Parameters Of Distribution Function Research Articles

High precision modeling of polarized signals: Moment expansion method generalized to spin-2 fields

The modeling and removal of foregrounds poses a major challenge to searches for signals from inflation using the cosmic microwave background (CMB). In particular, the modeling of CMB foregrounds including various spatial averaging effects introduces multiple complications that will have to be accounted for in upcoming analyses. In this work, we introduce the generalization of the intensity moment expansion to the spin-2 field of linear polarization: the spin-moment expansion. Within this framework, moments become spin-2 objects that are directly related to the underlying spectral parameter and polarization angle distribution functions. In obtaining the required expressions for the polarization modeling, we highlight the similarities and differences with the intensity moment methods. A spinor rotation in the complex plane with frequency naturally arises from the first order moment when the signal contains both spectral parameter and polarization angle variations. Additional dependencies are introduced at higher order, and we demonstrate how these can be accounted with several illustrative examples. Our new modeling of the polarized signals reveals to be a powerful tool to model the frequency dependence of the polarization angle. As such, it can be immediately applied to numerous astrophysical situations.

CONSTRUCTION OF SOME ARCHIMEDEAN COPULAS

We propose an approach allowing to manage the statistical data. At the same time, starting from the copulas of Gumbel,of Ali-Michael and Haq., we propose some copulas of the Archimedean family that we estimate contribute to the resolution of the problems related to the choice of the maximum or the optimal values for a group of random variables united within d random vectors of size n, independent and identifically distributed, suitably normalized as n tends to infinity. To our knowledge, there exists, in this case, the copula of Ali-Michael and Haq, Which goes in the same direction, however, the copula that we propose takes into account on the one hand the dependence parameters of the marginals and on the other hand the size of the samples including the dependence parameter of the joint distribution function

Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study.

Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons. The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry. The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method. 3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object. Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.

Effect of Slurry Concentration on the Ceramic Ball Grinding Characteristics of Magnetite

Ceramic grinding, which in this paper is defined as a method of using ceramic materials as grinding media, is favored by many processing plants as an emerging high-efficiency and energy-saving grinding method. This paper investigates the effect of slurry mass concentration on the grinding characteristics of magnetite by taking the feed of the secondary ball mill for processing magnetite as the research object. The study results show that the slurry mass concentration significantly affects the ceramic ball grinding characteristics of magnetite, especially for coarse particles. When the grinding concentration is higher than 50%, the breakage rate of magnetite plummets to 1/3 of the value at low mass concentrations. The standard deviation of the breakage rate relative to the concentration gradually decreases as the feed size falls, indicating that the coarser the feed size, the more sensitive the ceramic ball grinding is to the concentration, and thus industrial secondary ceramic ball mills need to avoid grinding under high-quality concentrations. The change in the consistency parameter of distribution function and zero-order output characteristics signals a radical variation in the grinding characteristics of magnetite using the ceramic ball grinding method compared to conventional grinding. Because the ceramic ball grinding method can greatly reduce energy consumption while lowering the chance of overgrinding, this grinding method deserves more attention as the world works to reach carbon neutrality and emissions peak.

Effect of hydrated shell layers on surface tension of electrolyte solutions: Insights from interpretable machine learning

To explore the effects of hydration shell layer on the surface tension of electrolytes solution and to build an effective prediction model, a machine learning based model is proposed to accurately predict and explain the surface tension of electrolytes solution. The model combines machine learning (ML) algorithms, force filed parameters of molecular dynamics simulations and radial distribution function (RDF) to accurately capture the structure feature for electrolytes solution. The prediction performed an extremely low average relative deviation. SHapleyAdditive explanation (SHAP) method is used to indicate the features order of importance from strong to weak. It noted that the second hydration shell on the influence of surface tension may beyond the first hydration shell. This work provides a method for one-step acquisition of surface tension data that not only to accurately predict physical and chemical properties of materials, but also to extend the application of molecular dynamics simulations, providing enlightening insights for detecting underlying physical mechanisms.

