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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Session 3: Irradiation and Thermal Stesses - NRC Graphite Behavior Model

Graphite anisotropic microstructure Graphite crystal structure and basal planes Response to irradiation and temperature C-axis and a-axis behavior The effect of porosity Nano-and micro-length scale Microscopic to macroscopic response Material property changes Defect length-scale factors Internal stress build-up Irradiation induced dimensional change Temperature effects Stress increases & property changes

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Improving the W Coating Uniformity by a COMSOL Model-Based CVD Parameter Study for Denser W f /W Composites

Tungsten (W) has the unique combination of excellent thermal properties, low sputter yield, low hydrogen retention, and acceptable activation. Therefore, W is presently the main candidate for the first wall and armor material for future fusion devices. However, its intrinsic brittleness and its embrittlement during operation bears the risk of a sudden and catastrophic component failure. As a countermeasure, tungsten fiber-reinforced tungsten (W f /W) composites exhibiting extrinsic toughening are being developed. A possible W f /W production route is chemical vapor deposition (CVD) by reducing WF 6 with H 2 on heated W fabrics. The challenge here is that the growing CVD-W can seal gaseous domains leading to strength reducing pores. In previous work, CVD models for W f /W synthesis were developed with COMSOL Multiphysics and validated experimentally. In the present article, these models were applied to conduct a parameter study to optimize the coating uniformity, the relative density, the WF 6 demand, and the process time. A low temperature and a low total pressure increase the process time, but in return lead to very uniform W layers at the micro and macro scales and thus to an optimized relative density of the W f /W composite. High H 2 and low WF 6 gas flow rates lead to a slightly shorter process time and an improved coating uniformity as long as WF 6 is not depleted, which can be avoided by applying the presented reactor model.

36 MATERIALS SCIENCE↗
NASA NTRS2015

Regolith and Environment Science and Oxygen and Lunar Volatile Extraction (RESOLVE): Lunar Advanced Volatile Analysis (LAVA) Capillary Fluid Dynamic Restriction Effects on Gas Chromatography

The Resource Prospector (RP) mission with the Regolith and Environment Science and Oxygen Lunar Volatile Extraction (RESOLVE) payload aims to show the presence of water in lunar regolith, and establish a proving ground for NASAs mission to Mars. One of the analysis is performed by the Lunar Advanced Volatiles Analysis (LAVA) subsystem, which consists of a fluid network that facilitates the transport of volatile samples to a gas chromatograph and mass spectrometer (GC-MS) instrument. The understanding of fluid dynamics directed from the GC to the MS is important due to the influence of flow rates and pressures that affect the accuracy of and prevent the damage to the overall GC-MS instrument. The micro-scale capillary fluid network within the GC alone has various lengths and inner-diameters; therefore, determination of pressure differentials and flow rates are difficult to model computationally, with additional complexity from the vacuum conditions in space and lack of a lunar atmosphere. A series of tests were performed on an experimental set-up of the system where the inner diameters of the GC transfer line connecting to the MS were varied. The effect on chromatography readings were also studied by applying these lines onto a GC instrument. It was found that a smaller inner diameter transfer line resulted in a lower flow rate, as well as a lower pressure differential across the thermal conductivity detector (TCD) unit of the GC and a negligible pressure drop across the mock-up capillary column. The chromatography was affected with longer retention times and broader peak integrations. It was concluded that a 0.050 mm inner diameter line still proved most suitable for the systems flow rate preferences. In addition, it was evident that this small transfer line portrayed some expense to GC signal characteristics and the wait time for steady-state operation.

