SEARCH · Search NASA

Results for “FORMULAS - STRUTS - EULER”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Bridging the gap between NMR measured mean silicate chain length and nano-scale silicate polymorphism of calcium silicate hydrates

Variable stoichiometry and silicate polymorphism in calcium-silicate-hydrates (C-S-H) has impeded the revelation of point defects distribution in the silicate tetrahedral network of C-S-H, which resembles tobermorite crystal structure with some bridging tetrahedra (BT) and paired tetrahedra (PT) vacancies in dreierketten chains. Here we use a computational approach to characterize silicate polymorphism by introducing the vacancy ratio of BT to PT (α) and establishing a three-term empirical mean chain length (MCL) formula for different calcium-to‑silicon ratios (Ca/Si) ranging from 1.2 to 2.3. The formula identifies BT and PT controls at low and high α respectively and allows an inverse mapping of polymorphic range based on NMR experiments. The proposed computational framework quantitatively describes silicate polymorphs and links NMR-measured MCL to C-S-H atomistic configurations at the molecular level.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Film formation mechanisms in mixed-dimensional 2D/3D halide perovskite films revealed by in situ grazing-incidence wide-angle X-ray scattering

We report mixed dimensionality 2D/3D hybrid halide perovskites retain the stability of 2D perovskites (formula (A')2(A)n-1PbnI3n+1) and long diffusion lengths of the 3D materials (formula AMX3), thereby affording solar cells with extended stability as well as state of the art efficiencies approaching that of the 3D materials. These films are made by spin coating precursor solutions with arbitrarily large average layer thickness n ($\langle$n$\rangle$ > 7) to give films with both 2D and 3D phases present. While the 2D and 3D perovskite film formation mechanisms have been studied previously, little is understood about composite 2D/3D film formation. We used in situ grazing-incidence wide-angle scattering (GIWAXS) with synchrotron radiation to fully characterize films fabricated from precursor solutions with stoichiometries of (BA) 2 (MA) n-1 Pb n I 3n+1 ($\langle$n$\rangle$ = 3, 4, 5, 7, “12,” “50,” and ∞ (MAPbI 3 )). Four different mechanisms are seen depending on the stoichiometry in the precursor solution. When $\langle$n$\rangle$ = 3, oriented perovskite grows directly. For $\langle$n$\rangle$ = 4-5, the needle-shaped solvate (MA) 2 Pb 3 I 8 ·2DMF forms concomitantly with the oriented perovskite which leads to 2D/3D composite films. For $\langle$n$\rangle$ ≥ 7, this solvate dominates and unoriented perovskite grows in secondarily. For 3D perovskite, the solvate is the only phase formed. Kinetic analysis shows faster and earlier growth of the solvate with increasing $\langle$n$\rangle$. Using this knowledge, we show that the undesirable solvate mechanism can be reduced by addition of excess ammonium iodide in the precursor solution to give highly oriented films.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Particlization in fluid dynamical simulations of heavy-ion collisions: The IS3D module

The IS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling of the Cooper–Frye formula which converts fluid dynamical information into local phase-space distributions for hadrons. The code package includes multiple choices for the non-equilibrium correction to these distribution functions: the 14-moment approximation, first-order Chapman–Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore to what extent heavy-ion experimental data are sensitive to different choices for δf n , presently the main source of theoretical uncertainty in the particlization stage. Here, we validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and space–time distributions to the Cooper–Frye formula.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Fast approximation to supershell partition functions: Explicit forms of the coefficients

In a previous work, we derived a formula for supershell partition functions, which are the cornerstone of the Super-Transition-Array approach to radiative-opacity calculations. The new expression takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients (denoted Γ $k$ ) for which we obtained a recursion relation. In the present short paper, as a complement of the previous one, we give an explicit formula for the coefficients Γ $k$ . Another recursion relation is also provided, as well as an alternative expression involving Bell polynomials. In conclusion, the connections with cycle indexes of permutation groups and with elementary symmetric polynomials are outlined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Design guidance for ferrites: Insights from density functional theory on magnetic properties

