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At least 217 records · Page 12

Super-Resolved Single-Molecule Tracking Studies of Rhodamine B Accumulation on Fresh and Aged Polyethylene Terephthalate

It is well-known that toxic organic micropollutants (OMs) accumulate on the surfaces of microplastics. However, much remains to be learned about the exact molecular level mechanisms of OM accumulation and how these evolve as the plastics age. In this work, super-resolved single-molecule tracking (SMT) is used for the first time to investigate the accumulation of Rhodamine B (RhB) dye on fresh and artificially aged polyethylene terephthalate (PET) surfaces. PET thin films serve as models for microplastics, while RhB serves as a proxy for the OMs they accumulate. Artificial aging of the films is accomplished by exposing them in a UV-ozone chamber. Water contact angle, spectroscopic ellipsometry, and carbonyl index measurements reveal a gradual decrease in film hydrophobicity, thickness, and carbonyl content with age. Atomic force microscopy (AFM) data reveal an increase in surface roughness and confirm that the films remain largely intact and continuous across the aging times explored. In SMT experiments, wide-field fluorescence videos acquired from the water/PET interface under 7.5 pM RhB reveal both mobile and immobile dye molecules. Measurements of the frame-to-frame displacements of the dye show that diffusion occurs by a desorption-mediated mechanism and that the diffusion rate varies with PET film age. The surface density of mobile dye molecules decreases with increasing PET age, while the population of immobile molecules becomes relatively larger, suggesting an age-dependent transformation of the mechanism(s) by which the dye is accumulated. SMT data reveal that both mobile and immobile molecules repeatedly adsorb over the same surface sites, consistent with the emergence of nanoscale PET surface heterogeneity also revealed by AFM. Estimates of the adsorption coefficients are obtained using a nearest-neighbor analysis, giving values from 9.9 × 10 5 to 2.1 × 10 6 M –1 for immobile molecules and from 1.8 × 10 5 to 2.5 × 10 5 M –1 for mobile molecules on fresh and 5 min aged PET, respectively. Here, anomalous age-dependent variations in the velocity of molecular motion on the PET surface and in the population of immobile molecules are shown to correlate with changes in the strength of RhB adsorption.

Adsorption↗

Chemical Evolution of Interstellar Dust into Planetary Materials

Comets are believed to retain some interstellar materials, stored in fairly pristine conditions since-their formation. The composition and properties of cometary dust grains should reflect those of grains in the outer part of the protosolar nebula which, at least in part, were inherited from the presolar molecular cloud. However, infrared emission features in comets differ from their interstellar counterparts. These differences imply processing of interstellar material on its way to incorporation in comets, but C and N appear to be retained. Overall dust evolution from the interstellar medium (ISM) to planetary materials is accompanied by an increase in proportion of complex organics and a decrease in pure carbon phases. The composition of cometary dust grains was measured in situ during fly-by missions to comet Halley in 1986. The mass spectra of about 5000 cometary dust grains with masses of 5 x 10(exp -17) - 5 x 10(exp -12) g provide data about the presence and relative abundances of the major elements H, C, N, O,Na, Mg, Al, Si, S, Cl, K, Ca, Ti, Cr, Fe, Ni. The bulk abundances of major rock-forming elements integrated over all spectra were found to be solar within a factor of 2, while the volatile elements H, C, N, O in dust are depleted in respect to their total cosmic abundances. The abundances of C and N in comet dust are much closer to interstellar than to meteoritic and are higher than those of dust in the diffuse ISM. In dense molecular clouds dust grains are covered by icy mantles, the average composition of which is estimated to be H:C:N:O = 96:14:1:34. Up to 40% of elemental C and O may be sequestered in mantles. If we use this upper limit to add H, C, N and O as icy mantle material to the abundances residing in dust in the diffuse ISM, then the resulting values for H. C, and N match cometary abundances. Thus, ice mantles undergoing chemical evolution on grains in the dense ISM appear to have been transformed into less volatile and more complex organic residues wherein the H, C and N are largely retained and ultimately accreted in cometary dust. The abundance of O is about the same for cometary dust, meteorites and interstellar dust. In all these samples, most of O in a solid phase is bonded to silicates. In dense molecular clouds, the abundance of O in dust+mantles is significantly higher then in cometary dust. This difference may reflect the greater lability of oxygenated species toward astrophysical processing. Laboratory studies show that O-bearing functional groups in organic compounds tend to be relatively easily removed by heating and/or UV and particle irradiation . In Halley's coma, O-containing organic grains, being unstable, were located closest to the nucleus. The decomposition of the organic grain component in the coma provided a significant extended source contribution to O-containing gaseous species such as CO and H2CO.

