Search NASA⌕ Search

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.

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

At least 55 records · Page 3

Resolving the Chemical Formula of Nesquehonite via NMR Crystallography, DFT Computation, and Complementary Neutron Diffraction

Nesquehonite is a magnesium carbonate mineral relevant to carbon sequestration envisioned for carbon capture and storage of CO 2 . Its chemical formula remains controversial today, assigned as either a hydrated magnesium carbonate [MgCO 3 · 3H 2 O], or a hydroxy- hydrated- magnesium bicarbonate [Mg(HCO 3 )OH · 2H 2 O]. Here, the resolution of this controversy is central to understanding this material‘s thermodynamic, phase, and chemical behavior. In an NMR crystallography study, using rotational-echo double-resonance 13 C{ 1 H} (REDOR), 13 C- 1 H distances are determined with precision, and the combination of 13 C static NMR lineshapes and density functional theory (DFT) calculations are used to model different H atomic coordinates. [MgCO 3 · 3H 2 O] is found to be accurate, and evidence from neutron powder diffraction bolsters these assignments. Refined H positions can help understand how H-bonding stabilizes this structure against dehydration to MgCO 3 . More broadly, these results illustrate the power of NMR crystallography as a technique for resolving questions where X-ray diffraction is inconclusive.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT

We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 ( s , $\phi$, and t ). We obtain numerical predictions for low-twist OPE data in several charge sectors using the extremal functional method. We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input. We find agreement between the analytic and numerical predictions. We also give evidence that certain scalar operators lie on double-twist Regge trajectories and obtain estimates for the leading Regge intercepts of the O(2) model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

An algebraic formula for two loop renormalization of scalar quantum field theory

We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Comparison of second-order spectral line widths formulae

Frequently used second-order spectral line width formulae from the projector operator and kinetic theory methods have not been formally compared previously. Here it is shown that a systematic second-order expansion of the projection operator expression including initial correlations agrees with the second-order kinetic theory result. The agreement assumes a common approximation in the projector operator method that introduces a screened radiator–perturber interaction to account for neglected electron–electron correlations. On the other hand, it is shown that the usual width expression from the projection operator approach neglecting initial correlations differs from kinetic theory. The differences, however, are at least third order in the radiator–perturber interaction. The comparisons suggest using the more compact width expression from kinetic theory, which includes initial correlations and a systematic screening of the radiator–perturber interactions, as the starting point for second-order width calculations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigation of Reactive Silver Ink Formula for Reduced Silver Consumption in Silicon Heterojunction Metallization

Silver is the most expensive non-silicon component in photovoltaic cells. This is particularly salient for silicon heterojunction (SHJ) cells, which rely on large quantities of low-temperature silver pastes (LT-SP). SHJ cells would benefit greatly from an industrially scalable metallization process that simultaneously offers low silver consumption, low finger resistivities (<20 μΩ·cm), and low processing temperatures. Printed reactive silver inks (RSI) are an innovative candidate to this end. Furthermore, this work furthers the research on RSI metallization by investigating the impact of ink formula on properties pertinent to SHJ cells, including electrical properties, line width, ink splatter, silver consumption, cell performance, and adhesion. We introduce a scalable, high-throughput flexible needle contact printing approach for metallization that solves many of the issues associated with drop-on-demand printing. The printed silver fingers are characterized using electrical measurements and top-down and cross-sectional microscopy. The best performing ink, consisting of silver acetate, ethylamine, and formic acid, achieved silver fingers with total resistivities of 3.1 μΩ·cm and contact resistivities of 3.2 mΩ·cm 2 when printed at 61 °C. This ink metallized a full-sized 156 mm × 156 mm SHJ cell. This is the first reported data for RSI metallization of a full-sized SHJ cell and shows how an optimized RSI can achieve similar performances to LT-SP while consuming 80–90% less silver.

14 SOLAR ENERGY↗

Spectral analysis of product formulas for quantum simulation

We consider the time-independent Hamiltonian simulation using the first order Lie–Trotter–Suzuki product formula under the assumption that the initial state is supported on a low-dimension subspace. By comparing the spectral decomposition of the original Hamiltonian and the effective Hamiltonian, we obtain better upper bounds for various conditions. Especially, we show that the Trotter step size needed to estimate an energy eigenvalue within precision ϵ using quantum phase estimation can be improved in scaling from ϵ to ϵ 1/2 for a large class of systems. Our results also depend on the gap condition of the simulated Hamiltonian.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analytical formula for pellet fuel source density in toroidal plasma configurations based on an areal deposition model

An analytical formula for the fuel source density η F (&Psi;) over a magnetic flux surface &Psi; following pellet injection is derived. During pellet motion the ablated and ionized fuel will be initially deposited nearby the pellet, prior to subsequent homogenization within the magnetic flux surfaces. Here in our research, it is assumed that the deposition area projected normal to the magnetic field is on the order of the cross-sectional area of the ionized ablation column whose axis is aligned with the magnetic field. Previous pellet deposition codes [1] employed a point source deposition approximation, which overpredicts the surface-averaged density, particularly when the obliquity between the pellet trajectory and the flux surface normal approaches 90 degrees. A key finding of this study is that as the obliquity approaches 90 degrees, grazing trajectory, the areal model predicts a well behaved η F and removes the unphysical divergence stemming from the point model. To illustrate the difference exhibited between areal and point models for near grazing trajectories, we considered vertical pellet injection into a CFETR-like tokamak with a negative triangularity plasma cross section using a pellet ablation/deposition module.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Convenient analytical formula for cluster mean diameter and diameter dispersion after nucleation burst

