processing; (2) “mesh” contains all mesh related files to generate mesh in Hanford Reach river corridor; (3) “model_run” contains the generated script for PFLOTRAN modeling; (4) “notebooks” contains all the Python script to generate the model; (5) “output” contains all the output from the computation; (6) “postprocessing” contains the Python script to generate scientific figure for manuscript. All files are .csv (comma-separated values), .h5 (HDF5 format), .in (input files), .ipynb (Jupyter notebooks), .p (Python pickle), .png (images), .PNG (images), .py (Python scripts), .pyc (Python bytecode), .r (R scripts), .sh (shell scripts), .txt (text files), .vtu (3D mesh/visualization format), .xz (compressed archive), or .zip (compressed archive).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Numerical simulation of asteroid geometry variance on airburst threat

For an atmospheric airburst the primary source of concern when assessing uncertainty is the size and velocity. Determining these properties provides the basis for threat assessment, as the total energy of the asteroid may then be estimated, and the threat investigated thoroughly. Even with clarity as to how much energy an asteroid may deposit, a great deal of uncertainty still exists for the actual energy deposition process. One such source of uncertainty is the geometry of the incoming asteroid. The geometry of an asteroid will alter the stress distribution during entry, which adds uncertainty to when fracture will occur. Here, in this study, we use Smoothed Particle Hydrodynamics to model the atmospheric airburst of Tunguska-scale asteroids with varying geometric profiles, including a sphere, ellipsoid, binary and superellipsoid. Each asteroid is modeled as a homogenous structure with strength. We assess uncertainty through a series of planar 2D simulation cases for each geometry, comparing the source of stochasticity across geometries. A single 3D airburst simulation for each geometry is also analyzed. Additionally, the 3D cases are compared to the highly uncertain Tunguska event, predicting variance in burst height across geometries, but all bounded by theoretical burst heights proposed for Tunguska.

Airburst↗
DOE OSTI2022

Long-term 3D MHD simulations of black hole accretion discs formed in neutron star mergers

ABSTRACT We examine the long-term evolution of accretion tori around black hole (BH) remnants of compact object mergers involving at least one neutron star, to better understand their contribution to kilonovae and the synthesis of r-process elements. To this end, we modify the unsplit magnetohydrodynamic (MHD) solver in flash 4.5 to work in non-uniform three-dimensional spherical coordinates, enabling more efficient coverage of a large dynamic range in length scales while exploiting symmetries in the system. This modified code is used to perform BH accretion disc simulations that vary the initial magnetic field geometry and disc compactness, utilizing a physical equation of state, a neutrino leakage scheme for emission and absorption, and modelling the BH’s gravity with a pseudo-Newtonian potential. Simulations run for long enough to achieve a radiatively inefficient state in the disc. We find robust mass ejection with both poloidal and toroidal initial field geometries, and suppressed outflow at high disc compactness. With the included physics, we obtain bimodal velocity distributions that trace back to mass ejection by magnetic stresses at early times, and to thermal processes in the radiatively inefficient state at late times. The electron fraction distribution of the disc outflow is broad in all models, and the ejecta geometry follows a characteristic hourglass shape. We test the effect of removing neutrino absorption or nuclear recombination with axisymmetric models, finding ${\sim} 50{{\ \rm per\ cent}}$ less mass ejection and more neutron-rich composition without neutrino absorption, and a subdominant contribution from nuclear recombination. Tests of the MHD and neutrino leakage implementations are included.

Fahlman, Steven (ORCID:0000000348759940)↗
NASA NTRS2008

Modeling of the Ablation of Fibrous Materials in the Knudsen Regime

During atmospheric entry of planetary probes, the thermal protection system (TPS) of the probe is exposed to high temperatures under low pressures. In these conditions, carbonous TPS materials undergo gasification in the Knudsen regime leading to mass loss and wall recession called ablation. This work aims to improve the understanding of materiaVenvironment interactions through a study of the coupling between carbon dioxide transport in the Knudsen regime, heterogeneous oxidation of carbon, and sutface recession. A 3D Monte-Carlo simulation tool is used for this study. The fibrous architecture of the materiils, consisting of high porosity random array of carbon fibers, is numerically reproduced on a 3D Cartesian grid. Mass transport in the Knudsen regime from the boundary layer to the surface, and inside this porous material is simulated by random walk. A reaction probability is used to simulate the heterogeneous oxidation reaction. The surface recession is followed by front tracking using a simplified marching cube approach. The output data of the simulations are ablation velocity and dynamic evolution of the material porosity. A parametric study is carried out to analyze the material behavior as a function of Knudsen number for the porous media (length of the mean free path compared to the mean pore diameter) and the intrinsic reactivity of the carbon fibers. The results enable extrapolation of laboratory experimental data to actual entry conditions.