Properties of Electron Swarm Parameters in Tetrahydrofuran

Reported electron collision cross sections data in the energy range ~ 0 to 300 eV from gaseous biomolecule Tetrahydrofuran (THF) have been used to calculate the electron energy distribution function (EEDF) and swarm parameters for electrically excited of THF, using a two-term solution of the Boltzmann equation. The electron swarm parameters namely (mean energy, drift velocity, diffusion coefficient, electron mobility, characteristic energy, attachment and ionization coefficient), at room temperature and atmospheric pressure are presented over a wide range of applied electric field strength E/N (E is the electric field and N is the gas number density) varying from 0.1 Td to 1000 Td (1Td = 10-17 Vcm2). The EEDF found to be non-Maxwellian. The electron swarm parameters are compared with those calculated using multi term kinetic theory and experimentally using the pulsed Townsend technique. The influence of inelastic cross section on the calculated transport parameters is also explained.

Propagation of Non-Adiabatic Heterogeneous Solid Combustion Waves with Effect to Internal Microstructure and Heat Release

ABSTRACT Propagation of combustion front with effect to the external heat loss is studied by the two-dimensional discrete periodic and disorder systems. Discrete periodic systems are modeled by the regular arrangement of burnt and unburnt point heat sources characterized by the identical rate of heat release and different heat loss parameter. Discrete disorder systems, namely, S1, S2 and S3 are considered with the concatenation of regular burnt and unburnt point heat sources distributed by different shaping parameter of beta distribution function. The unburnt point heat sources in a discrete disorder system are characterized by the different heat loss parameter and incorporation of two categories of distributions for the rate of heat release namely (i) gamma (a = 20) and (ii) gamma (a = 2). The oscillations in ignition time delay, with the manifestation of bifurcation pattern, have been detected for discrete periodic systems. In a discrete disorder system, the external heat loss plays a crucial role in developing the fingering instabilities and determining the early onset of unstable combustion, quenching and combustion limit. Degree of randomness in the distribution of heat release for the disorder system affects the duration of combustion, burn rate without affecting the combustion limit. Computed values of burn rate and combustion limit from the discrete combustion model have been compared with the available data from experiment.

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the stellar integrated galactic initial mass function (IGIMF) in the presence of cluster-to-cluster variations of the IMF. Variations of the IMF for a population of coeval clusters that populate the initial cluster mass function (ICLMF) are taken into account in the form of Gaussian distribution functions of the IMF parameters. For the tapered power-law function used in this work, these are the slope at the high-mass end, Γ, the slope at the low-mass end, γ, and the characteristic mass Mch. The level of variations is modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for the population of young clusters in the present-day Milky Way, which are σΓ = 0.6, σγ = 0.25, and σMch = 0.27 M⊙. We find that increasing the levels of dispersion for γ and Γ tends to moderately flatten the IGIMF at the low and high-mass end, respectively. The characteristic mass of the IGIMF is, however, strongly impacted by variations in Mch. Increasing the value of σMch shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can provide a simple explanation for the bottom-heavy stellar mass function that is inferred for early-type galaxies since these are likely the result of a merger of disk galaxies where the physical conditions of the star-forming gas may vary significantly both in time and space in the merging system. The effect of IMF variations on the IGIMF is compared to the effects of other processes and sources of systematic variations such as those due to variations in the shape of ICLMF, the gas-phase metallicity, and the galactic star formation rate (SFR) which can potentially affect the maximum mass of stellar clusters in a galaxy and set the mean value of the characteristic mass in clusters. For the various dependencies we have explored, we found that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. For the regimes at low metallicity where the IGIMF resembles a single power law, an increased level of IMF variations renders the IGIMF steeper and more bottom heavy, especially at low SFRs. On the other hand, variations in the IMF in the high mass regime can be easily dominated by variations in the slope of the ICLMF. We compare our results of the metallicity and SFR-dependent IGIMF to a sample of Milky Way ultra-faint dwarf (UFD) satellite galaxies that have available metallicity measurements. The present-day stellar mass function of these galaxies is a good analog to the IGIMF at the time their overall population of stars formed. We show that the slope of the stellar mass function of the UFD galaxies measured for stars in the mass range [0.4, 0.8] M⊙ can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. Our results suggest that the inclusion of IMF variations in models of galaxy formation and evolution is of vital importance in order to improve our understanding of star formation and star formation feedback effects on galactic scales.

