Lognormal Distribution Model Research Articles

Mathematical modeling of impulse response of viscous remanent magnetization

TEM survey under objects that containing superparamagnetic particles, the effects of magnetic viscosity can have a significant impact on the received signal. At present, such effects of magnetic viscosity are considered a nuisance, while some researchers point out that they contain useful information.The article presents a mathematical modeling of impulse response of viscous remanent magnetization. Using the lognormal particle distribution model, various impulse responses of the magnetization were modeled. The results of attempts to restore the distribution parameters and of model impulse responses are presented. An estimate of the effectiveness of the inversion of synthetic impulse responses is given.

Verification of sex- and age-specific reference intervals for 13 serum steroids determined by mass spectrometry: evaluation of an indirect statistical approach.

Conventionally, reference intervals are established by direct methods, which require a well-characterized, obviously healthy study population. This elaborate approach is time consuming, costly and has rarely been applied to steroid hormones measured by mass spectrometry. In this feasibility study, we investigate whether indirect methods based on routine laboratory results can be used to verify reference intervals from external sources. A total of 11,259 serum samples were used to quantify 13 steroid hormones by mass spectrometry. For indirect estimation of reference intervals, we applied a "modified Hoffmann approach", and verified the results with a more sophisticated statistical method (refineR). We compared our results with those of four recent studies using direct approaches. We evaluated a total of 81 sex- and age-specific reference intervals, for which at least 120 measurements were available. The overall agreement between indirectly and directly determined reference intervals was surprisingly good as nearly every fourth reference limit could be confirmed by narrow tolerance limits. Furthermore, lower reference limits could be provided for some low concentrated hormones by the indirect method. In cases of substantial deviations, our results matched the underlying data better than reference intervals from external studies. Our study shows for the first time that indirect methods are a valuable tool to verify existing reference intervals for steroid hormones. A simple "modified Hoffmann approach" based on the general assumption of a normal or lognormal distribution model is sufficient for screening purposes, while the refineR algorithm may be used for a more detailed analysis.

Research on Distribution Model and Detection Spacing of Compaction Degree of Asphalt Pavement Based on the PQI Method

The pavement quality indicator (PQI) is a non-destructive piece of equipment for detecting the compaction degree of asphalt pavement, which can avoid primary damage to the pavement compared with the traditional core-drilling method. In this paper, the PQI method was applied to evaluate the compaction quality of asphalt pavement through data collection, calibration and statistical analysis, and the probability-distribution characteristics of compaction degree were also explored, by fitting the data with probability-distribution models. Furthermore, the optimal detection-spacing was determined by comparing the statistical results of compaction degree measured at different detection-spacings. Test results showed that the calibrated PQI data was close to the actual data of the core sample, and their error rate was within 1%. The compaction degree of the test road was mostly located between 92% and 99%, and the variable coefficient was entirely below 2%, demonstrating that the pavement-compaction quality was satisfactory and uniform. The normal distribution model, lognormal distribution model and extreme-value distribution model had relatively high accuracy in fitting the compaction-degree frequency data, while the sine-wave distribution model was low in fitting accuracy. By comparing the predicted value with the actual value of compaction degree, the normal distribution model was determined as the most appropriate model for describing the frequency distribution of compaction degree. In addition, the detection spacing was selected as 50 m, considering the reliability, accuracy and efficiency. The research results provide technical support for the compaction quality-control of asphalt pavement in a non-destructive, timely, accurate and multi-point manner, ultimately contributing to the excellent service performance and service life of asphalt pavement.

