A new approach to solve correlated k-distribution function

The resorting profile of absorption coefficient is fitted with Voigt function by employing the similarity between it and a single mixed broadened Voigt line type. In this way, simple mathematical fitting formulae are obtained to solve k-distribution (k-D) function at any pressure and temperature. Thus, a new correlated k-D method is proposed on the basis of it. Finally, taking mid-latitude summer atmosphere as an example, longwave cooling rates are calculated for three major gases by the new method, and then compared with the corresponding results by line-by-line integration.     

The effects of the choice of the k-interval number on radiative calculations

The selection of the number of k-interval is a foundation to correlated k-distribution method and the problem of how to do it still remains unsettled. It is pointed out by numerical computation in this work that choosing the number of k-interval is a major factor affecting accuracy and speed in radiative calculation. To increase the number of k-interval is an efficient method to improve the accuracy. However, it is found by this study that there exists a saturation of the accuracy to an increase of the number. The optimal rules on the number of k-interval choosing are proposed in the paper. Then, five versions on atmospheric absorption by gases appropriate for GCMs are given according to them.     

Numerical study on surface acoustic wave method for determining Young's modulus of low-k films involved in multi-layered structures

The surface acoustic waves (SAWs) technique is becoming an attractive tool for accurately and nondestructively characterizing the mechanical property of the brittle low dielectric constant (low-k) thin film. The theoretical equations for describing SAWs propagating on the multi-layered structure are derived in this study. The dispersion features of SAWs propagating on different structures of low-k/SiO₂/Si substrate, SiO₂/low-k/Si substrate, low-k/Si substrate, and low-k/Cu/Si substrate are investigated to instruct an accurate and facile fitting process for determining Young's modulus of low-k films. The dependence of dispersion relation on the film thickness, elastic modulus of low-k materials as well as frequency are provided and discussed in detail. The study shows an obvious influence of layered structure on the dispersion relation of SAWs. For a fixed structure, the dispersion curvature increases with the decrease of Young's modulus of low-k films.     

The spectral-line moment-based (SLMB) modeling of the wide band and global blackbody-weighted transmission function and cumulative distribution function of the absorption coefficient in uniform gaseous media

The spectral-line moment-based (SLMB) modeling is proposed for the calculation of radiative properties of gases on any spectral width. The associated mathematical formulation is obtained by applying several concepts of the k-distribution methods such as the reordering of the wavenumber scale by monotonic variations of the absorption coefficient, together with the application of the k-moment method's principles. This approach gives both a general formula for the BTF and a simple and readily applicable approximation for the blackbody-weighted cumulated k-distribution function of the absorption coefficient. The model is applied for the computation of wide band BTFs and cumulative k-distributions for uniform columns of CO₂ and H₂O in the temperature range (300-2400 K) at atmospheric pressure. Model parameters are deduced from line-by-line (LBL) spectra calculated using the HITEMP database. Comparisons with LBL reference data as well as with contemporary modeling approaches (SLW, FSK, SNB) are performed and discussed.     

Contrast changes in portal vein and bile duct between centric and linear k-space ordering on three-dimensional segmented true fast imaging with steady-state precession magnetic resonance imaging

Purpose

To compare the degree of visualization of the bile duct and portal vein in terms of the difference in k-space ordering on a three-dimensional (3D) segmented true fast imaging with steady-state precession (trueFISP) sequence.

Materials and Methods

A breath-hold coronal 3D segmented trueFISP sequence was prospectively performed on 14 healthy volunteers. Images obtained with centric and linear k-space ordering in the k(x)–k(y) plane were compared by two independent radiologists qualitatively with depiction scores on a five-point scale (1=not seen to 5=excellent depiction) using the Wilcoxon signed-rank test. Images were also compared quantitatively using relative contrast values for the bile duct and portal vein against the hepatic parenchyma using a paired t-test.

Results

With centric ordering, both the mean depiction scores and relative contrast values for the portal vein were significantly lower than those with linear ordering (1.5 vs. 3.5, P<.01; and 0.08±0.19 vs. 0.51±0.10, P<.01, respectively). However, in the bile duct, there were no significant differences, only slight differences were found among the results obtained with centric and linear ordering (3.9 vs. 3.8, P=.72; and 0.59±0.06 vs. 0.68±0.06, P<.01, respectively).