Directional wind characteristics analysis in the mountainous area based on field measurement

Wind characteristics are one of the most important factors when designing long-span bridges. In a typical deep-cutting gorge, the wind field is influenced by local terrain and shows dependence on wind direction according to preliminary numerical simulations. Field measurement is then employed to evaluate the impact of wind direction further. Instead of the common method, which splits samples into sectors by referring to the canyon direction, a qualitative computation approach is adopted. Specifically, marginal probability distribution functions (PDFs) of various wind characteristic parameters are explored initially, followed by binary and ternary joint PDFs associated with wind direction using the modified Bernstein copula. The directional wind characteristics are then examined utilizing conditional PDFs and mathematical expectations for all wind directions. The results show that both the distribution and mean value of wind parameters in severe winds exhibit a substantial association with wind direction. The statistical properties change significantly and cannot be captured using the common method when airflows enter from downstream of the canyon and are blocked by the ridge near the bridge. When designing long-span bridges sensitive to wind action, the impact of wind direction should be carefully factored, especially when local terrain blocks the frequent incoming flow.

Geostationary operational environmental satellite-R advanced baseline imager reflective solar band absolute validation using Sonoran desert scenes

The advanced baseline imagers (ABIs) on board the geostationary operational environmental satellite (GOES)-R series, GOES-16 and GOES-17 satellites, have accumulated long data series that have been updated throughout their missions to enhance their utility for imaging the Earth’s weather, oceans, and environment. In preparing for a reprocessing effort aimed at improving the consistency and image quality and reducing radiometric uncertainties necessary for some Earth science applications, we developed a vicarious validation technique for five of the six reflective solar bands. This technique uses Sonoran desert surface reflectance data derived from the moderate resolution imaging spectrometer bidirectional reflectance distribution function parameters product along with other atmospheric products to generate a predicted at-sensor radiance for both GOES-16 and GOES-17 for comparison with ABI observations and to enable ABI intercomparisons. This technique identified known instrument biases and demonstrated absolute validation over the course of a year, showing its capability to detect changes, monitor stability, and assess radiometric uncertainties for operational data applications and future reprocessed data sets.

Combined water quality forecasting system based on multiobjective optimization and improved data decomposition integration strategy

AbstractWater quality forecasting has great practical significance for sustainable utilization of water resources and timely pollution prevention and control. However, owing to irregularity and volatility of water quality data, achieving accurate forecasts remains a challenging problem. Existing single forecasting models based on points forecasts fail to capture the uncertainty in water quality data or obtain high forecasting accuracy. To address those disadvantages, an uncertain combined water quality forecasting system based on time‐varying filtering empirical mode decomposition strategy and multiobjective immune selection optimization is proposed. Simulations are carried out with actual water quality data obtained during dry and wet periods. Empirical results show that the improved empirical mode decomposition strategy has better data denoising effect. Based on the multiobjective optimization algorithm, not only the Pareto optimal weights of the combined forecasting modules can be obtained but also the distribution function parameters can be effectively optimized. The proposed system can integrate the respective advantages of deep learning and neural network models to improve the forecasting accuracy, and effectively analyze the uncertainty of water quality, and provide technical support for the sustainable development of regional water environment.