Probabilistic Analysis on Aerostatic Displacement-dependent Wind Loads on a Stream-lined Box Girder

Due to the limitations of the bridge deck modeling and wind tunnel installations, the parametric uncertainties of aerostatic displacement-dependent wind loads have become an urgent problem for reliability analysis in bridge engineering. Computational fluid dynamic (CFD) simulations were conducted to investigate the distribution model of aerostatic coefficients. The Monte Carlo simulation (MCS) was used to generate random samples of stream-lined box cross-sections. Among these samples, wind attack angles of −8°–8° were considered, and the sample size of each angle group was set as 30. Then, the statistical properties for the variation and distribution of aerostatic coefficients were discussed. In addition, sub-samples with sizes of 5–20 were randomly sampled from the initial sample group to evaluate the influence of the sample scale. The coefficient of variation (COV) of aerostatic coefficients with respect to geometric uncertainties increased up to 0.217, which occurred at −7° wind attack angle. Lognormal distribution models obtained by hypothesis tests maintained a low deviation for estimating the distribution of aerostatic coefficients. The sample size had a significant effect on quantifying the error between empirical and theoretical distribution models. Simulation method proposed in this paper provides a systematic approach for probabilistic problems involving fluid-structure interaction and parametric uncertainties.

Species-Abundance Distribution Patterns of Plant Communities in the Gurbantünggüt Desert, China

It is important to study the species-abundance distribution pattern in a community to reveal the mechanism of community assembly. Six abundance models (log-normal distribution model, Zipf model, Zipf–Mandelbrot model, broken stick model, niche preemption model, and Volkov model) were used to fit the species-abundance distribution pattern of six scales (10 m × 10 m, 20 m × 20 m, 40 m ×40 m, 60 m × 60 m, 80 m × 80 m, 100 m × 100 m) in fixed, semifixed, and mobile sand dunes in the Gurbantünggüt Desert, respectively. The best-fitting model was determined using the K-S test, the Chi-square test, and the Akaike information criterion. The results showed that the values of soil salinity, nutrients, water content, Shannon–Wiener diversity index (H′), Pielou evenness index (E), and Simpson index (D) were ranked in all three habitats as fixed dunes > semifixed dunes > mobile dunes. The rank curves span a narrow range on the horizontal axis at scales of 10 m × 10 m and 20 m × 20 m, and species richness is minimal. As the scale increases, the span range of the curve gradually increases, and species richness becomes higher at scales of 40 m × 40 m, 60 m × 60 m, 80 m × 80 m, and 100 m × 100 m. At the 10 m × 10 m and 20 m × 20 m scales, the broken stick model fits best in the three dune habitats. At the 40 m × 40 m and 60 m × 60 m scales, the niche preemption model fits best in the three dune habitats. At the 80 m × 80 m and 100 m × 100 m scales, the Volkov neutral model fits best in the fixed and semifixed dune habitats, and the niche preemption model fits best in the mobile dune habitats. In fixed, semifixed, and mobile dunes, both niche and neutral processes played important roles in community construction, reflecting the manifestation of the community niche-neutral continuum.

Analysis on infestation and related ecology of chigger mites on large Chinese voles (Eothenomys miletus) in five provincial regions of Southwest China.

Based on a long-term field investigation in the five provincial regions of Southwest China between 2001 and 2019, the present paper studied the infestation and related ecology of chigger mites (chiggers) on the large Chinese vole (Eothenomys miletus), an endemic and dominant rodent species in the regions. A total of 52331 chiggers were collected from 2661 voles, and 52261 mites were identified as 185 species and 13 genera in the family Trombiculidae with very high species diversity. The identified 185 chigger species on E. miletus (a single rodent species) even exceeded those recorded in some countries. The overall infestation prevalence (Pm = 53.96%), mean abundance (MA = 19.64) and mean intensity (MI = 36.39) on E. miletus were much higher than those on some other rodent species in the same regions. Although the species composition showed a moderate similarity (J = 0.63) between male and female hosts (E. miletus), the infestation indices (Pm = 56.25%, MA = 21.67) of chiggers on male hosts were higher than those on the females (Pm = 51.23%, MA = 17.09) (P < 0.05). Two dominant chigger species, Leptotrombidium scutellare (Cr = 19.17%) and L. sinicum (Cr = 11.06%), showed an aggregated distribution pattern among different individuals of their host E. miletus, and a relatively high degree of positive association existed between the two dominant chigger species with PCC = 0.57, DI = 0.60 and OI = 0.62 (x2 = 857.46, P < 0.001). Leptotrombidium densipunctatum, Walchia koi, Helenicula hsui, L. scutellare and W. ewingi showed a high degree of environmental adaptability to their environments with high niche breadths. The theoretical curve of the species abundance distribution of chigger community on E. miletus was successfully fitted with Preston's lognormal distribution model. Based on the theoretical curve fitting, the expected total number of chigger species on E. miletus was roughly estimated to be 223 species, and 38 chigger species were probably missed in the sampling investigation.

