Search NASA⌕ Search

SEARCH · Search NASA

Results for “LOGARITHM”

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 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Parameterization of temperature and spectral distortions in future CMB experiments

CMB spectral distortions are induced by Compton collisions with electrons. We review the various schemes to characterize the anisotropic CMB with a non-Planckian spectrum. We advocate using logarithmically averaged temperature moments as the preferred language to describe these spectral distortions, both for theoretical modeling and observations. Numerical modeling is simpler, the moments are frame-independent, and in terms of scattering the mode truncation is exact.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Measurement of Absorption Coefficient of Paraformaldehyde and Metaldehyde with Terahertz Spectroscopy

The characteristic absorption spectra of paraformaldehyde and metaldehyde in the terahertz frequency region are obtained by terahertz time-domain spectroscopy (THz-TDS). In order to reduce the absorption of terahertz (THz) wave by water vapor in the air and the background noise, the measurement system was filled with dry air and the measurements were conducted at the temperature of 24°C. Meanwhile, the humidity was controlled within 10% RH. The THz frequency domain spectra of samples and their references from 0 to 2.5 THz were analyzed via Fourier transform. The refractive index and absorption coefficients of the two aldehydes were calculated by the model formulas. From 0.1 to 2.5 THz, there appear two weak absorption peaks at 1.20 and 1.66 THz in the absorption spectra of paraformaldehyde. Only one distinct absorption peak emerges at 1.83 THz for metaldehyde. There are significant differences between the terahertz absorption coefficients of paraformaldehyde and metaldehyde, which can be used as 'fingerprints' to identify these substances. Furthermore, the relationship between the average absorption coefficients and mass concentrations was investigated and the average absorption coefficient–mass concentration diagrams of paraformaldehyde and metaldehyde were shown. For paraformaldehyde, there is a linear relationship between the average absorption coefficient and the natural logarithm of mass concentration. For metaldehyde, there exists a simpler linear relationship between the average absorption coefficient and the mass concentration. Because of the characteristics of THz absorption of paraformaldehyde and metaldehyde, the THz-TDS can be applied to the qualitative and quantitative detection of the two aldehydes to reduce the unpredictable hazards due to these substances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Rapid Detection of Tetrodotoxin Using Surface-Enhanced Raman Spectroscopy and Fe{sub 3}O{sub 4}/SiO{sub 2}/Au Gold/Magnetic Nanoparticles

Fe{sub 3}O{sub 4} nanoparticles were first modified with tetraethoxylsilane to form Fe{sub 3}O{sub 4}/SiO{sub 2} nanoparticles, followed by the addition of 3-aminopropyltriethoxysilane and 3-thiolpropyltriethoxysilane to introduce –NH{sub 2} and –SH groups to the surface of Fe{sub 3}O{sub 4}/SiO{sub 2} nanoparticles. Gold nanoparticles were further assembled on the surface of Fe{sub 3}O{sub 4}/SiO{sub 2} via the electrostatic adsorption of –NH{sub 2} and the Au–S bond to produce stable core–shell Fe{sub 3}O{sub 4}/SiO{sub 2}/Au gold/magnetic nanoparticles. These Fe{sub 3}O{sub 4}/SiO{sub 2}/Au gold/magnetic nanoparticles were characterized by a variety of techniques such as transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDX), and afterwards conjugated with tetrodotoxin antibodies (Ab) and used as a Raman active substrate (Fe{sub 3}O{sub 4}/SiO{sub 2}/Au–Ab) with Rhodamine B (RhB)-labeled tetrodotoxin antibody as a Raman reporter (Ab–RhB). Upon mixing these reagents with tetrodotoxin (TTX), a sandwich complex [Fe{sub 3}O{sub 4}/SiO{sub 2}/Au–Ab···TTX···Ab–RhB] was generated due to the specific antibody–antigen interactions. The immunocomplex was subsequently separated by an externally applied magnetic source and concentrated into a pellet point, where the laser interrogation of the pellet produced a strong signal characteristic of RhB. The logarithmic intensity of the signal was found to be proportional to the concentration of TTX with a limit of detection of 0.01 μg/mL and a detection linearity range of ~ 0.01–0.5 μg/mL. The established method eliminates the complicated procedures of traditional centrifuging, column separation, and incubation and achieves a rapid detection of tetrodotoxin with improved detection sensitivity.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Comparative Study of the Effect of Magnetic Nanoparticle CoFe{sub 2}O{sub 4} on Fluctuation-Induced Conductivity of Y-123 and Y-358 Superconductors