Analytical calculation of the degree of linear polarization radiation of the OI 6300 Å red line in the Earth's ionosphere excited by electrons

The degree of linear polarization of the line OI 6300 Å of the oxygen atom in the Earth's ionosphere is analytically calculated. The calculations are performed under the assumption of collision excitation of the oxygen atom by electrons. The parameters of the anisotropic electron distribution corresponding to the measured polarization of 2%. The dependences of the degree of linear polarization on the parameters of the electron distribution function of the Earth's ionosphere are analyzed. Calculations indicate good ground-based observations of nonequilibrium conditions in the Earth's ionosphere.

Investigation of statistical correlation of negative parity energy levels in Tm nucleus with A=170

In this paper, the statistical properties of 1- to 7- negative parity levels in the 170Tm nucleus are considered with emphasis on the nearest neighbor spacing distribution in the framework of random matrix theory. The latest available experimental data for different negative parity energy levels in the E≤ 3000 keV region are used to classifiy in different sequences and are analysed. The Berry – Robnik distribution function and the least square extraction method have been used to determine the parameter of distribution function in considered sequences. The results show the adaptation of the statistical behavior of all considered negative parity levels with the Wigner distribution function and therefore, the statistical correlation of such levels. Also, the strong correlations are yield for the sequences prepared by levels with odd spin values while the 2- levels show a weak correlation and a Poisson-like behavior. The dependence of the statistical behavior of the negative parity levels to the energy was investigated which suggests the maximum correlation in the 1300 <E < 2100 keV energy region.

Simultaneous reconstruction of temperature-dependent optical and thermophysical parameters of insulation material by the GA-SQP/SQP technique

A combination genetic algorithm (GA) with sequential quadratic programming (SQP) algorithm is proposed to simultaneously identify the temperature-dependent thermal conductivity (κc(T)) and extinction coefficient (β(T)) of insulation material without any prior information of parameter distribution function. The GA is applied to obtain the initial values of κc(T) and β(T) because of its lesser dependence on initial guess, then the reconstruction results from GA are used as the initial values of SQP to reckon an optimal solution of κc(T) and β(T) and finally the established κc(T) in previous step are adopted as known parameters to reconstruct the β(T) by SQP algorithm, which is called a GA-SQP/SQP technique. The retrieval results from numerically generated temperature demonstrate that the GA-SQP/SQP technique can significantly improve the accuracy of estimated κc(T) and β(T) compared with the other traditional optimization algorithms. Corresponding experiment is performed to estimate the κc(T) and β(T) of insulation material at high temperatures by the GA-SQP/SQP technique and the results are validated.

Rate Capability of LiFePO4 Cathodes and the Shape Engineering of Their Anisotropic Crystallites

For cuboid and ellipsoid crystallites of LiFePO4 powders, by X-ray diffraction (XRD) and microscopic (TEM) studies, it is possible to determine the anisotropic parameters of the crystallite size distribution functions. These parameters were used to describe the cathode rate capability within the model of averaging the diffusion coefficient D over the length of the crystallite columns along the [010] direction. A LiFePO4 powder was chosen for testing the developed model, consisting of big cuboid and small ellipsoid crystallites (close to them). When analyzing the parts of big and small rate capabilities, the fitting values D = 2.1 and 0.3 nm2/s were obtained for cuboids and ellipsoids, respectively. When analyzing the results of cyclic voltammetry using the Randles-Sevcik equation and the total area of projections of electrode crystallites on their (010) plane, slightly different values were obtained, D = 0.9 ± 0.15 and 0.5 ± 0.15 nm2/s, respectively. We believe that these inconsistencies can be considered quite acceptable, since both methods of determining D have obvious sources of error. However, the developed method has a clearly lower systematic error due to the ability to actually take into account the shape and statistics of crystallites, and it is also useful for improving the accuracy of the Randles-Sevcik equation. It has also been demonstrated that the shape engineering of crystallites, among other tasks, can increase the cathode capacity by 15% by increasing their size correlation coefficients.