Lachaud, J.↗
DOE OSTI2021

CFD-Guided Evaluation of Spark-Assisted Gasoline Compression Ignition for Cold Idle Operation

A closed-cycle, three-dimensional (3D) computational fluid dynamics (CFD) analysis campaign was conducted to evaluate the performance of using spark plugs to assist gasoline compression ignition (GCI) combustion during cold idle operations. A conventional spark plug using single-sided J-strap design was put at a location on the cylinder head to facilitate spray-guided spark assistance. Ignition was modeled with an L-type energy distribution to depict the breakdown and the arc-to-glow phases during the energy discharge process. Several key design parameters were investigated, including injector clocking, number of nozzle holes, spray inclusion angle, number of fuel injections, fuel split ratio, and fuel injection timings. The study emphasized the region around the spark gap, focusing on flame kernel formation and development and local equivalence ratio distribution. Flame kernel development and the ignition process were found to correlate strongly with the fuel stratification and the flow velocity near the spark gap. The analysis results showed that the flame kernel development followed the direction of the local flow field. In addition, the local fuel stratification notably influenced early-stage flame kernel development due to varying injection spray patterns and the fuel injection strategies. Among these design parameters, the number of nozzle holes and fuel injection timing had the most significant effects on the engine combustion performance.

42 ENGINEERING↗
DOE OSTI2021

Distant Relatives: The Chemical Homogeneity of Comoving Pairs Identified in Gaia

Comoving pairs, even at the separations of $\mathcal{O}$(10 6 ) are a predicted reservoir of conatal stars. Here we present detailed chemical abundances of 62 stars in 31 comoving pairs with separations of 10 2 –10 7 au and 3D velocity differences <2 km s -1 . This sample includes both bound comoving pairs/wide binaries and unbound comoving pairs. Observations were taken using the Magellan Inamori Kyocera Echelle (MIKE) spectrograph on board the Magellan/Clay Telescope at high resolution (R~ 45,000) with a typical signal-to-noise ratio of 150 pixel -1 . With these spectra, we measure surface abundances for 24 elements, including Li, C, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Y, Zr, Ba, La, Nd, and Eu. Taking iron as the representative element, our sample of wide binaries is chemically homogeneous at the level of 0.05 dex, which agrees with prior studies on wide binaries. Importantly, even systems at separations 2 × 10 5 –10 7 au are homogeneous to 0.09 dex, as opposed to the random pairs, which have a dispersion of 0.23 dex. Assuming a mixture model of the wide binaries and random pairs, we find that 73 ± 22% of the comoving pairs at separations 2 × 10 5 –10 7 au are conatal. Our results imply that a much larger parameter space of phase space may be used to find conatal stars, to study M-dwarfs, star cluster evolution, exoplanets, chemical tagging, and beyond.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2006

Effects of Kinetic Processes in Shaping Io's Global Plasma Environment: A 3D Hybrid Model

The global dynamics of the ionized and neutral gases in the environment of Io plays an important role in the interaction of Jupiter s corotating magnetospheric plasma with Io. Stationary simulations of this problem have already been done using the magnetohydrodynamics (MHD) and the electrodynamics approaches. One of the major results of recent simplified two-fluid model simulations [Saur, J., Neubauer, F.M., Strobel, D.F., Summers, M.E., 2002. J. Geophys. Res. 107 (SMP5), 1-18] was the production of the structure of the double-peak in the magnetic field signature of the Io flyby. These could not be explained before by standard MHD models. In this paper, we present a hybrid simulation for Io with kinetic ions and fluid electrons. This method employs a fluid description for electrons and neutrals, whereas for ions a particle approach is used. We also take into account charge-exchange and photoionization processes and solve self-consistently for electric and magnetic fields. Our model may provide a much more accurate description for the ion dynamics than previous approaches and allows us to account for the realistic anisotropic ion velocity distribution that cannot be done in fluid simulations with isotropic temperatures. The first results of such a simulation of the dynamics of ions in Io s environment are discussed in this paper. Comparison with the Galileo IO flyby results shows that this approach provides an accurate physical basis for the interaction and can therefore naturally reproduce all the observed salient features.