Here, we propose an alternative method of estimating the mean diameter and dispersion of clusters of particles, formed in a cooling gas, right after the nucleation stage. Using a moment model developed by Friedlander [S. K. Friedlander, Ann. N. Y. Acad. Sci. 404, 354 (1983)], we derive an analytic relationship for both cluster mean diameter and diameter dispersion as a function of two of the characteristic times of the system: the cooling time and the primary constituents collision time. These formulas can be used to predict diameter and dispersion variation with process parameters, such as the initial primary constituents' concentration or cooling rate. It is also possible to use them as an input to the coagulation stage, without the need to compute complex cluster generation during the nucleation burst. We compared our results with a nodal code (NGDE) and got excellent agreement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

X-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula

Here, we study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simplified Formulas for External Pressure Design

Design of vessels for external pressure currently requires a chart-based solution or analytical approaches which are not necessarily intuitive. In this paper, we propose simple formulas for the external pressure evaluation of pipes and other cylindrical pressure vessels. We present a conceptual comparison between the elastic and elastic-plastic stability of structural columns and that of cylindrical vessels of long, intermediate, and short length. Their common features allow an accurate and straightforward approach for external pressure design. The approach is also extended to spherical caps, conical vessels, and formed heads.We compare the method presented to the current acceptance criteria from various design codes, including the ASME Boiler and Pressure Vessel Code Section VIII, Code Case 2286, and EN 13445-3, as well as codes for steel and aluminum structures. In further discussion, the simplified method is compared against the results of more than 500 experiments on the buckling of cylindrical and spherical vessels published over the past two centuries.This simple but accurate approximation is conceptually intuitive, analytically straightforward, and shows potential utility in pressure vessel design codes, as well as piping design codes such as B31 that currently reference ASME VIII for external pressure design.

Kirkland, Will↗

Empirical Formula for Puncture Energy of Flat Metal Plates by a Cylindrical Flat Punch

Impact problems of plate-like parts by punch-like objects with relatively large mass moving at slow speeds of a few feet per second constitute a subset of impact problems of interest at Sandia. This is in contrast to small objects moving in the range of hundreds or thousands of feet per second or higher. The objective of this work is to develop a simple formula that can be used to estimate a lower bound for the puncture energy of metal plates impacted by cylindrical, essentially rigid punches of circular cross-section and at nose. Such geometry is used as a basis in the design of puncture mitigation barriers or procedures. This was accomplished by deriving an expression using non-dimensional analysis and then calibrating it based on tests results in the range of speeds of interest. Lower bounds can then be determined based on confidence intervals or factors of safety.

36 MATERIALS SCIENCE↗

Useful formulas for non-magnetized electron cooling

Recent success of Low Energy RHIC Electron Cooler (LEReC) opened a road for development of high energy electron coolers based on non-magnetized electron bunches accelerated by RF cavities. Electrons in such coolers can have velocity distribution with various unequal horizontal, vertical and longitudinal velocity spreads. In this paper we revisit a formula of friction force in non-magnetized cooling and derive a number of useful expressions for different limiting cases.

43 PARTICLE ACCELERATORS↗

National Electric Vehicle Infrastructure Formula Program (ANNUAL REPORT | PLAN YEAR 2023–2024)

The 2021 Infrastructure Investment and Jobs Act, also known as the Bipartisan Infrastructure Law (BIL), invests $\$$7.5 billion to build out a national electric vehicle (EV) charging network and created the Joint Office of Energy and Transportation (Joint Office) to “study, plan, coordinate, and implement issues of joint concern between the two agencies.” The BIL represents a historic effort to electrify the U.S. transportation system, which has significant potential to reduce U.S. greenhouse gas emissions and help tackle the climate crisis. The U.S. transportation sector accounts for one-third of the nation’s greenhouse gas emissions—the largest share of all primary sectors, including electricity production, industry, commercial and residential, and agriculture. The National Electric Vehicle Infrastructure (NEVI) Formula Program, one of the BIL funding programs, was launched in February 2022, providing nearly $\$$5 billion over 5 years to help states, the District of Columbia, and Puerto Rico (hereafter referred to as “states”) create a network of EV charging stations beginning with designated Federal Highway Administration (FHWA) Alternative Fuel Corridors (AFCs), with an emphasis on the Interstate Highway System. The funding is made available to the states in allocations each year pending FHWA certification of the state’s annual deployment plan. The NEVI program is in its third year, so there's a lot to celebrate. As of July 2024, 39 states have released solicitations for their NEVI programs and eight states have opened their first NEVI-funded stations (61 ports in total), which have already powered thousands of charging sessions for EV drivers across America. Additional stations are in the pipeline with more than 2,500 additional ports having been awarded or conditionally awarded by the states. All states released their Fiscal Year (FY) 2024 deployment plan updates to reflect the new minimum requirements and guidance, and several states added newly designated EV AFCs in their FY 2024 deployment plan updates, bringing the total AFC network of EV corridors to more than 81,000 miles.