Fomenkova, M. N.↗

Mineral-Catalysed Formation of Marine NO and N 2 O on the Anoxic Early Earth

Microbial denitrification converts fixed nitrogen species into gases in extant oceans. However, it is unclear how such transformations occurred within the early nitrogen cycle of the Archean. Here 5we present experimental anoxic surface-catalyzed reduction of nitrite and nitrate via green rust and magnetite combined with diffusion and photochemical modeling. We find that in a Fe 2+ -rich marine environment, Fe minerals could have catalyzed abiotic denitrification reactions leading to the formation of nitric oxide (NO) and nitrous oxide (N 2 O). Nitrate did not exhibit reactivity in the presence of either mineral or aqueous Fe2+, however, both minerals induced rapid nitrite reduction 10to NO and N 2 O. While N 2 O escaped into the atmosphere (63% of nitrite-nitrogen, with green rust as catalyst), NO remained associated with precipitates (7%) serving as a potential shuttle to the benthic ocean.The modeling suggests that marine N 2 O emissions would have sustained 0.8-6 ppb of atmospheric N 2 O without a protective ozone layer. Our findings add detail to the as yet incompletely documented Archean nitrogen cycle, implying a globally distributed process driven 15by chemical kinetics similar to those of modern enzymatically mediated conversions.

Steffen Buessecker↗

Real-space local self-motion of protonated and deuterated water

Here, we report on the self-part of the Van Hove correlation function, the correlation function describing the dynamics of a single molecule, of water and deuterated water. The correlation function is determined by transforming inelastic scattering spectra of neutrons or x rays over a wide range of momentum transfer Q and energy transfer E to space R and time t. The short-range diffusivity is estimated from the Van Hove correlation function in the framework of the Gaussian approximation. The diffusivity has been found to be different from the long-range macroscopic diffusivity, providing information about local atomic dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Solutions of the Navier-Stokes equations for vortex breakdown

Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown in an unconfined viscous vortex are obtained numerically using the artificial compressibility technique of Chorin combined with an ADI finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. The solutions, which are obtained for Reynolds numbers up to 200 based on the free-stream axial velocity and a characteristic core radius, show that breakdown results from the diffusion and convection of vorticity away from the vortex core which, because of the strong coupling between the circumferential and axial velocity fields in strongly swirling flows, can lead to stagnation and reversal of the axial flow near the axis.

Grabowski, W. J.↗

Mathematical formulation of scatter-free propagation of solar cosmic rays

The observations of strong persistent velocity anisotropies in solar flare events demand a mathematical theory closer to the extreme of scatter-free (deterministic) propagation rather than diffusive (stochastic) transport, since the latter breaks down as inferred mean-free-paths exceed 0.1 AU. Equations are derived for the time-dependent phase-space density, and Laplace transform techniques are used to obtain solutions under rather general conditions. The case of an Archimedean spiral field has been solved numerically, and the results compared with observations from Mariner and Explorer spacecraft of nearly 0.4 MeV proton intensity and anisotropy histories. These can both be replicated if the inner boundary of the modulation region is placed beyond 2 AU.

Nolte, J. T.↗

Enhanced cosmic-ray acceleration rates in highly inclined astrophysical shocks

The theory of cosmic-ray acceleration by subluminal magnetohydrodynamics (MHD) astrophysical shocks according to the test particle approximation is extended to highly oblique shocks where flow speeds which appear nonrelativistic in the shock rest frame appear on transformation to the de Hoffmann-Teller or E identically equal to 0 frame to have upstream flow speeds approaching c. Monte Carlo simulation shows that relative to the predictions of diffusion theory, as the upstream E identically equal to 0 frame velocity approaches c, flatter spectra and faster acceleration rates occur. These spectral and acceleration time changes are similar to those found for relativistic, parallel MHD shocks and may affect all nonthermal active galactic nuclei emission from relativistic electrons. Also there is an additional means of increasing the upper limit of the cosmic-ray spectrum expected from active galactic nuclei, although the approximation used may not accurately reproduce the spectral shape.

