A noniterative method of obtaining Tchebycheff rational approximations
Noniterative method of obtaining rational forms as approximations to functions for power series expressions using Tchebycheff polynomial properties for improving accuracy
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Noniterative method of obtaining rational forms as approximations to functions for power series expressions using Tchebycheff polynomial properties for improving accuracy
Ionic liquids (ILs) with large electrochemical potential windows (EPWs) are ideally suited to improve the energy and power density of electrical devices for energy storage. However, guidelines are scarcely available for the selection or systematic screening of ILs for practical applications. Here, we present theoretical predictions for the EPW of thousands of cation-anion pairs based on a long-range corrected hybrid density functional theory. The cathodic and anodic potential limits were estimated from the highest occupied molecular orbital and lowest unoccupied molecular orbital energies of individual cations and anions. The approximate method predicts EPWs in reasonable agreement with existing experimental data for several commonly used ionic systems and can be used as a screening tool for a large library of ILs. Five most stable anions, with the cathode stability in the order of B[CN] 4 > PF 6 > BF 4 > BOB > NTf 2 , have been identified. These anions provide the largest EPWs when they are paired with conventional organic cations. The cation stability is reduced upon elongation of the alkyl chain length or branching of the molecular backbone.
We use the spectrally invariant method to study the variability of cloud optical thickness τ and droplet effective radius reff in transition zones (between the cloudy and clear sky columns) observed from Solar Spectral Flux Radiometer (SSFR) and Shortwave Array Spectroradiometer-Zenith (SASZe) during the Marine ARM GPCI Investigation of Clouds (MAGIC) field campaign. The measurements from the SSFR and the SASZe are different, however inter-instrument differences of self-normalized measurements (divided by their own spectra at a fixed time) are small. The spectrally invariant method approximates the spectra in the cloud transition zone as a linear combination of definitely clear and cloudy spectra, where the coefficients, slope and intercept, character-ize the spectrally invariant properties of the transition zone. Simulation results from the SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) model demonstrate that (1) the slope of the visible band is positively correlated with the cloud optical thickness τ while the intercept of the near-infrared band has high negative cor-relation with the cloud drop effective radius reff even without the exact knowledge of τ; (2) the above relations hold for all Solar Zenith Angle (SZA) and for cloud-contaminated skies. In observations using redundant measure-ments from SSFR and SASZe, we find that during cloudy-to-clear transitions, (a) the slopes of the visible band de-crease, and (b) the intercepts of the near-infrared band remain almost constant near cloud edges. The findings in simulations and observations suggest that, while the optical thickness decreases during the cloudy-to-clear transition, the cloud drop effective radius does not change when cloud edges are approached. These results sup-port the hypothesis that inhomogeneous mixing dominates near cloud edges in the studied cases.
Abstract. Measurements of the optical properties (absorption, scattering and extinction) of PM1, PM2.5 and PM10 made at two sites around Sacramento, CA, during the June 2010 Carbonaceous Aerosols and Radiative Effects Study (CARES) are reported. These observations are used to establish relationships between various intensive optical properties and to derive information about the dependence of the optical properties on photochemical aging and sources. Supermicron particles contributed substantially to the total light scattering at both sites, about 50 % on average. A strong, linear relationship is observed between the scattering Ångström exponent for PM10 and the fraction of the scattering that is contributed by submicron particles (fsca, PM1) at both sites and with similar slopes and intercepts (for a given pair of wavelengths), suggesting that the derived relationship may be generally applicable for understanding variations in particle size distributions from remote sensing measurements. At the more urban T0 site, the fsca, PM1 increased with photochemical age, whereas at the downwind, more rural T1 site the fsca, PM1 decreased slightly with photochemical age. This difference in behavior reflects differences in transport, local production and local emission of supermicron particles between the sites. Light absorption is dominated by submicron particles, but there is some absorption by supermicron particles ( ∼ 15 % of the total). The supermicron absorption derives from a combination of black carbon that has penetrated into the supermicron mode and from dust, and there is a clear increase in the mass absorption coefficient of just the supermicron particles with increasing average particle size. The mass scattering coefficient (MSC) for the supermicron particles was directly observed to vary inversely with the average particle size, demonstrating that MSC cannot always be treated as a constant in estimating mass concentrations from scattering measurements, or vice versa. The total particle backscatter fraction exhibited some dependence upon the relative abundance of sub- versus supermicron particles; however this was modulated by variations in the median size of particles within a given size range; variations in the submicron size distribution had a particularly large influence on the observed backscatter efficiency and an approximate method to account for this variability is introduced. The relationship between the absorption and scattering Ångström exponents is examined and used to update a previously suggested particle classification scheme. Differences in composition led to differences in the sensitivity of PM2.5 to heating in a thermodenuder to the average particle size, with more extensive evaporation (observed as a larger decrease in the PM2.5 extinction coefficient) corresponding to smaller particles; i.e., submicron particles were generally more susceptible to heating than the supermicron particles. The influence of heating on the particle hygroscopicity varied with the effective particle size, with larger changes observed when the PM2.5 distribution was dominated by smaller particles.
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This note discusses the validity of certain band models and scaling approximations for computing transmissions in the v4 band of methane along inhomogeneous paths in the atmosphere of Jupiter. It is shown that Goody's random band model approximates the results of a rigorous numerical line-by-line calculation of the transmission profile of a Jovian model atmosphere.
The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.
The flap-lag equations of motion of a torsionally rigid and centrally hinged spring-restrained rigid blade are developed using quasi-steady blade-element aerodynamic theory. These equations have periodic coefficients and are applicable to both wind-turbine rotors with velocity gradients and helicopter rotors in forward flight. By solving these equations both by the Floquet-Liapunov method and by an approximate method, the range of applicability of the latter method is established. Flap-lag and pure flapping stability boundaries illustrating the effects of flow and rotor parameters are presented. Finally, some discussion on the techniques for generating the Floquet transition matrix and on the relative merits of the coordinate axes system is presented.
The analysis of large area rotationally periodic space structures presented in the paper combines the finite element method, transfer matrix procedures, approximation methods, and periodic structure analysis to obtain computational efficiency. The computations used in the analysis indicate that additive damping mechanisms can be evaluated from the frequency response of the structure. The transient response can also be obtained from the frequency response to complete the dynamic analysis.
In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.
Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.
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The transient motion in angles of attack and sideslip during a constant rolling maneuver has been analyzed. Simplified expressions are presented for the determination of the pertinent modes of motion as well as the modal coefficient corresponding to each mode. Calculations made with and without the derivatives for side force due to sideslip and lift-curve slope indicate that although these derivatives increase the total damping of the system they do not markedly affect the transient motion.
A preliminary aircraft engine design methodology is being developed that utilizes a cascade optimization strategy together with neural network and regression approximation methods. The cascade strategy employs different optimization algorithms in a specified sequence. The neural network and regression methods are used to approximate solutions obtained from the NASA Engine Performance Program (NEPP), which implements engine thermodynamic cycle and performance analysis models. The new methodology is proving to be more robust and computationally efficient than the conventional optimization approach of using a single optimization algorithm with direct reanalysis. The methodology has been demonstrated on a preliminary design problem for a novel subsonic turbofan engine concept that incorporates a wave rotor as a cycle-topping device. Computations of maximum thrust were obtained for a specific design point in the engine mission profile. The results (depicted in the figure) show a significant improvement in the maximum thrust obtained using the new methodology in comparison to benchmark solutions obtained using NEPP in a manual design mode.
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Approximation method for thermal diffusion factor of almost Lorentzian gas mixture with better convergence properties than Chapman-Enskog approximation