A grand challenge in materials research is identifying the relationship between composition and performance. Herein, we explore this relationship for magnetic properties, specifically magnetic saturation (M s ) and magnetocrystalline anisotropy energy (K) of ferrites. Ferrites are materials derived from magnetite (chemical formula = Fe 3 O 4 ) that comprise metallic elements such as Fe, Mn, Ni, Co, Cu and Zn. Experimentally, synthesizing and characterizing ferrites is time consuming. Further, selection of compositions to achieve particular magnetic properties currently relies on intuition. To address this, in this work, density functional theory (DFT) is used to predict M s and K for 571 ferrite structures. These structures are primarily double-substituted non-stoichiometric ferrites with formulae M1 x M2 y Fe 3–x–y O 4 , where M1 and M2 can be Mn, Ni, Co, Cu and/or Zn and 0 ≤ x ≤ 1 and y = 1–x. Calculated magnetic properties for the structures in this study vary from 0.04 × 10 5 to 9.6 × 10 5 A m −1 for M s and from 0.02 × 10 5 to 14.08 × 10 5 J m −3 for K. All structures are made publicly available in a FAIR database.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗

DOE OSTI2021

Analytical modeling for redox flow battery design

Deeper market penetration of redox flow batteries requires optimization of the cell performance. Though important for optimization, detailed analytical solutions have not been developed for electrolyte flow, mass and charge transport, and reaction kinetics within redox flow batteries. To this end, here we present analytical solutions to active species concentration and over-potential based on advection-diffusion transport for ions and Bulter-Volmer model for interface reaction kinetics. The solutions were validated with results from a finite element model. These solutions were then applied to investigate the relationship between over-potential and state of charge, current density, reaction rate constant, flow velocity, diffusivity, total active species concentration, and electrode structure. Explicit formulas were identified for minimum activation over-potential and limiting current density as well as their dependence on electrolyte properties, operation conditions, and electrode structure. With our new mathematical formulas, this work provides a theoretical framework for flow battery design.

25 ENERGY STORAGE↗

DOE OSTI2022

Average charge states of heavy ions in rarefied hydrogen

In this work, we present the results of experiments on measuring the charges of heavy ions from Rn (Z=86) to Og (Z=118) in rarefied hydrogen performed at the DGFRS and DGFRS-2 separators. Two formulae are proposed that can be used to calculate the charges of ions in H 2 and which take into account the influence of the shell structure of atoms on the charge value. The accuracy of estimating the charge of ions of superheavy atoms was measured to be 2%. The charges of Ra, Th, and No ions were measured at a hydrogen pressure from 0.5 to 3.3 mbar, which allowed us to evaluate the effect of H 2 density on the charge value. A formula is proposed to account for the effect of gas density when performing experiments at different gas pressures. It is shown that the results of experiments performed at different separators DGFRS and DGFRS-2 are in good agreement with each other.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Time interval distributions of nuclear events in a digital spectrometer

This study compares the theoretical formula for time interval density distributions (TIDs) in counters with pileup rejection to TIDs measured using a digital spectrometer with trapezoid filtering. The TIDs were derived from successive time stamps of 60 Co and 133 Ba γ rays detected with a HPGe spectrometer. The results demonstrate that the theoretical formula is applicable up to 40% count loss and can be used to retrospectively deduce the incident event rate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

The Fermi function and the neutron's lifetime

The traditional Fermi function ansatz for nuclear beta decay describes enhanced perturbative effects in the limit of large nuclear charge Z and/or small electron velocity β. We define and compute the quantum field theory object that replaces this ansatz for neutron beta decay, where neither of these limits hold. We present a new factorization formula that applies in the limit of small electron mass, analyze the components of this formula through two loop order, and resum perturbative corrections that are enhanced by large logarithms. We apply our results to the neutron lifetime, supplying the first two-loop input to the long-distance corrections. Our result can be summarized as τ n x |V ud | 2 [1 + 3λ 2 ] [1 + Δ R ] = $\frac{5263.284(17) s}{1 + 27.04(7) x 10^{-3}}$ with |V ud | the up-down quark mixing parameter, τ n the neutron's lifetime, λ the ratio of axial to vector charge, and Δ R the short-distance matching correction. We find a shift in the long-distance radiative corrections compared to previous work, and discuss implications for extractions of |V ud | and tests of the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Fading study of Harshaw LiF:Mg,Ti thermoluminescence dosimeters exposed to neutron doses