Lieu, R.↗

Experimenting with the GMAO 4D Data Assimilation

The Global Modeling and Assimilation Office (GMAO) has been working to promote its prototype four-dimensional variational (4DVAR) system to a version that can be exercised at operationally desirable configurations. Beyond a general circulation model (GeM) and an analysis system, traditional 4DV AR requires availability of tangent linear (TL) and adjoint (AD) models of the corresponding GeM. The GMAO prototype 4DVAR uses the finite-volume-based GEOS GeM and the Grid-point Statistical Interpolation (GSI) system for the first two, and TL and AD models derived ITom an early version of the finite-volume hydrodynamics that is scientifically equivalent to the present GEOS nonlinear GeM but computationally rather outdated. Specifically, the TL and AD models hydrodynamics uses a simple (I-dimensional) latitudinal MPI domain decomposition, which has consequent low scalability and prevents the prototype 4DV AR ITom being used in realistic applications. In the near future, GMAO will be upgrading its operational GEOS GCM (and assimilation system) to use a cubed-sphere-based hydrodynamics. This versions of the dynamics scales to thousands of processes and has led to a decision to re-derive the TL and AD models for this more modern dynamics, thus taking advantage of a two-dimensional MPI decomposition and improved scalability properties. With the aid of the Transformation of Algorithms in FORTRAN (l'AF) automatic adjoint generation tool and some hand-coding, a version of the cubed-sphere-based TL and AD models, with a simplified vertical diffusion scheme, is now available, enabling multiple configurations of standard implementations of 4DV AR in GEOS. Concurrent to this development, collaboration with the National Centers for Environmental Prediction (NCEP) and the Earth System Research Laboratory (ESRL) has allowed GMAO to implement a hybrid-ensemble capability within the GEOS data assimilation system. Both 3Dand 4D-ensemble capabilities are presently available thus allowing GMAO to now evaluate the performance and benefit of various ensemble and variational assimilation strategies. This presentation will cover the most recent developments taking place at GMAO and show results from various comparisons from traditional techniques to more recent ensemble-based ones.

Todling, R.↗

Computational Studies of Magnetic Nozzle Performance

An extensive literature review of magnetic nozzle research has been performed, examining previous work, as well as a review of fundamental principles. This has allow us to catalog all basic physical mechanisms which we believe underlie the thrust generation process. Energy conversion mechanisms include the approximate conservation of the magnetic moment adiabatic invariant, generalized hall and thermoelectric acceleration, swirl acceleration, thermal energy transformation into directed kinetic energy, and Joule heating. Momentum transfer results from the interaction of the applied magnetic field with currents induced in the plasma plume., while plasma detachment mechanisms include resistive diffusion, recombination and charge exchange collisions, magnetic reconnection, loss of adiabaticity, inertial forces, current closure, and self-field detachment. We have performed a preliminary study of Hall effects on magnetic nozzle jets with weak guiding magnetic fields and weak expansions (p(sub jet) approx. = P(sub background)). The conclusion from this study is that the Hall effect creates an azimuthal rotation of the plasma jet and, more generally, creates helical structures in the induced current, velocity field, and magnetic fields. We have studied plasma jet expansion to near vacuum without a guiding magnetic field, and are presently including a guiding magnetic field using a resistive MHD solver. This research is progressing toward the implementation of a full generalized Ohm's law solver. In our paper, we will summarize the basic principle, as well as the literature survey and briefly review our previous results. Our most recent results at the time of submittal will also be included. Efforts are currently underway to construct an experiment at the University of Michigan Plasmadynamics and Electric Propulsion Laboratory (PEPL) to study magnetic nozzle physics for a RF-thruster. Our computational study will work directly with this experiment to validate the numerical model, in order to study magnetic nozzle physics and optimize magnetic nozzle design. Preliminary results from the PEPL experiment will also be presented.