RESOLVE↗
NASA NTRS2019

Magnification, dust, and time-delay constraints from the first resolved strongly lensed Type Ia supernova iPTF16geu

We report lensing magnifications, extinction, and time-delay estimates for the first resolved, multiply imaged Type Ia supernova iPTF16geu, at z = 0.409, using Hubble Space Telescope (HST) observations in combination with supporting ground-based data. Multiband photometry of the resolved images provides unique information about the differential dimming due to dust in the lensing galaxy. Using HST and Keck AO reference images taken after the SN faded, we obtain a total lensing magnification for iPTF16geu of μ = 67.8(+2.6−2.9), accounting for extinction in the host and lensing galaxy. As expected from the symmetry of the system, we measure very short time-delays for the three fainter images with respect to the brightest one: −0.23 ± 0.99, −1.43 ± 0.74, and 1.36 ± 1.07 d. Interestingly, we find large differences between the magnifications of the four supernova images, even after accounting for uncertainties in the extinction corrections: ∆m(1) = −3.88(+0.07−0.06), ∆m(2) = −2.99(+0.09−0.08), ∆m(3) = −2.19(+0.14−0.15),and ∆m(4) = −2.40(+0.14−0.12) mag, discrepant with model predictions suggesting similar image brightnesses. A possible explanation for the large differences is gravitational lensing by substructures, micro- or millilensing, in addition to the large-scale lens causing the image separations. We find that the inferred magnification is insensitive to the assumptions about the dust properties in the host and lens galaxy.

S Dhawan↗
NASA NTRS2017

Tortuosity Computations of Porous Materials using the Direct Simulation Monte Carlo

Low-density carbon fiber preforms, used as thermal protection systems (TPS) materials for planetary entry systems, have permeable, highly porous microstructures consisting of interlaced fibers. Internal gas transport in TPS is important in modeling the penetration of hot boundary-layer gases and the in-depth transport of pyrolysis and ablation products. The gas effective diffusion coefficient of a porous material must be known before the gas transport can be modeled in material response solvers; however, there are very little available data for rigid fibrous insulators used in heritage TPS.The tortuosity factor, which reflects the efficiency of the percolation paths, can be computed from the effective diffusion coefficient of a gas inside a porous material and is based on the micro-structure of the material. It is well known, that the tortuosity factor is a strong function of the Knudsen number. Due to the small characteristic scales of porous media used in TPS applications (typical pore size of the order of 50 micron), the transport of gases can occur in the rarefied and transitional regimes, at Knudsen numbers above 1. A proper way to model the gas dynamics at these conditions consists in solving the Boltzmann equation using particle-based methods that account for movement and collisions of atoms and molecules.In this work we adopt, for the first time, the Direct Simulation Monte Carlo (DSMC) method to compute the tortuosity factor of fibrous media in the rarefied regime. To enable realistic simulations of the actual transport of gases in the porous medium, digitized computational grids are obtained from X-ray micro-tomography imaging of real TPS materials. The SPARTA DSMC solver is used for simulations. Effective diffusion coefficients and tortuosity factors are obtained by computing the mean-square displacement of diffusing particles.We first apply the method to compute the tortuosity factors as a function of the Knudsen number for computationally designed materials such as random cylindrical fibers and packed bed of spheres with prescribed porosity. Results are compared to literature values obtained using random walk methods in the rarefied and transitional regime and a finite-volume method for the continuum regime. We then compute tortuosity factors for a real carbon fiber material with a transverse isotropic structure (FiberForm), quantifying differences between through-thickness and in-plain tortuosities at various Knudsen regimes.

Tortuosity↗
DOE OSTI2023

Probing the Mechanical Performance of Micro-architected Porous Structures Through In Situ Characterization and Analysis

Micropores play critical roles in both natural and man-made materials. Such pores take on a variety of shapes and sizes ranging from spherical to irregular sphere-like voids with diameters spanning from the nanometer to millimeter scales. When porous structures are mechanically loaded, the pores direct the stress around their free surfaces, altering the material’s mechanical response relative to fully dense materials. In this study, for the first time, we create micro-architected porous samples using nanolithography and investigate the role of pore morphology by conducting a series of in situ micropillar compression tests in scanning electron microscopy. The findings demonstrate that porosity is the primary factor influencing the mechanical response of these micro-architected materials, as often seen on a macroscopic level. Additionally, we observed that pore geometry had a significant impact on Young’s modulus, yield stress, and strain energy density as a secondary parameter. Then, the extracted Young’s modulus was compared to macroscopic empirical models and determined the analytical models sufficiently described the impact of porosity in the microscopic scale but failed to capture the impact of second-order parameters. Furthermore, these results suggest how porous materials can be tailored to achieve desired mechanical properties based on the engineering applications of interest.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Flexible Wing Base Micro Aerial Vehicles: Composite Materials for Micro Air Vehicles