Conclusion

For visualizing the bile duct, centric k-space ordering on 3D segmented trueFISP sequence is recommended, while linear ordering is recommended for portal vein visualization.     

Simulation of elasto optical properties of K2SO4 crystals

The electronic optical spectra of the mechanically free and stressed crystals of potassium sulfate, K₂SO₄, in the orthorhombic phase Pnma have been calculated by the Cambridge Serial Total Energy Package (CASTEP) code. On the basis of these calculations, the components of stress elasto optical tensors based on the changes of refractive index n (π_im) and birefringence Δn () (i, k, m=1, 2, …, 6) have been obtained for the indices i, k ,m=1, 2, 3. Absolute magnitudes of the calculated tensor π_im are probably underestimated because the magnitudes of the calculated elastic stiffness tensor c_rm are found to be overestimated about two times. Features of the spectral dependences n(E) and k(E) of refractive and absorption indices of the mechanically free and stressed potassium sulfate crystals have been analyzed.     

Removal of lead(II) by adsorption onto Viscumalbum L.: Effect of temperature and equilibrium isotherm analyses

The removal efficiency of Viscumalbum L. from lead containing aqueous solutions was investigated. The effect of adsorbent mass, pH of solution, initial Pb(II) concentration and temperature was investigated using a batch adsorption technique. The optimum pH for Pb(II) adsorption was found as 3.0 for Viscumalbum L. Results were analyzed by the Langmuir, Freundlich, Temkin and Harkins-Jura, equation using linearized correlation coefficient at different temperature. The characteristic parameters for each isotherm have been determined. The Langmuir model agrees very well with experimental data than the other models. According to Langmuir isoterm, the monolayer saturation capacity (Q_o) is 769.23 mg/g at 25 °C. Models and the isotherm constant were evaluated depending on temperature. Thermodynamic parameters such as ΔH^o, ΔS^o and ΔG^o were calculated. The adsorption process was found to be endothermic and spontaneous. The experimental data were analyzed using the first- and the second-order kinetic models. The rate constants of adsorption for both kinetics models have been calculated. The second-order model provides the best correlation of the data.     

Extension of the weak-line approximation and application to correlated-k methods

Global climate models require accurate and rapid computation of the radiative transfer through the atmosphere. Correlated-k methods are often used. One of the approximations used in correlated-k models is the weak-line approximation. We introduce an approximation T_γ which reduces to the weak-line limit when optical depths are small, and captures the deviation from the weak-line limit as the extinction deviates from the weak-line limit. This approximation is constructed to match the first two moments of the gamma distribution to the k-distribution of the transmission. We compare the errors of the weak-line approximation with T_γ in the context of a water vapor spectrum. The extension T_γ is more accurate and converges more rapidly than the weak-line approximation.     

Effect of sintering atmosphere on the electrical and optical properties of (ZnO)1−x(MnO2)x NTCR ceramics

Nominal composition of (ZnO)_1−x(MnO₂)_x (0.005≤x≤0.2) ceramics have been prepared by the standard solid-state reaction method in three different sintering atmospheres: Ar, air, and reductive atmosphere. The effect of sintering atmosphere on the electron spin resonance (ESR), negative temperature coefficient of resistivity (NTCR), and photoluminescence (PL) properties of (ZnO)_1−x(MnO₂)_x ceramics has been investigated in detail. The results demonstrate that the sintering atmosphere has significant effects on the ESR signals of (ZnO)_1−x(MnO₂)_x; the NTCR of the samples sintered in air is larger than those sintering in Ar and reductive atmosphere; the deep-level PL related to oxygen vacancy increases when sintered in the reductive atmosphere.     

Numerical explanation for accurate radiative cooling rates resulting from the correlated k-distribution hypothesis

Numerical simulations are conducted to demonstrate that (a) correlation between spectral absorption at two levels decreases with increasing level distance; and (b) the contribution to the flux gained by one layer from another decreases rapidly with the layer separation. The combination of the two facts explains why the existence of poor correlation between distant layers produces insignificant radiative cooling rate error. Therefore, the overall accuracy of cooling rate calculations under the correlated k-distribution hypothesis is high.     