Ebersohn, Frans H.↗

Digital-computer normal shock position and restart control of a Mach 2.5 axisymmetric mixed-compression inlet

Digital computer control of a mixed-compression inlet is discussed. The inlet was terminated with a choked orifice at the compressor face station to dynamically simulate a turbojet engine. Inlet diffuser exit airflow disturbances were used. A digital version of a previously tested analog control system was used for both normal shock and restart control. Digital computer algorithms were derived using z-transform and finite difference methods. Using a sample rate of 1000 samples per second, the digital normal shock and restart controls essentially duplicated the inlet analog computer control results. At a sample rate of 100 samples per second, the control system performed adequately but was less stable.

Neiner, G. H.↗

Lightning induced currents in aircraft wiring using low level injection techniques

Various techniques were studied to predict the transient current induced into aircraft wiring bundles as a result of an aircraft lightning strike. A series of aircraft measurements were carried out together with a theoretical analysis using computer modeling. These tests were applied to various aircraft and also to specially constructed cylinders installed within coaxial return conductor systems. Low level swept frequency CW (carrier waves), low level transient and high level transient injection tests were applied to the aircraft and cylinders. Measurements were made to determine the transfer function between the aircraft drive current and the resulting skin currents and currents induced on the internal wiring. The full threat lightning induced transient currents were extrapolated from the low level data using Fourier transform techniques. The aircraft and cylinders used were constructed from both metallic and CFC (carbon fiber composite) materials. The results show the pulse stretching phenomenon which occurs for CFC materials due to the diffusion of the lightning current through carbon fiber materials. Transmission Line Matrix modeling techniques were used to compare theoretical and measured currents.

Stevens, E. G.↗

Transport properties of liquid metal hydrogen under high pressures

A theory is developed for the compressibility and transport properties of liquid metallic hydrogen, near to its melting point and under high pressure. The interionic force law is assumed to be of the screened Coulomb type, because hydrogen has no core electrons. The random phase approximation is used to obtain the structure factor S(k) of the system in terms of the Fourier transform of this force law. The long wavelenth limit of the structure factor S(o) is related to the compressibility, which is much lower than that of alkali metals at their melting points. The diffusion constant at the melting point is obtained in terms of the Debye frequency, using a frequency spectrum analogous with the phonon spectrum of a solid. A similar argument is used to obtain the combined shear and bulk viscosities, but these depend also on S(o). The transport coefficients are found to be about the same size as those of alkali metals at their melting points.

Brown, R. C.↗

MTF and point-spread function for a large-area CCD imager

The MTF degradation due to lateral diffusion is calculated for a back illuminated CCD imager for typical device parameters. The discrete nature of the CCD and finite size of the photosensitive elements result in an additional MTF degradation. The Fourier transform approach is utilized to calculate the effective point spread function for these processes in the time domain. Experimental data are presented on the point spread function for a three phase, double level anodized aluminum 160 x 100 thinned and back illuminated CCD imager and compared with the theoretical results. A simple modification of the Crowell and Labuda model suggested by these results is presented.

Ando, K. J.↗

Computational Modeling of Molten Salt Infiltration and Oxidation in Nuclear Graphite