This paper will discuss the development of the University of Florida's Micro Air Vehicle concept. A series of flexible wing based aircraft that possess highly desirable flight characteristics were developed. Since computational methods to accurately model flight at the low Reynolds numbers associated with this scale are still under development, our effort has relied heavily on trial and error. Hence a time efficient method was developed to rapidly produce prototype designs. The airframe and wings are fabricated using a unique process that incorporates carbon fiber composite construction. Prototypes can be fabricated in around five man-hours, allowing many design revisions to be tested in a short period of time. The resulting aircraft are far more durable, yet lighter, than their conventional counterparts. This process allows for thorough testing of each design in order to determine what changes were required on the next prototype. The use of carbon fiber allows for wing flexibility without sacrificing durability. The construction methods developed for this project were the enabling technology that allowed us to implement our designs. The resulting aircraft were the winning entries in the International Micro Air Vehicle Competition for the past two years. Details of the construction method are provided in this paper along with a background on our flexible wing concept.

Ifju, Peter G.↗
DOE OSTI2020

Permeability Hysteresis From Microchannels Opening During Dissolution/Reprecipitation Cycle

Abstract Permeability is a critical parameter for geological resources characterization. Its evolution with respect to porosity is particularly interesting and many research initiatives focus on deriving such relationships, to understand some hydraulic impacts of microstructure alteration. Permeability evolution from chemical reactions, for instance, can become complex as flow channels may open during rock dissolution. In this contribution, we show that this phenomenon can lead to irregular porosity‐permeability curves and permeability hysteresis after reprecipitation. Current approaches describing permeability as a simple function of porosity can therefore not capture this behavior, and we advocate instead the use of dynamic modeling for such scenarios. We demonstrate our approach by modeling a dissolution/precipitation cycle for a unit cell pore channel and quantify the process at larger scale on three different rock samples, whose microstructures are reconstructed from segmented micro‐Computerised Tomography scans.

Lesueur, Martin↗
NASA NTRS2017

From Tomography to Material Properties of Thermal Protection Systems

A NASA Ames Research Center (ARC) effort, under the Entry Systems Modeling (ESM) project, aims at developing micro-tomography (micro-CT) experiments and simulations for studying materials used in hypersonic entry systems. X-ray micro-tomography allows for non-destructive 3D imaging of a materials micro-structure at the sub-micron scale, providing fiber-scale representations of porous thermal protection systems (TPS) materials. The technique has also allowed for In-situ experiments that can resolve response phenomena under realistic environmental conditions such as high temperature, mechanical loads, and oxidizing atmospheres. Simulation tools have been developed at the NASA Ames Research Center to determine material properties and material response from the high-fidelity tomographic representations of the porous materials with the goal of informing macroscopic TPS response models and guiding future TPS design.

Tomography↗
NASA NTRS2013

NASA Models of Space Radiation Induced Cancer, Circulatory Disease, and Central Nervous System Effects

