Log-normal Distribution Function Research Articles

Distributions of Particle Sizes in Black Soil and Their Environmental Significance in Northeast China

In recent years, black soil has decreased and degenerated heavily due to complicated functions of natural and artificial factors. Hence, characterizing distributions of particle sizes in black soil and their environmental influencing factors is important for understanding black soil degradation. A total of 116 surface soil samples in the top 20 cm from a typical black soil region in northeastern China were collected, and the spatial distribution of particle size parameters were characterized. Particle size-sensitive components were extracted quantitatively using the log-normal distribution function, and their environmental implications were investigated. The contents of black soil mechanical composition ranged from 7.8% to 79.3% for clay, 17.7% to 80.3% for silt, and 0% to 73.7% for sand, respectively. Median particle size ranged from 1.71 to 142.67 μm, with a coefficient of variation of 60%, indicating silt accounted for the majority of the composition. Four environmentally sensitive components were identified, including long-distance transported airborne deposits of clay dust (C1), successions from local parent materials (C2), short-distance deposits of silt particles (C3), and a component strongly disturbed by human activities (C4). C1 and C2 had relatively low variations, with C1 exhibiting the smallest variation, and C2 contributing highest proportion, showing no significant differences across all samples. C3 widely existed across samples, suggesting common wind erosion within the black soil region. C3 and C4 varied spatially, which was caused by the low vegetation coverage and high human disturbance of agricultural topsoil. The results suggest that windbreaks should be encouraged to reduce wind erosion in the black soil regions.

Dynamic optimal power flow with cross entropy covariance matrix adaption evolutionary strategy for systems with electric vehicles and renewable generators

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

Performance evaluation and coefficients of reliability for waste stabilization ponds in northeast Brazil

This paper assesses the reliability of Waste Stabilization Ponds (WSP) and proposes an alternative approach to WSP design based on the calculation of coefficient of reliability (COR) from an acceptable measure of violation of discharge standards. For that, data were collected from 10 full-scale systems operating in Northeast Brazil. All systems receive predominantly domestic effluent and are composed of one facultative pond and two serial maturation ponds. Different levels of restriction for effluent discharge were considered regarding the parameters: BOD, COD, total suspended solids, ammonia and thermotolerant coliforms. The Log-normal Probability Distribution Function (PDF) was able to represent the behavior of the concentration data in the effluent and, therefore, allowed the COR calculation. The COR was obtained from the coefficient of variation (CV) of the concentrations and the standardized normal variable associated with a 95% probability of non-exceedance. The observed dispersion of the results proved to be detrimental to the adoption of a single COR value for the evaluated parameters. In addition, the comparison between observed and design/operational concentration for optimal performance showed that the 95% reliability scenario represents a less achievable target for WSP systems.

Multi-level micromechanical analysis of elastic properties of ultra-high performance concrete at high temperatures: Effects of imperfect interface and inclusion size

Ultra-high performance concrete (UHPC), as a typical multi-phase composite material, is vulnerable to mechanical degradation and explosive spalling at high temperatures. In this work, the temperature-dependent elastic modulus of UHPC is estimated through the step-by-step homogenization from gel matrix level to ultra-high performance fiber-reinforced concrete level. Totally three forms of C-S-H gels are considered to determine the elastic properties of the initial matrix, and the phase transformation and volume fractions of individual phases at high temperatures are calculated based on the hydration and dehydration kinetics models. Moreover, the effects of imperfect interface and inclusion size are taken into account by introducing the spring-layer interface model and log-normal size distribution function to the homogenization scheme. The predicted elastic moduli are validated by analytical and experimental results, showing that accurate predictions can be obtained at up to 800°C. Interestingly, the imperfect interface matters when high-modulus inclusions are embedded in the low-modulus matrix, and the effect of imperfect interface on effective elastic modulus varies a lot at different microscopic levels. The findings highlight the synergistic effects of imperfect interface and inclusion size on the elastic properties, which is helpful to the mechanical design of UHPC at high temperatures.