In this study, a comparative investigation of the electrical conductivity fluctuations in nano-CoFe{sub 2}O{sub 4} added to Y{sub 3}Ba{sub 5}Cu{sub 8}O{sub 18±x} (Y-358) and YBa{sub 2}Cu{sub 3}O{sub 7−d} (Y-123) products is performed. All products were made using the solid-state reaction process. X-ray powder diffraction (XRD) analyses confirmed the formation of different phases. Scanning electron microscope (SEM) analysis shows the reduction of grain size with increasing the quantity of nano-CoFe{sub 2}O{sub 4} particles for both the Y-123 and Y-358 samples. The decrease of grain size is more accentuated in the case of the Y-358 samples compared with the Y-123 ones. The data of conductivity fluctuations are examined in terms of the derivative of the electrical resistivity with respect to temperature and the logarithmic derivative of the conductivity with regard to temperature. The results illustrate the existence of a transition with two stages; intragrain and intergrain. It is demonstrated that the addition of CoFe{sub 2}O{sub 4} nanoparticles affects the electrical conductivity fluctuations, the values of the critical exponents, and the fluctuation dimensionality in YBCO systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Critical Properties of Perovskite Manganese Oxides Pr{sub 1−x}Ba{sub x}MnO{sub 3}

The critical properties of polycrystalline Pr{sub 1−x}Ba{sub x}MnO{sub 3} (x = 0.13 and 0.23) samples prepared by using a standard ceramic fabrication method were investigated. Pr{sub 1−x}Ba{sub x}MnO{sub 3} exhibited a second-order magnetic transition. As per the modified Arrott plot method and double logarithmic M-μ{sub 0}H curve, the critical exponents (CE) were calculated as β = 0.459 ± 0.03, γ = 1.346 ± 0.02, δ = 4.32 ± 0.04, and T{sub C} ≈ 130 K, for x = 0.13, and β = 0.424 ± 0.03, γ = 1.362 ± 0.02, δ = 4.19. ± 0.03, and T{sub C} ≈ 163 K, for x = 0.23. To confirm the reliability of such CE values, the M (H) data of Pr{sub 1−x}Ba{sub x}MnO{sub 3} were checked by the scaling equation M(H, t) = |t|{sup β}f{sub ±}(H/|t|{sup β + γ}), where t=(T/(T{sub C}))−1 refers to the reduced temperature, f{sub ±} is the scaling function above (+)/below (−) T{sub C}. The β values for Pr{sub 1−x}Ba{sub x}MnO{sub 3} (x = 0.13 and 0.23) are between β = 0.365 (3D Heisenberg exponent) and β = 0.5 (mean-field exponent), whereas γ values are fairly close to γ = 1.386. This reveals long- and short-range order coexisting in Pr{sub 1−x}Ba{sub x}MnO{sub 3}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing

We propose a new Monte Carlo method to efficiently sample a multimodal distribution (known up to a normalization constant). We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which can also be seen as a generalization of well-tempered metadynamics. The dynamics is based on an adaptive importance technique. The importance function relies on the weights (namely the relative probabilities) of disjoint sets which form a partition of the space. These weights are unknown but are learnt on the fly yielding an adaptive algorithm. In the context of computational statistical physics, the logarithm of these weights is, up to an additive constant, the free-energy, and the discrete valued function defining the partition is called the collective variable. The algorithm falls into the general class of Wang–Landau type methods, and is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets in order to escape more quickly from metastable states, and (ii) the target distribution is biased using only a fraction of the free-energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Exact Solutions of the Precursor Film Equation