Graphite is utilized as a moderator and reflector in advanced nuclear reactor designs due to its high thermal conductivity, neutron moderation properties, and resistance to radiation damage. However, its longterm performance and reliability are challenged by degradation mechanisms such as molten salt infiltration in molten salt reactors (MSRs) and oxidation in gas-cooled reactors (GCRs). These mechanisms can compromise the structural integrity and operational lifetime of graphite components, necessitating a more detailed assessment of their physical behavior. This report focuses on the development of computational models for molten salt infiltration and oxidation of graphite to aid the design and performance analysis of graphite components. For molten salt infiltration, a computational framework is developed that couples incompressible Navier-Stokes and phase-field model to simulate the penetration of molten salt into graphite?s interconnected pore structure. Initial model verification is performed using two-phase flows in two dimensions, demonstrating the models ability to capture fundamental physical behavior and agree with analytical solution. This framework is then applied to a realistic IG110 nuclear graphite , where a computed tomography extracted pore geometry is used to analyse the infiltration behavior of FLiNaK molten salt. This model provides insights into how the microstructure and other relevant parameters influence the transport pathways of molten salt into graphite, potentially offering a means to rapidly evaluate a graphite grade?s resistance to infiltration. For oxidation, the report details pore-scale mass and heat transport models, describing the diffusion of gases, reaction kinetics, and thermal effects. Additionally, this report highlights inconsistencies in the existing volume-averaged macroscopic model, particularly in upscaling of reaction kinetics and flux terms, and surface to volume transformations. These inconsistencies suggest that current formulations may not accurately capture the experimentally observed graphite oxidation process, highlighting the need for improved model development. This work advances the development of physics-based computational models for graphite degradation, contributing to improved predictive models for next-generation nuclear reactor designs. Future efforts will focus on refining the infiltration model to address non-physical behaviors and enhance its robustness. Additionally, for oxidation, further studies will employ the principles of volume averaging to rigorously derive the upscaled equations, potentially in collaboration with subject matter experts.

Computational Modeling of Molten Salt Infiltration↗

Soil porous microstructure control over soil organic matter mobility: A multimethod workflow for understanding chemistry-dependent organic matter binding in soil

Soil organic matter (SOM) has attracted a great deal of interest; particularly for its potential to mitigate human derived CO 2 emissions. Studies have demonstrated that SOM plays a critical role in carbon storage and CO 2 sequestration. However, the sorption properties of SOM, which influence its transport in pore water and stabilization within the soil, remain poorly understood. This study develops a workflow to: (1) examine compound-specific advective and diffusive transport and desorption behaviors, (2) quantify desorption rates through stop-flow and continuous-flow column experiments, and (3) evaluate the impact of soil microporosity on SOM mobility using high-resolution imaging and extractions. Intact core column experiments were conducted on Uncultivated (Natural) and Cultivated soil samples, both were arid soils, collected in Washington State. X-ray computed tomography was employed to measure porosity and pore connectivity, while Fourier-transform ion cyclotron resonance mass spectrometry was used to analyze SOM composition. The findings revealed that cultivation increased total carbon and nitrogen levels due to irrigation and fertilization, enhancing carbon capture potential in arid soils. In contrast, the Natural soil, characterized by higher porosity and connectivity, contained more oxidized carbon. Pore network analysis indicated that soil compaction in the Cultivated soil may lead to longer diffusion pathways, significantly influencing SOM transport and stability.

Hydraulic Properties↗

Focal Gray Matter Plasticity as a Function of Long Duration Head Down Tilted Bed Rest: Preliminary Results