Interactions between suspended sediments and submerged macrophytes-epiphytic biofilms under water flow in shallow lakes

Suspended sediments (SS) pollution is one of the factors affecting the transfer from turbid water state to clear water state in shallow lakes. However, the interactions between suspended sediments and submerged plants are far from clear. In this study, we investigated the settlement laws of SS in overlying water and its impact on the epiphytic biofilm of Myriophyllum verticillatum and Vallisneria natans under water flow. At least 90% of turbidity can be removed from overlying water, and the decreasing trend of water turbidity fitted the logarithmic decay model in all treatments. The size distribution of SS fit the log-normal distribution model in the first 240 min after SS addition. It should be noted that the main peak particle sizes were lower in treatments with submerged macrophytes (8.71-13.18 μm) than without plants (15.14-19.95 μm). Water flow and SS addition significantly increased the thickness of biofilms attached to M. verticillatum (p < 0.05), but they together significantly reduced the biofilm thickness on V. natans (p < 0.05). SS increased the bacterial α-diversity but decreased eukaryotic one in epiphytic biofilms. However, water flow had a more significant impact on microbial communities (especially eukaryotes) than SS and plant species. The relative abundances of dominant phylum Proteobacteria, class Alphaproteobacteria and Betaproteobacteria, and class Verrucomicrobiae increased in epiphytic biofilms after SS addition. Co-occurrence networks reveal that photosynthetic microbes in epiphytic biofilms played an important role in microbial communities under water flow and SS, and many hub microbes were increased by SS addition but reduced by water flow. These data highlight that SS decline can be predicted by the logarithmic decay model and, SS and water flow can affect the epiphytic-biofilm on submerged macrophytes.

Lifespan evaluation of polyimide films modified by nano-TiO 2 based on weibull distribution and lognormal distribution

The electrical lifespan data of polyimide (PI) films modified by nano TiO2 are dispersible due to the difference of preparation process and test environment. Among the existing studies on solid insulation lifespan evaluation, phenomenological models generally assume that the test data of the electrical equipment life obey a specific probability distribution based on intuition or some experiences, and it often is ignored that the accuracy of lifespan evaluation depends on whether the probability distribution model can accurately reflect the dispersibility of lifespan data. Therefore, in order to reduce the error caused by subjective factors on the selection of probability distribution model, PI films modified by nano-TiO2 with mass fraction of 3% and thickness of 25 μm were prepared in this paper. The lifespan distribution, failure probability distribution and density distribution function of lognormal distribution and Weibull distribution were compared. The median lifespan for the lognormal probability distribution model and the characteristic lifespan for the Weibull probability model were obtained by lifespan evaluation. It is found that the lifespan evaluation result of lognormal distribution is more radical than that of Weibull distribution. But, lognormal distribution is better than Weibull distribution model in evaluating the consistency of ageing mechanism for the samples under different voltages.

Evaluation of Different Models for Predicting Soil Water Retention from A Semiarid Region of Duhok

A study was carried out to examine the capability of bi and uni- models to explore water retention data for two different textured soils from a semiarid region Duhok-Iraqi Kurdistan. A soil hydraulic model, can be used to derive the parameters of soil hydraulic properties for describing soil water movement. The program "SWRC Fit," which performs nonlinear fitting of soil water retention curves for the two examined soils using six models, was employed for this purpose. The six models are the Brooks Corey, van Genuchten, Kosugi, Fredlund and Xing model as uni models and Durner and Seki as a bimodal model used for this purpose. The program can be carried out straightly from a web page at http://purl.org/net/swrc/; The program was used for determining Fifteen parameters of soil hydraulic for two different textured soils. As related to Berderash sandy loam soil the LN uni-model revealed better performance than the FX, BC and VG models and at same time the FX, BC and VG models exhibit similar fitting precision on average. Whereas bi-models is shown that the Durner’s bi- model (DB) revealed very well fitting performance than that of the bi-log-normal distribution model (BL) models, regarding to Zawita clay soil it revealed that the uni -models, of BC, VG, FX and LN revealed good fitting performance with similar fitting precision on average. Whereas in bi- models it was noticed that the log-normal distribution model (BL) gave very well-suitable performance than that of the Durner’s b- model (DB). After comparing between the uni-models and bi-models of the six mentioned soil hydraulic models from accuracy and coefficient determination (R2), for two different textured soils under the study it can be illustrated: firstly, for fine texture soil (clay soil) the most precision fitting performance was found by model (BL), whereas for light texture soil (sandy loam soil) the most very well-fitting performance was noticed by (DB) model, and secondly the bi-models hydraulic were better than uni-models in fitting performance.