The risks of late effects from galactic cosmic rays (GCR) and solar particle events (SPE) are potentially a limitation to long-term space travel. The late effects of highest concern have significant lethality including cancer, effects to the central nervous system (CNS), and circulatory diseases (CD). For cancer and CD the use of age and gender specific models with uncertainty assessments based on human epidemiology data for low LET radiation combined with relative biological effectiveness factors (RBEs) and dose- and dose-rate reduction effectiveness factors (DDREF) to extrapolate these results to space radiation exposures is considered the current "state-of-the-art". The revised NASA Space Risk Model (NSRM-2014) is based on recent radio-epidemiology data for cancer and CD, however a key feature of the NSRM-2014 is the formulation of particle fluence and track structure based radiation quality factors for solid cancer and leukemia risk estimates, which are distinct from the ICRP quality factors, and shown to lead to smaller uncertainties in risk estimates. Many persons exposed to radiation on earth as well as astronauts are life-time never-smokers, which is estimated to significantly modify radiation cancer and CD risk estimates. A key feature of the NASA radiation protection model is the classification of radiation workers by smoking history in setting dose limits. Possible qualitative differences between GCR and low LET radiation increase uncertainties and are not included in previous risk estimates. Two important qualitative differences are emerging from research studies. The first is the increased lethality of tumors observed in animal models compared to low LET radiation or background tumors. The second are Non- Targeted Effects (NTE), which include bystander effects and genomic instability, which has been observed in cell and animal models of cancer risks. NTE's could lead to significant changes in RBE and DDREF estimates for GCR particles, and the potential effectiveness of radiation mitigator's. The NSRM- 2014 approaches to model radiation quality dependent lethality and NTE's will be described. CNS effects include both early changes that may occur during long space missions and late effects such as Alzheimer's disease (AD). AD effects 50% of the population above age 80-yr, is a degenerative disease that worsens with time after initial onset leading to death, and has no known cure. AD is difficult to detect at early stages and the small number of low LET epidemiology studies undertaken have not identified an association with low dose radiation. However experimental studies in mice suggest GCR may lead to early onset AD. We discuss modeling approaches to consider mechanisms whereby radiation would lead to earlier onset of occurrence of AD. Biomarkers of AD include amyloid beta (A(Beta)) plaques, and neurofibrillary tangles (NFT) made up of aggregates of the hyperphosphorylated form of the micro-tubule associated, tau protein. Related markers include synaptic degeneration, dentritic spine loss, and neuronal cell loss through apoptosis. Radiation may affect these processes by causing oxidative stress, aberrant signaling following DNA damage, and chronic neuroinflammation. Cell types to be considered in multi-scale models are neurons, astrocytes, and microglia. We developed biochemical and cell kinetics models of DNA damage signaling related to glycogen synthase kinase-3(Beta) (GSK3(Beta)) and neuroinflammation, and considered multi-scale modeling approaches to develop computer simulations of cell interactions and their relationships to A(Beta) plaques and NFTs. Comparison of model results to experimental data for the age specific development of A(Beta) plaques in transgenic mice will be discussed.

Cucinotta, Francis A.↗
DOE OSTI2025

Non-Destructive, Three-Dimensional Imaging of Processes in the Rhizosphere Utilizing High Energy Photons

Soil structure, which can be described as the aggregation and distribution of pore spaces, regulates carbon, nutrient, and water cycling across the Earth system. Yet the inability to make quantitative, dynamic, in situ measurements of soil structure and rhizosphere carbon flow has prevented meaningful incorporation of soil structural processes into Earth System Models (ESMs). The key limitations are: (i) Lack of scale integration between micron-scale soil structure and ecosystem-scale models, (ii) Poor functional linkage between soil structural properties and biogeochemical processes, and (iii) Absence of dynamic 3D measurements of rhizosphere structural changes and carbon transformations. To address these challenges, we developed a new integrated positron emission tomography (PET) - microcomputed tomography (CT) imaging platform that enables the first 4D (spatial 3D and time), non-invasive, quantitative imaging of carbon allocation and rhizosphere structural dynamics in living plants and intact soils. The system combines: • Rhizo-PET (R-PET): a high-resolution positron emission tomography scanner optimized for 11 CO 2 tracing in plant roots. • a-Se micro-CT: a high-contrast, high-spatial resolution CT system based on amorphous selenium (a-Se) direct conversion technology, enabling micron-scale visualization of soil structure and root–soil interfaces. Together, these advances allow us to quantify how carbon exudates move, transform, and stabilize within the rhizosphere, directly informing missing processes in BER-relevant carbon cycle models.