An efficient method for computing atmospheric radiances in clear-sky and cloudy conditions

A computationally efficient method is developed to simulate the radiances in a scattering and absorbing atmosphere along an arbitrary path in the spectral region ranging from visible to far-infrared with a spectral resolution of 1 cm⁻¹. For a given spectral region, the method is based on fitting radiances pre-calculated from the discrete ordinate radiative transfer (DISORT) at several wavenumbers. Radiances at other wavenumbers are interpolated based on the pre-computed total absorption and scattering optical thicknesses and the surface albedo. The computational efficiency and accuracy of the method are tested in comparison with rigorous simulations for various scenarios under the same conditions. For both clear-sky and cloud atmospheres, the present method is at least 140 times faster than the direct application of DISORT. Across the spectral range, the standard relative differences between the new method and the DISORT are less than 2% for clear-sky conditions. Root-mean-square (RMS) differences of the top of the atmosphere (TOA) brightness temperatures between the new method and DISORT, for atmospheric infrared sounder (AIRS) channels over clear-sky, ice cloudy and water cloudy skies, are within the noise equivalent differential temperature (NEDT) of the AIRS sensor. The fast method is also applied to simulations of the spectral downwelling radiance measured by the Fourier transform infrared (FTIR) interferometer, and to the simulations of the AIRS upwelling radiances under clear-sky and cloudy conditions.     

A correlated-k model of radiative transfer in the near-infrared windows of Venus

We present a correlated-k-based model for generating synthetic spectra in the near-infrared window regions, from 1.0 to 2.5 μm, emitted from the deep atmosphere of Venus on the nightside. This approach is applicable for use with any near-infrared instrument, ground-based and space-borne, for analysis of the thermal emissions in this spectral range. We also approach this work with the view of using the model, in conjunction with a retrieval algorithm, to retrieve minor species from the Venus Express/VIRTIS instrument. An existing radiative-transfer model was adapted for Venusian conditions to deal with the prevailing high pressures and temperatures and other conditions. A comprehensive four-modal cloud structure model based on Pollack et al. [Near-infrared light from venus’ nightside: a spectroscopic analysis. Icarus 1993;103:1-42], using refractive indices for a 75% H₂SO₄25% H₂O mixture from Palmer and Williams [Optical constants of sulfuric acid; application to the clouds of Venus? Appl Opt 1975;14(1):208-19], was also implemented. We then utilized a Mie scattering algorithm to account for the multiple scattering effect between cloud and haze layers that occur in the Venusian atmosphere. The correlated-k model is shown to produce good agreement with ground-based spectra of Venus in the near infrared, and to match the output from a line-by-line radiative-transfer model to better than 10%.     

Evaluation of solution methods for radiative heat transfer in gaseous oxy-fuel combustion environments

The exact solution to radiative heat transfer in combusting flows is not possible analytically due to the complex nature of the integro-differential radiative transfer equation (RTE). Many different approximate solution methods for the solution of the RTE in multi-dimensional problems are available. In this paper, two of the principal methods, the spherical harmonics (P₁) and the discrete ordinates method (DOM) are used to calculate radiation. The radiative properties of the gases are calculated using a non-gray gas full spectrum k-distribution method and a gray method. Analysis of the effects of numerical quadrature in the DOM and its effect on computation time is performed. Results of different radiative property methods are compared with benchmark statistical narrow band (SNB) data for both cases that simulate air combustion and oxy-fuel combustion. For both cases, results of the non-gray full spectrum k-distribution method are in good agreement with the SNB data. In the case of oxy-fuel simulations with high partial pressures of carbon dioxide, use of gray method for the radiative properties may cause errors and should be avoided.     

Resonance-enhanced multiphoton ionization spectroscopy of CH3 and CD3. Two-photon absorption selection rules and rotational line strengths of the ν3- and ν4-active vibronic transitions

To explore the possibility of K-level resolved, 2+1 resonance-enhanced multiphoton ionization (REMPI) processes of the methyl radical, the two-photon absorption selection rules and rotational line strengths of the 3₀¹ and 4₀¹ vibronic bands of the transition (n=3 or 4) were reported. Stringent selection rules, which were imposed upon these two-photon transitions, are the initial K″=3p (p=0,1,2,…), ΔK=±2, ΔU=±3, and ΔN=0,±1,±2 (O, P, Q, R, and S branches). The previously assigned 2₂² vibronic band of the methyl radical should be studied by the REMPI with a better spectral resolution and analyzed by the newly derived two-photon absorption selection rules and rotational line strength formulas.     