Sensitivity and signal fading were tested in Harshaw LiF:Mg,Ti thermoluminescence dosimeters (TLDs) exposed to neutron and beta/photons doses. A significant difference in the signal fading rate was observed for TLDs exposed to neutrons compared with TLDs exposed to betas. This difference may have been related to differences in glow curves for dosimeters exposed to different beams and to differences in glow curve evolution after exposure. A fading-correction algorithm was developed to correct the cumulative sensitivity + signal fading of TL doses for the fading time t using the formulae: y = 0.147∗exp(-t/4.36) + 0.308∗exp(-t/34.1) + 0.73 for neutrons, and: y = 0.132∗exp(-t/10.72) + 0.174∗exp(-t/31.5) + 0.8 for betas/photons. The formula was validated using the dose recovery test, where the average deviation of fading-corrected doses from delivery doses was within 1%. In conclusion, the proposed fading-correction approaches may significantly improve the accuracy of Harshaw TL dosimetry with LiF:Mg,Ti cards for both neutron and beta/gamma irradiation.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2023

How does humidity data impact land surface modeling of hydrothermal regimes at a permafrost site in Utqia$\mathrm{\dot{g}}$vik, Alaska?

Humidity is a basic and crucial meteorological indicator commonly measured in several forms, including specific humidity, relative humidity, and absolute humidity. These different forms can be inter-derived based on the saturation vapor pressure (SVP). In past decades, dozens of formulae have been developed to calculate the SVP with respect to, and in equilibrium with, liquid water and solid ice surfaces, but many prior studies use a single function for all temperature ranges, without considering the distinction between over the liquid water and ice surfaces. These different approaches can result in humidity estimates that may impact our understanding of surface-subsurface thermal-hydrological dynamics in cold regions. In this study, we compared the relative humidity (RH) downloaded and calculated from four data sources in Alaska based on five commonly used SVP formulas. These RHs, along with other meteorological indicators, were then used to drive physics-rich land surface models at a permafrost-affected site. Here, we found that higher values of RH (up to 40%) were obtained if the SVP was calculated with the over-ice formulation when air temperatures were below freezing, which could lead to a 30% maximum difference in snow depths. The choice of whether to separately calculate the SVP over an ice surface in winter also produced a significant range (up to 0.2 m) in simulated annual maximum thaw depths. The sensitivity of seasonal thaw depth to the formulation of SVP increases with the rainfall rate and the height of above-ground ponded water, while it diminishes with warmer air temperatures. These results show that RH variations based on the calculation of SVP with or without over-ice calculation meaningfully impact physically-based predictions of snow depth, sublimation, soil temperature, and active layer thickness. Under particular conditions, when severe flooding (inundation) and cool air temperatures are present, care should be taken to evaluate how humidity data is estimated for land surface and earth system modeling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Unveiling the dark matter of riverine dissolved organic matter and its role in molecular chemodiversity

Chemodiversity of riverine dissolved organic matter (DOM) plays a crucial role in global elemental cycles and ecosystem function. However, DOM “dark matter”—molecules without assigned specific formulae—remain unexplored in the interpretation of chemodiversity. Here, we systematically investigated the characteristics and drivers of dark matter and its impacts on DOM chemodiversity using 551 river water and sediment samples. Compared to known matter with specific formulae, dark matter exhibited lower molecular weight and diversity, but higher compositional dissimilarity, with dissolved organic carbon (DOC) as the primary driver. Including dark matter into chemodiversity analysis changed mass, diversity, and compositional dissimilarity of DOM from –10.1 to –0.04 %, –0.7 to 4.9 %, and 0.4 to 28.8 % in waters, and from –17.5 to 5.7 %, –10.5 to 19.2 %, and –22.3 to 33.1 % in sediments, respectively. DOC mediated these ecosystem-dependent effects: lower DOC amplified the effects on chemodiversity in waters, whereas in sediments, the effects shifted from negative to positive with changing DOC. Furthermore, ignoring dark matter would overestimate the regulatory role of DOC on sediment DOM chemodiversity. In conclusion, collectively, our findings clarify the influence of dark matter on DOM chemodiversity assessments across environmental gradients, improving understanding of riverine DOM and refining its analytical framework.