Developing seismic fragility curves for existing reinforced concrete structures in Algeria

This paper presents a method for developing fragility curves for assessing the seismic performance of existing reinforced concrete structures in Algeria. A two-storey 1980s reinforced concrete building in the northern city of Constantine was studied using the proposed method as part of a vulnerability assessment and strengthening proposal. Fragility curves for the existing and strengthened structure were derived and log-normal cumulative distribution function parameters were obtained for the four defined damage states by considering maximum inter-storey drift ratio. Incremental dynamic analysis was then used to assess spectral acceleration by conducting 300 non-linear time-history analyses based on 15 ground motions. The records were then selected and scaled to fit with Algerian design response spectra, and fragility curves were subsequently developed. The method can be used for any type of reinforced concrete structure in Algeria, including bridges.

Evaluation of brain injury criteria based on reliability analysis

Among the proposed brain injury metrics, Brain Injury Criteria (BrIC) is a promising tool for performing safety assessment of vehicles in the future. In this paper, the available risk curves of BrIC were re-evaluated with the use of reliability analysis and new risk curves were constructed for different injury types based on literature data of tissue-level tolerances. Moreover, the comparison of different injury metrics and their corresponding risk curves were performed. Tissue-level uncertainties of the effect and resistance were considered by random variables. The variability of the tissue-level predictors was quantified by the finite element reconstruction of 100 frontal crash tests which were performed in Simulated Injury Monitor environment. The applied tests were scaled to given BrIC magnitudes and the injury probabilities were calculated by Monte Carlo simulations. New risk curves were fitted to the observed results using Weibull and Lognormal distribution functions. The available risk curves of diffuse axonal injury (DAI) could be slightly improved, and combined AIS 4+ risk curves were obtained by considering subdural hematoma and contusion as well. The performance of several injury metrics and their risk curves were evaluated based on the observed correlations with the tissue-level predictors. The cumulative strain damage measure and the BrIC provide the highest correlation (R² = 0.61) and the most reliable risk curve for the evaluation of DAI. Although the observed correlation is smaller for other injury types, the BrIC and the associated reliability analysis-based risk curves seem to provide the best available method for estimating the brain injury risk for frontal crash tests.

Optimal Power Flow Solution Based on Jellyfish Search Optimization Considering Uncertainty of Renewable Energy Sources

Today’s electrical power system became more complex interconnected network that is expanding every day. The transmission lines of the power system are more severely loaded than ever before. Hence, the power system is facing many problems such as power losses increasing, voltage instability, line overloads, etc. The optimization of real and reactive powers due to the installation of energy resources at appropriate buses can minimize the losses and improve the voltage profile especially, for congested networks. As a result, the optimal power flow problem (OPF) is considered more important tool for the processes of planning and operation of power systems. OPF is a very significant tool for power system operators to meet the electricity demand of the consumers efficiently, and for the reliable operation of the power system. However, the incorporation of renewable energy sources (RESs) into the electrical grid is a very challenging problem due to their intermittent nature. In this paper, the proposed power flow model contains three different types of energy sources: thermal power generators representing the conventional energy sources, wind power generators (WPGs), and solar photovoltaic generators (SPGs) representing RESs. Uncertain output powers from WPGs and SPGs are forecasted with the aid of Weibull and lognormal probability distribution functions (PDF), respectively. The under and overestimation output powers of RESs are taken into consideration while formulating the objective function through adding a penalty and reserve cost, respectively. Moreover, carbon tax is imposed to the main objective function to help in reducing carbon emissions. A jellyfish search optimizer (JS) is employed to reach optimization in the modified IEEE 30-bus test system to validate its feasibility. To examine the effectiveness of the proposed JS algorithm, its simulation results are compared with the results of four other nature-inspired global optimization algorithms. The developed OPF algorithm considers several practical cases such as generation uncertainty of renewable energy sources, time-varying load and the ramp rate limits of thermal generators. The simulation results show the effectiveness of the JS algorithm in solving the OPF problem in terms of minimization of total generation cost and solution convergence.