33 ADVANCED PROPULSION SYSTEMS↗

MC Formula Protocol for H35HF Fueling (CRADA Final Report)

The National Renewable Energy Lab (NREL), Frontier Energy, and the industry partners worked together to help SAE J2601-5 develop an H35 high-flow (HF) medium-duty (MD) and heavy-duty (HD) fueling protocol. The team upgraded NREL's hydrogen filling simulations (H2FillS) model to accommodate an MC Formula fueling (t-final) table generation capability by leveraging NREL's high-performance computing system. Based on protocol boundary conditions (e.g., allowable maximum flow rate, range of storage system size) set by SAE J2601-5, the team generated the fueling tables and then validated the reliability of those tables by installing them on NREL's HD dispenser and ZBT's H35HF dispenser and then performing H35HF fueling experiments. Through the validation process, this team certified that the fueling tables generated were reliable to install in commercial H35HF dispensers and then performed H35HF fueling of commercial MD/HD vehicles.

08 HYDROGEN↗

Diabetes-specific formula with standard of care improves glycemic control, body composition, and cardiometabolic risk factors in overweight and obese adults with type 2 diabetes: results from a randomized controlled trial

Background and aims Medical nutrition therapy is important for diabetes management. This randomized controlled trial investigated the effects of a diabetes-specific formula (DSF) on glycemic control and cardiometabolic risk factors in adults with type 2 diabetes (T2D). Methods Participants ( n = 235) were randomized to either DSF with standard of care (SOC) (DSF group; n = 117) or SOC only (control group; n = 118). The DSF group consumed one or two DSF servings daily as meal replacement or partial meal replacement. The assessments were done at baseline, on day 45, and on day 90. Results There were significant reductions in glycated hemoglobin (−0.44% vs. –0.26%, p = 0.015, at day 45; −0.50% vs. −0.21%, p = 0.002, at day 90) and fasting blood glucose (−0.14 mmol/L vs. +0.32 mmol/L, p = 0.036, at day 90), as well as twofold greater weight loss (−1.30 kg vs. –0.61 kg, p < 0.001, at day 45; −1.74 kg vs. –0.76 kg, p < 0.001, at day 90) in the DSF group compared with the control group. The decrease in percent body fat and increase in percent fat-free mass at day 90 in the DSF group were almost twice that of the control group (1.44% vs. 0.79%, p = 0.047). In addition, the percent change in visceral adipose tissue at day 90 in the DSF group was several-fold lower than in the control group (−6.52% vs. –0.95%, p < 0.001). The DSF group also showed smaller waist and hip circumferences, and lower diastolic blood pressure than the control group (all overall p ≤ 0.045). Conclusion DSF with SOC yielded significantly greater improvements than only SOC in glycemic control, body composition, and cardiometabolic risk factors in adults with T2D.

Tey, Siew Ling↗

MC Formula Protocol for H35HF Fueling

A publicly available and verified high-flow fueling protocol for H35 medium-duty (MD) and heavy-duty (HD) hydrogen-powered buses and trucks does not exist. This could lead to transit agencies needing to select suppliers for purchase of new fleet vehicles, and to multiple providers responding with incompatible vehicle designs in the future. With the expansion of MD/HD vehicles using 35 MPa storage, there will be a need for publicly accessible H35HF stations, and these will require the use of a standardized prescriptive fueling protocol. The development of a fully tested and validated H35 high-flow (H35HF) MC Formula fueling protocol for MD and HD buses and trucks can provide guidelines to design H35 stations and vehicles, enable other manufacturers and vehicle original equipment manufacturers (OEMs) to enter this space, and ultimately accelerate to popularize the hydrogen market.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

Tauberian-Cardy formula with spin

We prove a $2$ dimensional Tauberian theorem in context of $2$ dimensional conformal field theory. The asymptotic density of states with conformal weight $(h,\bar{h})\to (\infty,\infty)$ for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is controlled by the twist parameter and insensitive to spin. The sensitivity of the leading piece towards spin is discussed. We identify a universal piece in microcanonical entropy when the averaging window is large. An asymptotic spectral gap on $(h,\bar{h})$ plane, hence the asymptotic twist gap is derived. We prove an universal inequality stating that in a compact unitary $2$D CFT without any conserved current $Ag\leq \frac{\pi(c-1)r^2}{24}$ is satisfied, where $g$ is the twist gap over vacuum and $A$ is the minimal "areal gap", generalizing the minimal gap in dimension to $(h',\bar{h}')$ plane and $r=\frac{4\sqrt{3}}{\pi}\simeq 2.21$. We investigate density of states in the regime where spin is parametrically larger than twist with both going to infinity. Moreover, the large central charge regime is studied. We also probe finite twist, large spin behavior of density of states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