Retrieving aerosols single scattering albedo from MODIS reflectances

Single scattering albedo (SSA) is a key parameter to estimate aerosol direct radiative forcing. However, retrieving SSA from satellite observations is still challenging. In this study, a new method optimizing the aerosol optical model based on four basic aerosol components is developed for retrieving SSA from Moderate Resolution Imaging Spectroradiometer (MODIS) data. The new method takes advantage of the relationship between aerosol composition and reflectance at multiple wavelengths to derive SSA, which considers the variation of aerosol species with time and location. A sensitivity study considering the uncertainties from the top of the atmosphere (TOA) apparent reflectance, aerosol optical depth (AOD) at 550 nm and land surface bidirectional reflectance distribution function (BRDF) parameters is performed to test the stability of the proposed method. The results demonstrate the high accuracy and robustness of the new method. The root mean square error (RMSE) is within 0.03 at 470 and 550 nm based on the sensitivity study. The aerosol components used in our method show better representativeness of real aerosol components than that used in the Second Simulation of a Satellite Signal in the Solar Spectrum - Vector (6SV) model. The aerosols SSA values are retrieved from real MODIS observations with the new method and compared with the AERONET SSA product at two polluted AERONET sites in Asia. A better consistency with the correlation coefficient (R) of 0.27– 0.55 and the RMSE within 0.04 at 470 and 550 nm wavelengths between MODIS SSA retrievals and the AERONET SSA product is obtained with the new method compared with that of deep blue (DB) SSA. The new method can help to better understand aerosol radiative forcing regionally and globally.

NEW DIRECTIONS IN PREDICTING AND MODELING TRUCK LOAD POPULATIONS INCLUDING OVERLOADS

Overload trucks often appear as a sizeable portion of truck populations on highways. Within most transportation jurisdictions in the United States, overloads refer to truck weights in excess of 356 kN (80 kips). The load populations exhibit an inconsistent pattern-often with two or more distinct peaks. This paper represents new directions in modeling truck load patterns with capabilities to offer the continuity as well as the bimodal feature of the load data. The method presented is data-driven and uses a bimodal distribution function. The extension of the model to predict the truck load population when data are incomplete or not available is also presented. The parameters required in the model are estimated via the fuzzy regression analysis in the proposed method. The fuzzy regression analysis allows the utilization of subjective and limited information. The Weigh-in-Motion (WIM) data obtained from several stations were used to quantify the parameters of this bimodal distribution function by employing the fuzzy regression analysis. The procedure on obtaining an appropriate distribution function for truck load population is explained along with illustrative examples.

Precisely modeling offshore jacket structures considering model parameters uncertainty using Bayesian updating

Digital twin (DT) is recognized as a promising tool to perform reliability analysis for offshore platforms. An open issue in developing the DT reliability analysis tool is to establish a high-fidelity highly-precise virtual model for the offshore platform of interest, where the virtual model is able to update its model parameters using actual sensory measurements to eliminate/reduce the effect of parameters uncertainty. To address this challenging issue, this paper proposes a Markov Chain Monte Carlo (MCMC)-based Bayesian updating method to build the requested virtual model for an offshore jacket platform. In this new method, the natural frequencies and mode shapes of the offshore jacket platform, extracted both from the structural dynamic responses of a finite element (FE) model and the sensory measurements in the physical system, are used to construct the likelihood function of the Bayesian inference. Then, the posterior probability distribution function (PDF) of the uncertain parameters is derived under the assumption of uniform prior distribution, which will be used to generate the Markov Chains by implementing the Metropolis-Hastings sampling. Hence, the most probable values of the uncertain parameters can be obtained from the Markov Chains for updating the FE model. A numerical study demonstrates high effectiveness of the proposed model updating method, even with high-level measurement noise and model uncertainty.