42 ENGINEERING↗
DOE OSTI2021

In vivo visualization of butterfly scale cell morphogenesis in Vanessa cardui

Many organisms exhibit functional micro- and nanoscale materials with structural definition and performance that challenge synthetic fabrication techniques, yet we know little about the processes that enable their formation. Using butterfly scales as a model system for functional biomaterials, we establish a timeline of scale formation and quantify relevant structural parameters for developing painted lady butterflies. We overcome challenges of previous efforts by imaging structure formation directly in living organisms, which allows us to continuously observe the evolving wing tissue and the fine details of individual scale cells. Visualization of scale structure formation in live butterflies forms the basis for modeling the underlying biomechanical processes and opens avenues for their translation into advanced fabrication strategies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Understanding Low Level Jets in the US Atlantic Offshore

Low level jets (LLJs) in the atmosphere exhibit a local windspeed maximum in the boundary layer, with positive shear beneath the jet and negative shear above the jet. Wind turbines tend to experience increased loads with varying wake recovery characteristics in the presence of an LLJ, therefore understanding the mechanism and impact of LLJs is crucial to wind energy development. The US Mid-Atlantic offshore region is a huge potential wind energy resource, yet LLJs in this area are poorly understood. In particular, the coastal offshore environment does not exhibit the same diurnal cycle that leads to strong LLJs in the well-characterized Great Plains region. In this study, we use the Weather Research and Forecasting model (WRF) plus lidar buoy data to identify case studies for LLJ events in 2020 in the New York Bight. A reduced order model is presented to explain the onset of these events based on the competing effects of baroclinicity and eddy diffusivity. Finally, using the macro-scale WRF, we drive a micro-scale large eddy simulation (LES) to generate a more detailed characterization of the Marine Boundary Layer during an LLJ. Gaining a better understanding of LLJs and their impacts on offshore wind in the mid-Atlantic is crucial for a transition toward renewable energy.

atmospheric boundary layer↗
NASA NTRS1994

HAPEX-Sahel: A large-scale study of land-atmosphere interactions in the semi-arid tropics

The Hydrologic Atmospheric Pilot EXperiment in the Sahel (HAPEX-Sahel) was carried out in Niger, West Africa, during 1991-1992, with an intensive observation period (IOP) in August-October 1992. It aims at improving the parameteriztion of land surface atmospheric interactions at the Global Circulation Model (GCM) gridbox scale. The experiment combines remote sensing and ground based measurements with hydrological and meteorological modeling to develop aggregation techniques for use in large scale estimates of the hydrological and meteorological behavior of large areas in the Sahel. The experimental strategy consisted of a period of intensive measurements during the transition period of the rainy to the dry season, backed up by a series of long term measurements in a 1 by 1 deg square in Niger. Three 'supersites' were instrumented with a variety of hydrological and (micro) meteorological equipment to provide detailed information on the surface energy exchange at the local scale. Boundary layer measurements and aircraft measurements were used to provide information at scales of 100-500 sq km. All relevant remote sensing images were obtained for this period. This program of measurements is now being analyzed and an extensive modelling program is under way to aggregate the information at all scales up to the GCM grid box scale. The experimental strategy and some preliminary results of the IOP are described.