We find and analyze exact solutions to equations with logarithmic nonlinearity. To construct the soltuions, we use the classical group analysis methods, as well as the method of invariant manifolds and the Lagrangian coordinate method. Bibliography: 23 titles. Illustrations: 5 figures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Regularity of a Boundary Point for the p(x)-Laplacian

We study the behavior of solutions to the Dirichlet problem for the p(x)-Laplacian with a continuous boundary function. We prove the existence of a weak solution under the assumption that p is separated from 1 and ∞. We present a necessary and sufficient Wiener type condition for regularity of a boundary point provided that the exponent p has the logarithmic modulus of continuity at this point.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Depth of k-Valued Logic Functions Over Arbitrary Bases

The behavior of the Shannon function of the depth of k-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all k, k ≥ 3, for an arbitrary basis of k-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all k, k ≥ 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Criteria for the Best Approximation by Simple Partial Fractions on Semi-Axis and Axis

We study uniform approximation of real-valued functions f, f(∞) = 0, on ℝ{sup +} and ℝ by real-valued simple partial fractions (the logarithmic derivatives of polynomials). We obtain a criterion for the best approximation on ℝ{sup +} and ℝ in terms of the Chebyshev alternance. This criterion is similar to the known criterion on finite segments. For the problem of approximating odd functions on ℝ we construct an alternance criterion with a weakened condition on the poles of fractions. We present a criterion for the best approximation by simple partial fractions on ℝ{sup +} and ℝ in terms of Kolmogorov. We prove analogs of the de la Vallee-Poussin alternation theorem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Two-Dimensional Problem of Thermoelasticity for a Half Space in the Presence of Heat Release in a Ribbon-Shaped Domain Parallel to its Boundary

Using a logarithmic single-layer potential, thermoelastic displacement potential, Airy stress function, and Boussinesq function, we solve two-dimensional problems of stationary heat conduction and thermoelasticity under the conditions of plane deformation of a semiinfinite body in the presence of heat release in a ribbon-shaped domain parallel to its boundary (in this domain, either a temperature or a heat flux is given). The boundary of the body is kept at temperature equal to zero. We study the distribution of stresses in the domain of heat release with given heat sources of constant intensity at constant temperature.

42 ENGINEERING↗
DOE OSTI2023

Effect of tension during sulfonation stabilization for UHMWPE-derived carbon fibers

Polyethylene is a promising low-cost alternative precursor material for carbon fiber production, but it has yet to show mechanical properties near or surpassing polyacrylonitrile-derived carbon fibers. The high molecular weight and order of ultra-high molecular weight polyethylene (UHMWPE) may offer a pathway to realizing this promise by enabling long-range graphitic structure formation and superior mechanical properties. The tension applied during the precursor stabilization process is crucial to maintaining the shape of the fibers during the conversion process, but no published study has yet probed the relationship between sulfonation tension and carbon fiber microstructure and mechanical properties. In this work, a logarithmic sweep of tensile stress was applied to UHMWPE fibers during the stabilization process followed by carbonization. Increasing tension significantly reduced fiber shrinkage, resulted in straighter fibers with less severe kink bands, and greatly improved the mechanical properties of the fibers. Raman spectroscopy and X-ray diffraction revealed that in all cases the carbon fibers were largely amorphous, but increasing tension resulted in increased size and alignment of the turbostratic crystallites with the fiber axis. Large voids were present in the sample fibers, so the Griffith-Irwin relation was employed to predict the potential ultimate tensile strength of the fibers with voids reduced to sizes comparable to commercially produced fibers. Furthermore, this work demonstrates the importance of tension applied during the stabilization of polyethylene fibers for carbon fiber production and establishes a framework for achieving high mechanical properties from these precursors.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗
DOE OSTI2019