Cross-comparative Analysis of Frequentist and Bayesian Perspectives on Failure Time Distributions

In reliability analysis, both the Weibull and the lognormal distributions could be analyzed using the observed data logarithms. While the Weibull data logarithm is skewed, the lognormal data logarithm is symmetrical. This review work initiates discussions on and syntheses of the various views held on the use of the frequentist and Bayesian approaches to drawing statistical inferences on failure time distributions of survival models. Of greater concern was the discussion on the use of the exponential, Weibull and log-normal distributions in reliability analysis. Various methods have been used to discriminate between the two most important distributions. They include: Coefficients of variation (CV); the standard deviation of the data logarithms (SD); the percentile position of the mean of the data logarithm (PP); the cumulated logarithm dispersion before and after the mean (CLD); ratio of the maximum likelihood (RML); Kullback-Leibler Divergence (KLD); and Minimized Kullback-Leibler Divergence (RMKLD). In the (CV, SD, PP and CLD) study, a stress-strength data set was used for the analysis. The stress data followed a lognormal distribution, while the strength data followed a Weibull distribution, therefore for the stress-strength analysis the lognormal-Weibull combination was used. In the ratio of the maximum likelihood (RML) study, it was averred that though each of the distributions had great applications, none of them produced a good fit. In the study using Kullback-Leibler Divergence (KLD); and Minimized Kullback-Leibler Divergence (RMKLD), test results revealed that RML=0.345&gt;0. Hence the lognormal distribution was selected. Similarly, the RMKLD=0.6028&gt;0, therefore the Weibull distribution was selected. In the final analysis, none of the study results could reject the Weibull in favour of the lognormal distribution model. In respect of the frequentist and the Bayesian approach to conducting statistical inferences, it came out strongly that it was high time psychologist who had adopted the use of the frequentist framework moved away from it and started using the Bayesian approach. A shift towards the use of the Bayesian, lognormal-Weibull approach is thus recommendable.

Performance analysis of OFDM based FSO communication system with TCM codes

Various channel coding schemes have been used over free space optical (FSO) links to alleviate the effects of turbulence induced fading. In this paper, performance analysis for TCM coded orthogonal frequency division multiplexing (OFDM) based FSO communication systems, operating over atmospheric turbulence channels. Analysis have been done in terms of bit error rate (BER) as a function of signal to noise ratio (SNR), considering the log-normal distribution model during weak turbulence and gamma-gamma distribution model for moderate and strong turbulence conditions. The integration of TCM with OFDM can solve bandwidth issue and bit rate degradation during wireless communication. Various modulation schemes have been studied for the said system keeping in mind different requirements such as band width and data rate etc. The simulation results and analysis have shown that the TCM coder with 16-QAM provides considerable coding gain as compared to uncoded system during all turbulence conditions. This system acts as high-performance wireless communication system (HPWCS) by providing BER of 10−9 which is necessary for stable operation on communication system.