Chemodiversity↗

DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗

DOE OSTI2022

Finite orbit width effects in large aspect ratio stellarators

New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al. , J. Comput. Phys. , vol. 418, 2020, 109512; Velasco et al. , Nucl. Fusion , vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. ( Plasma Phys. Control. Fusion , vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Synthesis and Transport Properties of the Family of Zintl Phases Ca 3 RESb 3 (RE = La–Nd, Sm, Gd–Tm, Lu): Exploring the Roles of Crystallographic Disorder and Core 4f Electrons for Enhancing Thermoelectric Performance

Zintl phases with complex crystal structures have been studied as promising candidate-materials for thermoelectric (TE) applications. Here, we report the syntheses of the family of rare-earth metal Zintl phases with the general formula Ca 4–x RE x Sb 3 (x ≈ 1; RE = La–Nd, Sm, Gd–Tm, Lu). The structural elucidation is based on refinements of single-crystal X-ray diffraction data for 12 unique chemical compositions. The cubic structure is confirmed as belonging to the anti-Th 3 P 4 structure type (space group I4¯3d, no. 220, Z = 4), where the Ca and RE atoms share the same atomic site with ca. 75% and 25% occupancies, respectively. Such crystallographic disordering of divalent Ca and trivalent RE atoms in the structure provides a pathway to intricate bonding. The latter, together with the presence of heavy elements such as Sb and the lanthanides, are expected to enhance the scattering probability of phonons, thereby leading to as low thermal conductivity κ as that of the ordered RE 4 Sb 3 . The drive of the hypothetical parent compound Ca 4 Sb 3 to be stabilized by alloying with rare-earth metals can be understood following the Zintl-Klemm concept, as the resultant formula may be rationalized as (Ca 2+ ) 3 RE 3+ (Sb 3– ) 3 , indicating the realization of closed-shell electronic configurations for all elements. This notion is confirmed by electronic structure calculations, which reveal narrow bandgaps E g = 0.77 and 0.53 eV for Ca 3 LaSb 3 and Ca 3 LuSb 3 , respectively. Additionally, the incorporation of RE atoms into the structure drives the phase into a state of a degenerate semiconductor with dominant hole charge carriers.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Hybrid and Inorganic Vacancy-Ordered Double Perovskites A 2 WCl 6

We report hybrid and all-inorganic, vacancy-ordered double perovskites of d 2 W 4+ with the formula A 2 WCl 6 (A = CH 3 NH 3 + , Rb + , and Cs + ). These compounds, which are reddish in color, can be distinguished from structurally similar compounds obtained by hydrothermal methods on the basis of structure, spectroscopic, and magnetic properties. The latter are green and incorporate oxygen, with the actual formula Cs 2 WO x Cl 6–x and distinct optical absorption and emission behavior. Furthermore, the local-moment magnetism of the pure-red d 2 compounds reported here does not correspond to the appropriate Kotani model, suggesting as-yet undiscovered physics in these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Novel Strategy To Analyze Fourier Transform Ion Cyclotron Resonance Mass Spectrometry Data of Biomass Pyrolysis Oil for Oligomeric Structure Assignment

Among the most prominent challenges for the analysis of biomass pyrolysis products is the characterization of the abundant oligomer fraction of bio-oil. This fraction is principally made up of pyrolytic lignins and dehydrated, highly modified sugar oligomers, called humins, in liquid phase. An emerging technique for analysis of this oligomer fraction is high-resolution Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR MS), which allows for accurate determination of C x H y O z formulae for detected oligomers. Additionally, using simple dehydration and fragmentation reaction schemes, similar formulae can be developed from cellulose-, hemicellulose- and lignin-derived oligomers, which are primary depolymerization products. In this paper, FT-ICR MS analysis is coupled with combinatoric dehydration and fragmentation modeling in order to match experimentally detected bio-oil oligomers with hypothetical pathways for their formation during pyrolysis. In this way, we present a novel strategy by which oligomeric structures can be proposed for bio-oils. Using this approach, it becomes possible to advance the understanding of both the molecular structures comprising the bio-oil oligomer fraction and the pathways by which these structures form during biomass pyrolysis reactions.

09 BIOMASS FUELS↗