Design of a wideband microstrip nanoantenna array

This paper presents the design of a logarithmic array of microstrip nano-antennas at terahertz frequencies. For applications in which small antennas are required, microstrip antennas are preferred. However, they have a narrow bandwidth. To overcome this problem in microstrip antennas, a log-periodic nanoantenna design is presented which exhibits a wide bandwidth and ultra-compact design. This antenna is smaller in size compared to log-periodic antennas in microwave bands and comparable and better radiation characteristics. The proposed Log-periodic microstrip nanoantenna array consists of seven patch elements on a dielectric layer and are fed directly by a feed line through the branch lines connected to each of the elements. Scaling factor, τ = 0.95 is considered for this design and inset feed is used. In this structure, the substrate has a relative dielectric constant of ε{sub r} = 4.4 and a thickness of h = 800 nm. For good performance at high frequencies, gold is used for the design of the antenna. The considered operating frequency is 3.3 THz corresponding to a wavelength of 91 µm. Good impedance matching and a wide bandwidth of 800 GHz is obtained.

42 ENGINEERING↗
DOE OSTI2019

On the relationship between the energy characteristics of the isodesmic reactions of polychlorinated dioxins and their toxicity

Thermodynamic functions (ΔG{sub f} and ΔH{sub f}) of clorinated dibenzo-p-dioxins (Cl{sub n}DD) with n = 0–8 were calculated at the DFT level of theory using the B3LYP functional and extended 6–31** basis sets and used to analyze possible relationship of the structures and energy characteristics of these compounds with their toxicity. A new sequence of successive isodesmic reactions, which makes it possible to calculate chemical potentials μ{sub G} and μ{sub H} from the ΔG{sub f} and ΔH{sub f} values, has been proposed. In the framework of this approach, satisfactory linear correlations between the chemical potentials μ and the logarithms of toxicity of the corresponding polychlorodioxins were obtained for the first time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Uncovering the driving forces of carbon dioxide emissions in Chinese manufacturing industry: An intersectoral analysis

As the pillar of national economy, manufacturing industry is the largest primary energy consumer and emitter of carbon dioxide (CO2) in China. Therefore, capturing the determinants of CO2 emissions in manufacturing industry is extremely important for national efforts to mitigate carbon emissions. This paper explores the major driving forces behind CO2 emission changes in China's manufacturing industry during 2000-2015 from perspectives of the whole sector and 28 subsectors, by applying the temporal logarithmic mean Divisia index (LMDI) method. Moreover, an intersectoral LMDI model is built to uncover the intersectoral discrepancies of CO2 emissions among 28 subsectors. The temporal analysis indicates that industrial activity and energy intensity are crucial factors respectively contributing to the increase and mitigation of CO2 emissions. The intersectoral analysis reveals that energy intensity is the dominant factor responsible for the intersectoral discrepancies of CO2 emissions among 28 subsectors. The great mitigation towards CO2 emissions can be achieved if energy efficiency is largely improved in carbon-intensive subsectors. Priority should be given by governments to the industrial technology advancement, such as subsidies for energy-saving technological transformation and promotion of international advanced techniques and equipment, which can greatly improve production efficiency and mitigate emissions in manufacturing industry.

China↗
DOE OSTI2019

Kinetics and Mechanisms of Dolime Dissolution in Steelmaking Slag

The kinetics of dolime dissolution containing 20 and 50 pct of magnesium oxide in steelmaking slags has been studied in a high-temperature experiment. The dissolution tests were carried out under static conditions at temperatures of between 1573 K and 1873 K (1300 °C to 1600 °C). Cylindrical samples of dolime were introduced into pre-melted slag at predetermined time intervals. The changes in mass and geometrical parameters of the samples, as well as CaO and MgO concentrations in the melt, were determined to calculate mass transfer and diffusion coefficients. The results revealed that the rate-limiting step in the process of dolime dissolution is diffusion. The increase in MgO content in the initial sample caused a drop in dolime dissolution rate and diffusion coefficients. The prediction of MgO solubility in steel slag, as well as the effect of slag basicity, was carried out using the thermodynamic software FactSage 7.1. In addition, the activation energy of diffusion has been calculated using the dependence of the logarithm of diffusion coefficients on the inverse temperature.

36 MATERIALS SCIENCE↗