European option pricing using Gumbel distribution

A risk-neutral-density (RND) function plays a key role in determining option prices accurately. The RND function is useful in understanding the negative skewness and the excess kurtosis of the stock returns. RND models bases on the log-normal distribution (for example, Black–Scholes (BS) model (Black, F and M Scholes (1973). The pricing of options and corporate liabilities, The Journal of Political Economy 3, 637–654)) are less accurate to capture the negative skewness and the excess kurtosis of stock returns (Markose, S and A Alentorn (2011). The generalized extreme value distribution, implied tail index, and option pricing, The Journal of Derivatives 18(3), 35–60). The Extreme Value Theory (EVT) is useful in addressing the tail behavior of stock returns. The tail shape parameter in a Generalized Extreme Value (GEV) distribution class helps control tails’ size and shape. This paper model, the RND function in pricing the European call option, is modeled using a GEV distribution class, namely, a Gumbel distribution. It then compares GEV distribution option values with the BS values. It observes that the BS model underprices the call option values near maturity compared to those obtained by the GEV model. The Gumbel distribution for stock returns is useful in reducing the pricing bias of the BS model.

Sizing and Sitting of DERs in Active Distribution Networks Incorporating Load Prevailing Uncertainties Using Probabilistic Approaches

In this study, a microgrid scheme encompassing photovoltaic panels, an energy storage system, and a diesel generator as a backup supply source is designed, and the optimal placement for installation is suggested. The main purpose of this microgrid is to meet the intrinsic demand without being supplied by the upstream network. Thus, the main objective in the design of the microgrid is to minimize the operational cost of microgrid’s sources subject to satisfy the loads by these sources. Therefore, the considered problem in this study is to determine the optimal size and placement for generation sources simultaneously for a microgrid with the objectives of minimization of cost of generation resources along with mitigation of power losses. In order to deal with uncertainties of PV generation and load forecasting, the lognormal distribution model and Gaussian process quantile regression (GPQR) approaches are employed. In order to solve the optimization problem, the lightning attachment procedure optimization (LAPO) and artificial bee colony (ABC) methods are employed, and the results are compared. The results imply the more effectiveness and priority of the LAPO approach in comparison with ABC in convergence speed and the accuracy of solution-finding.

Damage-control steel frames equipped with SMA connections and ductile links subjected to near-field earthquake motions: A spectral energy factor model

To achieve a delicate balance between self-centring behaviour and energy dissipation, it was proposed to develop the damage-control steel frame equipped with shape memory alloy (SMA) connections and ductile links showing the partially self-centring behaviour. This paper examined the inelastic seismic demand of the novel structure, and the emphasis was given to the spectral energy factor of the system subjected to near-field earthquake motions. Based on single-degree-of-freedom (SDF) systems representing the novel structure and a near-field earthquake database, nonlinear spectral analyses were performed considering a wide range of structural period and hysteretic parameters, and more than 25 million energy factors were obtained. The probabilistic characteristics of the energy factors were examined in detail. The analysis database confirmed that the energy factors were sensitive to structural period and hysteretic parameters. In addition, a right-skewed distribution feature of the energy factors was observed. Thus, a spectral energy factor model for damage-control steel frames equipped with SMA connections and ductile links was developed using the lognormal distribution model. Nonlinear regression analyses were conducted to develop a series of prediction equations. The good agreement between the histograms of the energy factor and predictions by the regression equations confirmed the adequacy of the proposed model. The proposed model was eventually applied to evaluating the damage-control behaviour of a prototype structure under near-field earthquake motions, and the sufficiency of the model for assessing the structural damage-control behaviour from a statistic perspective was confirmed.

Towards moss biocrust effects on surface soil water holding capacity: Soil water retention curve analysis and modeling