An efficient approach for the implementation of the SNB based correlated-k method and its evaluation

The current implementation of the SNB based correlated-k method consumes a significant portion of the total cpu time on the on-line inversion of the cumulative distribution function. An approach was developed to pre-calculate the absorption coefficients of real gases from the inversion procedure. This approach results in significant improvement in the efficiency of the SNB based correlated-k method with slight loss in accuracy. This approach was evaluated against other implementation approaches of the SNB based correlated-k method in several non-isothermal and/or inhomogeneous problems.     

The k-moment method for the narrow band modeling of radiative properties of nonuniform gaseous media

Moments of the absorption coefficient distribution function are used for the derivation of statistical narrow band (SNB) model parameters of nonuniform optical paths in gases. The approach yields approximations for the path-averaged first- and second-order k-moments from which equivalent SNB parameters are determined in the frame of the Malkmus model. The approach is assessed through comparisons with LBL data. The nonuniform approximation is shown to enable the computation of transmissivities and radiation intensities with accuracy similar to or higher than those achieved by the Curtis-Godson one.     

The relationship between absorption coefficient and temperature and their effect on the atmospheric cooling rate

Several approaches are considered to determine the temperature effect on the absorption coefficient within a correlated k-distribution method. Taking in the 610- region for example, the absorption coefficients and atmospheric cooling rates calculated using these approaches are compared with line-by-line integration. It is emphasized in this paper by numerical calculation that the effect of pressure on absorption coefficient is related to temperature and vise versa; the larger the pressure, the larger the effect of temperature on absorption coefficient. Results show that the temperature effect must be considered in radiative calculations although its effect on the absorption coefficient is much smaller than that of pressure.     

An improved treatment of overlapping absorption bands based on the correlated k distribution model for thermal infrared radiative transfer calculations

This paper discusses several schemes for handling gaseous overlapping bands in the context of the correlated k distribution model (CKD). Commonly used methods are generally based on certain spectral correlation assumptions; thus they are either less accurate or less efficient and rarely apply to all overlapping bands. We propose a new treatment, which we developed from the traditional absorber amount weighted scheme and improved for application to various bands. This approach is quite efficient for treating the gaseous mixture as if it were a “single gas.” Numerical experiments demonstrate that the new scheme achieves high accuracy with a fast operating speed. To validate the new scheme, we conducted spectrally integrated calculations and sensitivity experiments in the thermal infrared region. Compared to line-by-line integration results, errors in cooling rates were less than 0.2 K/day below 70 Km and rose to 1 K/day from above 70 Km up to 100 Km; flux differences did not exceed 0.8 W/m² at any altitude. Changes in CO₂ and H₂O concentrations slightly influenced the accuracy of the results.     

Microbial inactivation in cloudy apple juice by multi-frequency Dynashock power ultrasound

The study determined the efficacy of Dynashock wave power ultrasound as an alternative processing technique for apple juice against a number of pathogenic and spoilage microorganisms. The effects of several implicit, intrinsic and extrinsic properties on the Dynashock wave inactivation of the microorganisms were also investigated. Results showed that acid adaptation increased the resistance of Escherichia coli O157:H7 and Salmonella spp. but decreased that of Listeria monocytogenes. Spoilage yeast mixed inoculum composed of Debaryomyces hansenii, Torulaspora delbrueckii, Clavispora lusitaniae, Pichia fermentans and Saccharomyces cerevisiae was found to be more resistant than any of the adapted or non-adapted pathogens. Among the individual, acid-adapted E. coli O157:H7, the MN-28 isolate was found most resistant; while three other individual isolates had greater resistance than the composited E. coli inoculum. Increased in pulp content decreased the efficacy of Dynashock waves, but co-treatment with ultraviolet-C rays significantly enhanced inactivation in the cloudy apple juice. The results demonstrated the potential of Dynashock wave technology, together with other antimicrobial hurdles as alternative juice processing technique/s.