Agricultural Water Optimal Allocation Using Minimum Cross-Entropy and Entropy-Weight-Based TOPSIS Method in Hetao Irrigation District, Northwest China

Affected by the temporal and spatial changes of natural resources, human activities, and social economic system policies, there are many uncertainties in the development, utilization, and management process of irrigation district agricultural water resources, which will increase the complexity of the use of irrigation district agricultural water resources. Decision makers find it challenging to cope with the complexity of fluctuating water supplies and demands that are critical for water resources’ allocation. In response to these issues, this paper presents an optimization modeling approach for agricultural water allocation at an irrigation district scale, considering the uncertainties of water supply and demand. The minimum cross-entropy method was used to estimate the parameters of hydrologic frequency distribution functions of water supply and demand, which are the basis for agricultural water resources’ optimal allocation and the evaluation of water resources’ carrying capacity in the Hetao Irrigation District. Interval Linear Fractional Programming was used to find water availability, shortage, and use efficiency in different irrigation areas of the Hetao Irrigation District (HID) under different scenarios. The denominator of fractional planning is the environmental goal, and the numerator is the economic goal; so, the objective function of fractional programming is the utility rate required in the post-optimization analysis. Future water availability and shortage scenarios are adopted consistent with the Representative Concentration Pathways’ (RCPs’) framework, and future water use scenarios are developed using the Shared Socioeconomic Pathways’ (SSPs’) framework. Results revealed that under SSP1, the annual water consumption increased from 30 billion m3 to 60 billion m3, almost doubling in Urad. The annual water consumption under SSP2 and SSP3 increased slightly, from 30 billion m3 to about 50 billion m3. The amount of water available for well irrigation in Urad decreased from 300 to 250 billion m3, while the amount of water available for canal irrigation in Urad remained at 270 billion m3 from 2010 s to 2030 s, only dropping to 240 billion m3 in 2040 s. The entropy-weight-based Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method was applied to evaluate agricultural water resources’ allocation schemes because it can avoid the subjectivity of weight determination and can reflect the dynamic changing trend of irrigation district agricultural water resources’ carrying capacity. The approach is applicable to most regions, such as the Hetao Irrigation District in the Upper Yellow River Basi with limited precipitation, to determine water strategies under the changing environment.

Multiscale Piezoelasticity of Methane Gas Hydrates: From Bonds to Cages to Lattices

For the past several decades, natural gas, also called methane gas, has been recognized as a green energy resource. It can generate energy by burning and produces fewer pollutants and carbon dioxide than coal and petroleum. For these reasons, it is also being viewed as a bridge fuel to renewable energy. Conservative estimates suggest that 80% of the naturally occurring hydrates on the planet contains natural gas. This vast amount translates to approximately twice the amount of energy stored in fossil fuels and oils. In addition, the special guest–host structure of gas hydrates provides a significant storage capacity, which makes the hydrate become a competitive candidate for carbon dioxide sequestration. However, the instability of hydrates during exploration becomes the biggest barrier for methane gas extraction and carbon dioxide sequestration. Thus, to overcome this barrier, this paper aims to investigate the stability limits and study the piezo effect of structure I (sI) methane gas hydrates at 0 K. This work investigates the structure, thermodynamics, and elasticity of sI methane hydrates subjected to pressure loads, at three scales, atoms, cages, and lattice, using the density functional theory in conjunction with homogenization methods and the theory of mixtures. The distribution functions of bond parameters are characterized in the hydrate system, which provides a novel understanding on the spread of values at the smallest scale. The roles of different types of cages at the mesoscale have been identified, such as continuous phase and disperse inclusion. At the continuum scale, the different deformation mechanisms are observed (affine and non-affine), which correspond to different fracture mechanisms (brittle and ductile) under tensile and compressive pressures, respectively. Taken together, the systematic atomic–cage–lattice multiscale characterization proves fruitful in linking processes that connect mechanical properties, cage geometry, and hydrogen bonding. The multiscale methodology can be generalized to other gas hydrates to improve the fundamental understanding and obtain engineering correlations.