As ecosystem engineers in drylands, biocrusts possibly generate great influences on surface soil water holding capacity and availability, but these effects have not yet been sufficiently investigated, especially through analyzing and modeling their soil water retention curve (SWRC). On the Loess Plateau of China, the naturally developed moss biocrusts and surface bare soil were sampled in five replicates on loess soil and aeolian sand respectively, and their SWRCs from saturation (soil water potential = 0 hPa) to dry (soil water potential = −15,000 hPa) were measured with a sandbox (low water potential range) in combination with a pressure plate (high water potential range). The measured SWRCs were compared to the van Genuchten (VG), Brooks and Corey (BC), and Log-Normal Distribution (LND) models, and the model with best performance was adopted to further determine the effects of biocrusts on surface soil water holding capacity and water availability through comparing the differences in soil water content (θ) at specific water potentials between the biocrusts and uncrusted soil. Our results showed that (i) the biocrusts always had higher θ as compared with the bare soil across the whole water potential range, and the increasing effects of the biocrusts was much stronger on aeolian sand (165%) in comparison to that on loess soil (15%). (ii) As compared with the bare soil, the saturated water content, field capacity, wilting point, and available water content of the aeolian sand increased by 52%, 256% (0.192 vs. 0.054 cm3 cm−3), 65%, and 1000% by the biocrusts, respectively; while that of the loess soil increased by 28%, 9% (0.240 vs.0.220 cm3 cm−3), 27%, and 8% by the biocrusts, respectively. (iii) The increased water holding capacity of the biocrusts was possibly attributed to their higher percentage (18% vs. 16%) of microscopic pores (0.3–5 μm) on the loess soil and their increasing (16% vs. 1%) microscopic pores and decreasing (18% vs. 50%) medium pores (30–75 μm) on the aeolian sand. (iv) The VG and LND models performed better (R2 > 0.98, RMSE ≤ 0.019 cm3 cm−3, RE ≤ 7.4%) than the BC model in simulating the SWRCs of the biocrusts and bare soil, and their fitting errors were mostly distributed in the high (−500 to −1000 hPa) and low (<−5000 hPa) water potential ranges. As indicated by SWRCs, we conclude that biocrusts greatly increase surface soil water holding capacity and water availability, leading in turn to a positive feedback mechanism of the biocrusted layer, which may affect surface hydropedological process (e.g., infiltration and evaporation) in drylands.

Methodology for Selection and Analysis of Representative Test Roads Required for Vehicle Durability Evaluation

Measurement of customer usage loads is one of the essential and critical activity for evaluation of vehicle durability. The customer usage loads are measured on representative public roads of finite lengths, typically for about 500 km to 1000 km consisting of a mix of different road types. It is always a big challenge for the test engineer to make sure that these selected road patches are good representatives of the diverse road conditions of the target market. In this paper, a methodology is presented for the selection of these test roads, with the use of objective road roughness values (in terms of International Roughness Index –IRI). Detail study was carried out to analyse the best-fit probability distribution model for road roughness values, and the lognormal (three-parameter) distribution model is observed to be the best suitable model. It is shown that this model provides a better objective definition and classification of customer usage of the target market. The proposed methodology is generic, vehicle independent, and objectively helps to select the best representative test roads with 95% confidence. Thereby also helps in optimising the cost and time of the service load measurement campaign.

Particle size distribution modeling and kinetic study for coagulation treatment of tannery industry wastewater at response surface optimized condition

The presence of considerable amounts of Total Suspended Solids (TSS) in wastewater streams can pose a severe threat to aquatic and human life. A high level of TSS will increase water temperature at an alarming rate and decrease dissolved oxygen levels. This study aims to remove TSS from raw tannery wastewater using an active coagulating protein extracted from Moringa oleifera (MO) seeds. The process variables such as, coagulant dosage and pH are varied to test the potential of the coagulant extracted using NaCl and KCl salt solutions, for TSS removal from tannery wastewater. The results show that the NaCl extracted coagulant could effectively remove 89.87% of TSS whereas the KCl extracted coagulant eliminated 76.23% of TSS, at the optimum condition of 40 mL coagulant dosage and 7 pH. The assessment of coagulation rate parameters using differential method of analysis reveals that at optimum condition, the TSS reduction process obeys second order kinetics with a rate constant 3.556 × 10– 5 (mg/L)– 1 min– 1. The volume distribution of suspended solids in raw wastewater is fitted with a log-normal distribution model and Gaussian distribution model. From the magnitude of the coefficient of determination (R2) and Akaike information criterion (AIC) of the Gaussian model (R2 = 0.6864 and AIC = 3.89), it is concluded that the Gaussian model is better than the log-normal distribution model (R2 = 0.4708 and AIC = 6.31) for explaining the volumetric distribution of suspended particles. The numeric distribution of suspended solids in raw wastewater is explained well by the variable β model (R2 = 0.668) rather than the power law model (R2 = 0.196). The 3D response surface plot indicates that maximum TSS removal can be achieved at an optimal condition of 40 mL coagulant dose and 7 pH. The quadratic model developed for the treatment process utilizing the NaCl extracted coagulant shows better response prediction ability (R2 = 0.8118) when compared to the model built for the KCl extracted coagulant (R2 = 0.7911). Both the model equations have a p-value less than 0.05 which indicates that the proposed models are statistically significant. The elliptical contours for TSS removal using NaCl extracted coagulant demonstrate the significant interactions between the process variables. This study exhibited the applicability of MO seed extract for real-time tannery wastewater treatment.