Gutorbe, J-P.↗
NASA NTRS1995

Measurement of high-degree solar oscillation frequencies

We present m-averaged solar p- and f-mode oscillation frequencies over the frequency range nu greater than 1.8 and less than 5.0 mHz and the spherical harmonic degree range l greater than or equal to 100 and less than or equal to 1200 from full-disk, 1000 x 1024 pixel, Ca II intensity images collected 1993 June 22-25 with a temporal cadence of 60 s. We itemize the sources and magnitudes of statistical and systematic uncertainties and of small frequency corrections, and we show that our frequencies represent an improvement in accuracy and coverage over previous measurements. Our frequencies agree at the 2 micro Hz level with Mount Wilson frequencies determined for l less than or equal to 600 from full-disk images, and we find systematic offsets of 10-20 micro Hz with respect to frequencies measured from Big Bear and La Palma observations. We give evidence that these latter offsets are indicative of spatial scaling uncertainties associated with the analysis of partial-disk images. In comparison with theory, our p-mode frequencies agree within 10 micro Hz of frequencies predicted by the Los Alamos model but are as much as 100 micro Hz smaller than frequencies predicted by the Denmark and Yale models at degrees near 1000. We also find systematic differences between our n = 0 frequencies and the frequencies closely agreed upon by all three models.

Bachmann, K. T.↗
NASA NTRSDate not supplied

AI-Enhanced Computational Tools for Entry Systems Modeling

To advance the understanding of complex atmospheric entry phenomena, NASA’s Entry Systems Modeling (ESM) team [1] has developed high-fidelity computational tools addressing multiscale challenges, from material microstructures to full-scale heatshield response. This abstract highlights a subset of ESM tools, focusing on AI integration to enhance workflows and predictive modeling. - PuMA [2] computes effective material properties from high-resolution micro-CT scans, supporting TPS analysis for NASA missions. - TomoSAM [3] automates 3D tomography dataset segmentation for PuMA using the Segment Anything Model, reducing manual effort and improving accuracy. - PATO [4] models porous reactive materials under extreme conditions, with advancements such as unified solvers, mechanical erosion, and TPS coatings for NASA missions. - arcjetCV [5] employs deep learning to analyze arc jet test footage, measuring recession rates, shape changes, and shock standoff distances, bridging simulations, and experiments to reveal TPS ablation behavior. - ARCHeS [6] simulates arc heater plasma flows, modeling turbulence, radiation, and electromagnetic interactions to optimize arc heater performance, validate TPS under extreme conditions, and serve as a foundation for developing digital twins of arc heater facilities. - SPARTA [7] simulates rarefied hypersonic flows and gas-surface interactions for planetary entry missions, leveraging GPU architectures for scalable and efficient aerothermal and ablation analyses. AI-driven solutions, such as deep learning segmentation, have streamlined workflows in ESM tools and still hold significant potential to further accelerate processes and enhance automation in entry systems modeling. [1] Haskins, J.B. (2023), [2] Ferguson, J.C. (2018), [3] Meurisse, J.B.E. (2018), [4] Semeraro, F. (2023), [5] Quintart, A. (2024) [6] Meurisse, J.B.E. (2022), [7] Plimpton, S.J. (2019)

Predictive Modeling↗
DOE OSTI2023

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ~10 4 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. Finally, the average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ~ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

Atomistic simulations↗
DOE OSTI2025

Direct measurement of thermal Knudsen forces in rarefied gas environments

At micro- and nanoscales, momentum transfer between surfaces is influenced by various physical mechanisms, including quantum fluctuations, electromagnetic interactions, electric charges, and the dynamics of (rarefied) gases. Under non-isothermal conditions, rarefied gases give rise to thermal Knudsen forces whose magnitudes strongly depend on the gas species and surface characteristics. Knudsen forces are particularly relevant in nanotechnology, optical manipulation, and aerospace systems, where gas rarefaction occurs due to highly confined geometries, sub-micrometer length scales, and reduced particle densities. Despite their significance, predictive modeling of Knudsen forces is limited by a lack of comprehensive experimental data across diverse materials and surface morphologies. Here, in this work, we present a highly sensitive and adaptable measurement platform capable of directly quantifying Knudsen forces using a suspended, interchangeable micro-cantilever within controlled rarefied helium and nitrogen environments. The system integrates optical fiber interferometry to precisely capture out-of-plane displacements at sub-micrometer resolution, driven by Knudsen forces. From the empirical data, we derive a robust correlation linking the magnitudes of Knudsen forces to energy accommodation coefficients, offering deeper insights into the underlying gas–surface interaction mechanisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