Long duration spaceflight (i.e., 22 days or longer) has been associated with changes in sensorimotor systems, resulting in difficulties that astronauts experience with posture control, locomotion, and manual control. The microgravity environment is an important causal factor for spaceflight induced sensorimotor changes. Whether these sensorimotor changes are solely related to peripheral changes from reduced vestibular stimulation, body unloading, body fluid shifts or that they may be related to structural and functional brain changes is yet unknown. However, a recent study reported associations between microgravity and flattening of the posterior eye globe and protrusion of the optic nerve [1] possibly as the result of increased intracranial pressure due to microgravity induced bodily fluid shifts [3]. Moreover, elevated intracranial pressure has been related to white matter microstructural damage [2]. Thus, it is possible that spaceflight may affect brain structure and thereby cognitive functioning. Long duration head down tilt bed rest has been suggested as an exclusionary analog to study microgravity effects on the sensorimotor system [4]. Bed rest mimics microgravity in body unloading and bodily fluid shifts. In consideration of the health and performance of crewmembers both in- and post-flight, we are conducting a prospective longitudinal 70-day bed rest study as an analog to investigate the effects of microgravity on brain structure [5]. Here we present results of the first six subjects. Six subjects were assessed at 12 and 7 days before-, at 7, 30, and ~70 days in-, and at 8 and 12 days post 70 days of bed rest at the NASA bed rest facility in UTMB, Galveston, TX, USA. At each time point structural MRI scans (i.e., high resolution T1-weighted imaging and Diffusion Tensor Imaging (DTI)) were obtained using a 3T Siemens scanner. Focal changes over time in gray matter density were assessed using the voxel based morphometry 8 (VBM8) toolbox under SPM. Longitudinal processing in VBM8 includes linear registration of each scan to the mean of the subject and subsequently transforming all scans in to MNI space by applying the warp from the mean subject to MNI to the individual gray matter segmentations. Modulation was applied so that all images represented the volume of the original structure in native space. Voxel wise analysis was carried out on the gray matter images after smoothing, using a flexible factorial design with family wise error correction. Focal changes in white matter microstructural integrity were assessed using tract based spatial statistics (TBSS) as part of FMRIB software library (FSL). TBSS registers all DTI scans to standard space. It subsequently creates a study specific white matter skeleton of the major white matter tracts. For each subject, for each DTI metric (i.e. fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD)), the maximum value in a line perpendicular to the skeleton tract is projected to the skeleton. Non-parametric permutation based t-tests and ANOVA's were used for voxel-wise comparison of the skeletons. For both VBM and TBSS, comparison of pre bed rest measurements did not show significant differences. VBM analysis revealed decreased gray matter density in bilateral areas including the frontal medial cortex, the insular cortex and the caudate (see Figure) from 'pre to in bed rest'. Over the same time period, there was an increase in gray matter density in the cerebellum, occipital-, and parietal cortex, including the precuneus (see Figure). The majority of these changes did not recover from 'during to post bed rest'. TBSS analysis did not reveal significant changes in white matter microstructural integrity after correction for multiple comparisons. Uncorrected analyses (p<.015) revealed an increase in RD in the cerebellum and brainstem from pre bed rest to the first week in bed rest that did not recover post bed rest. Extended bed rest, which is an analog for microgravity, can result in gray matter changes and potentially in microstructural white matter changes in areas that are important for neuro motor behavior and cognition. These changes did not recover at two weeks post bed rest. Whether the effects of bed rest wear off at longer times post bed rest, and if they are associated with behavior are important questions that warrant further research.

Koppelmans, V.↗

Aerosol Microphysics and Chemical Measurements at Mt. Soledad and Scripps Pier during the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE) from February 2023 to February 2024 UCSD Library Collection

This dataset includes guest instrument measurements and other PI products for aerosol microphysics and chemical measurements collected at Mt. Soledad and Scripps Pier during the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE) from February 2023 to February 2024. The measurements include the following instruments at Mt. Soledad: High-Resolution Time-of-Flight Aerosol Mass Spectrometer (HR-ToF-AMS, Aerodyne), Scanning Electrical Mobility Spectrometer (SEMS, Brechtel Manufacturing Inc.), Aerodynamic Particle Sizer (APS, Droplet Measurements Technologies), Single Particle Soot Photometer (SP2, Drople Measurements Technologies), Meteorological Station (WXT520, Vaisala), Ozone (Teco), and trace gas proxies (Teledyne). In addition, the analyses of particle filters collected at Mt. Soledad for three dry-diameter size cuts (<1 micron, <0.5 micron, <0.18 micron) and at Scripps Pier for one dry-diameter size cut (<1 micron) by Fourier Transform Infrared (FTIR) and X-ray Fluorescence (XRF) are reported. A differential mobility analyzer operated as a scanning mobility particle sizer (SMPS, TSI Inc.), a printed particle optical spectrometer (POPS, Grimm), and a continuous flow diffusion cloud condensation nuclei (CCN, DMT) counter provide the mobility aerosol size distribution (30-360 nm), optical size distribution (150 - 6000 nm), size-resolved CCN distribution (30-360 nm) at 0.2, 0.4, 0.6, 0.8, and 1.0% supersaturation. Measurements are reported for both sampling from an isokinetic aerosol inlet and from a Counterflow Virtual Impactor (CVI, Brechtel Manufacturing Inc.). The data are available at the following link: https://library.ucsd.edu/dc/collection/bb0898306q

54 ENVIRONMENTAL SCIENCES↗

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