Joint Modeling of Received Power, Mean Delay, and Delay Spread for Wideband Radio Channels

We propose a multivariate log-normal distribution to jointly model received power, mean delay, and root mean square (rms) delay spread of wideband radio channels, referred to as the standardized temporal moments. The model is validated using experimental data collected from five different measurement campaigns (four indoor scenarios and one outdoor scenario). We observe that the received power, the mean delay, and the rms delay spread are correlated random variables, and therefore, should be simulated jointly. Joint models are able to capture the structure of the underlying process, unlike the independent models considered in the literature. The proposed model of the multivariate log-normal distribution is found to be a good fit for a large number of wideband data sets.

Bubble size distributions in gas–liquid–solid systems and their influence on flotation separation in a bubble column

Measurements of bubble size distributions are very important in flotation which is widely used in different chemical industries such as the recovery of valuable minerals, wastewater treatment, deinking of waste paper, and oil recovery from tar sands. Although numerous authors determined bubble size distributions (BSD-s) in gas–liquid systems, BSD-s have been rarely determined in gas–liquid–solid systems. Moreover, the influence of BSD-s on flotation has not been quantified under a wide range of experimental conditions. Thus, this paper is focused on measurements of bubble size distributions by changing surfactant dosage, solid percentage, air velocity and particle size as well as establishing the relationships between bubble size distribution properties and flotation performances. It was found that the experimental bubble size distributions are successfully fitted by using the log-normal distribution model in which the two model parameters (μ and σ) are used. The results showed that the most important factors affecting the Sauter mean diameter (d32), the model parameters and the flotation recoveries are the surfactant dosage and the solid percentage. The increase in the surfactant dosage decreased d32 probably due to the decrease in liquid surface tension. The increase in solid percentage resulted in an increase in d32 perhaps due to the increase in the pulp viscosity at high solid percentage. The lower the d32, the lower the flotation recovery. The results show that d32 and the model parameters represent the true BSD-s. However, a thorough understanding of bubble size distributions is needed to better understand flotation performances.

Influence of Meteorological Factors on the COVID-19 Transmission with Season and Geographic Location.

The purpose of this study is to investigate whether the relationship between meteorological factors (i.e., daily maximum temperature, minimum temperature, average temperature, temperature range, relative humidity, average wind speed and total precipitation) and COVID-19 transmission is affected by season and geographical location during the period of community-based pandemic prevention and control. COVID-19 infected case records and meteorological data in four cities (Wuhan, Beijing, Urumqi and Dalian) in China were collected. Then, the best-fitting model of COVID-19 infected cases was selected from four statistic models (Gaussian, logistic, lognormal distribution and allometric models), and the relationship between meteorological factors and COVID-19 infected cases was analyzed using multiple stepwise regression and Pearson correlation. The results showed that the lognormal distribution model was well adapted to describing the change of COVID-19 infected cases compared with other models (R2 > 0.78; p-values < 0.001). Under the condition of implementing community-based pandemic prevention and control, relationship between COVID-19 infected cases and meteorological factors differed among the four cities. Temperature and relative humidity were mainly the driving factors on COVID-19 transmission, but their relations obviously varied with season and geographical location. In summer, the increase in relative humidity and the decrease in maximum temperature facilitate COVID-19 transmission in arid inland cities, while at this point the decrease in relative humidity is good for the spread of COVID-19 in coastal cities. For the humid cities, the reduction of relative humidity and the lowest temperature in the winter promote COVID-19 transmission.