Lipatov, Alexander S.↗
DOE OSTI2023

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz–tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

47 OTHER INSTRUMENTATION↗
NASA NTRS2014

Simulation of Fluid Flow and Collection Efficiency for an SEA Multi-element Probe

Numerical simulations of fluid flow and collection efficiency for a Science Engineering Associates (SEA) multi-element probe are presented. Simulation of the flow field was produced using the Glenn-HT Navier-Stokes solver. Three-dimensional unsteady results were produced and then time averaged for the heat transfer and collection efficiency results. Three grid densities were investigated to enable an assessment of grid dependence. Simulations were completed for free stream velocities ranging from 85-135 meters per second, and free stream total pressure of 44.8 and 93.1 kilopascals (6.5 and 13.5 pounds per square inch absolute). In addition, the effect of angle of attack and yaw were investigated by including 5 degree deviations from straight for one of the flow conditions. All but one of the cases simulated a probe in isolation (i.e. in a very large domain without any support strut). One case is included which represents a probe mounted on a support strut within a finite sized wind tunnel. Collection efficiencies were generated, using the LEWICE3D code, for four spherical particle sizes, 100, 50, 20, and 5 micron in diameter. It was observed that a reduction in velocity of about 20% occurred, for all cases, as the flow entered the shroud of the probe. The reduction in velocity within the shroud is not indicative of any error in the probe measurement accuracy. Heat transfer results are presented which agree quite well with a correlation for the circular cross section heated elements. Collection efficiency results indicate a reduction in collection efficiency as particle size is reduced. The reduction with particle size is expected, however, the results tended to be lower than the previous results generated for isolated two-dimensional elements. The deviation from the two-dimensional results is more pronounced for the smaller particles and is likely due to the reduced flow within the protective shroud. As particle size increases differences between the two-dimensional and three dimensional results become negligible. Taken as a group, the total collection efficiency of the elements including the effects of the shroud has been shown to be in the range of 0.93 to 0.99 for particles above 20 microns. The 3D model has improved the estimated collection efficiency for smaller particles where errors in previous estimates were more significant.

Water Content↗
NASA NTRS2022

A SUBLIME 3D Model for Cometary Coma Emission: The Hypervolatile-rich Comet C/2016 R2 (PanSTARRS)

The coma of comet C/2016 R2 (PanSTARRS) is one of the most chemically peculiar ever observed, in particular due to its extremely high CO/H2O and N(+2)/H2O ratios, and unusual trace volatile abundances. However, the complex shape of its CO emission lines, as well as uncertainties in the coma structure and excitation, has lead to ambiguities in the total CO production rate. We performed high-resolution, spatially, spectrally, and temporally resolved CO observations using the James Clerk Maxwell Telescope and Submillimeter Array to elucidate the outgassing behavior of C/2016 R2. Results are analyzed using a new, time-dependent, three-dimensional radiative transfer code (SUBlimating gases in LIME; SUBLIME, based on the open-source version of the LIne Modeling Engine), incorporating for the first time, accurate state-to-state collisional rate coefficients for the CO–CO system. The total CO production rate was found to be in the range of (3.8 − 7.6) × 10^(28) per s between 2018 January 13 and February 1 (at r(H) = 2.8–2.9 au), with a mean value of (5.3 ± 0.6) × 10^(28) per s. The emission is concentrated in a near-sunward jet, with a half-opening angle of ∼62° and an outflow velocity of 0.51 ± 0.01 km/s, compared to 0.25 ± 0.01 km/s in the ambient (and nightside) coma. Evidence was also found for an extended source of CO emission, possibly due to icy grain sublimation around 1.2 × 10^(5) km from the nucleus. Based on the coma molecular abundances, we propose that the nucleus ices of C/2016 R2 can be divided into a rapidly sublimating apolar phase, rich in CO, CO2, N2, and CH3OH, and a predominantly frozen (or less abundant), polar phase containing more H2O, CH4, H2CO, and HCN.

Martin Andrew Cordiner↗
DOE OSTI2020

Additive Manufacturing Interface Profiles for Jet Studies on the Vertical Shock Tube

Understanding the mixing between two fluids of disparate densities (i.e., variable density mixing) is important for the lab's mission. Experiments are required to validate our codes, such as RAGE, FLAG, and the BHR mix model. The role initial conditions (ICs) have on instability growth and the transition to turbulence is not completely understood and comparisons with experiments are needed. The Extreme Fluids team focuses on experiments at Los Alamos that utilize gases and low shock velocities (Mach <2 in air). These experiments have the advantage of high fidelity diagnostics capable of temporally and spatially resolved velocity and density measurements. One main difficulty is setting up a specific interface profile between the two gases. While attempts have been made to do so without the aid of a solid structure (i.e., a membrane), the results are limited in the range of possible shapes and reproducibility. Membranes provide the best way to provide a deterministic initial condition. However, fragments from the membrane can interfere with the flow and instability growth, as well as the diagnostics. In this project, we focused on exploring the materials and techniques available via modern additive manufacturing (i.e., 3D printing) to test if they could address some of the shortcomings of prior membrane designs. Our goal was to find a material that would have minimal impact on our experiment while also providing us with a means to produce complex initial conditions. This report details our work to explore the range of additive manufacturing capabilities and the jet-like structures we were able to generate using three-dimensional initial conditions.

36 MATERIALS SCIENCE↗