Introduction of a Mixed Lognormal Probability Distribution Function and a New Displacement Correction Method for Precipitation to the Ensemble-Based Variational Assimilation of the All-Sky Microwave Imager Brightness Temperatures

Introduction of a Mixed Lognormal Probability Distribution Function and a New Displacement Correction Method for Precipitation to the Ensemble-Based Variational Assimilation of the All-Sky Microwave Imager Brightness Temperatures

The choice of droplet size probability distribution function for oil spill modeling is not trivial

The droplet size distribution (DSD) formed by gas-saturated oil jets is one of the most important characteristics of the flow to understand and model the fate of uncontrolled deep-sea oil spills. The shape of the DSD, generally modeled as a theoretical lognormal, Rosin-Rammler or non-fundamental distribution function, defines the size and the mass volume range of the droplets. Yet, the fundamental DSD shape has received much less attention than the volume median size (d50) and range of the DSD during ten years of research following the Deepwater Horizon (DWH) blowout. To better understand the importance of the distribution function of the droplet size we compare the oil rising time, surface oil mass, and sedimented and beached masses for different DSDs derived from the DWH literature in idealized and applied conditions, while keeping d50 constant. We highlight substantial differences, showing that the probability distribution function of the DSD for far-field modeling is, regardless of the d50, consequential for oil spill response.

The inconsistency of h-index: A mathematical analysis

Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function, the equation that defines the h index can be formulated; this equation shows that h has a complex dependence on the number of papers (N). We also investigate the correlation between h and the number of papers exceeding various citation thresholds, from 5 to 500 citations. The best correlation is for the 100 threshold but numerous data points deviate from the general trend. The size-independent indicator h/N shows no correlation with the probability of publishing a paper exceeding any of the citation thresholds. In contrast with the h index, the total number of citations shows a high correlation with the number of papers exceeding the thresholds of 10 and 50 citations; the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations. Thus, in synthetic series, the number of citations and the mean number of citations are much better indicators of research performance than h and h/N. We discuss that in real citation distributions there are other difficulties.

Dynamic Signatures of Lipid Droplets as New Markers to Quantify Cellular Metabolic Changes.

The metabolic properties of live cells are very susceptible to intra- or extracellular perturbations, making their measurements challenging tasks. We show that the dynamics of lipid droplets (LDs) carry information to measure the lipid metabolism of live cells. Coherent anti-Stokes Raman scattering microscopy was used to statistically quantify LD dynamics in living cells in a label-free manner. We introduce dynamic signatures of cells derived from the LD displacement, speed, travel length, and directionality, which allows for the detection of cellular changes induced by stimuli such as fluorescent labeling, temperature change, starvation, and chemical treatment. Histogram fittings of the dynamic signatures using log-normal distribution functions provide quantification of changes in cellular metabolic states. The LD dynamics also enable separation of subpopulations of LDs correlated with different functions. We demonstrate that LD dynamics measured by chemical imaging are new markers to quantify the metabolic changes in live cells.

Io's SO2 atmosphere from HST Lyman-α images: 1997 to 2018

The atmosphere of Jupiter's volcanic moon Io consists of mainly sulfur dioxide (SO2), and this main constituent has been studied with a variety of observing techniques across many wavelengths over the years. Here we study absorption by SO2 at the hydrogen Ly-α line (1216 Å) in a large set of images taken by the Space Telescope Imaging Spectrograph (STIS) onboard the Hubble Space Telescope (HST) between 1997 and 2018. An advanced statistical analysis using a Monte-Carlo trial method is applied to derive the SO2 column density from the Ly-α intensity, which includes the uncertainties of the used variables such as solar and background flux. Our analysis produces a probability distribution function of the SO2 column density and highlights some short-comings of the observing technique. Most importantly, the HST/STIS images of the surface-reflected Ly-α flux are only sensitive to SO2 column densities between ~1015 cm−2 and ~5×1016 cm−2. Due to strong non-linearity in the relationship between the SO2 abundance and the Ly-α flux at the low and high values of detected flux, SO2 abundance directly retrieved from the STIS images will generally fall within these boundaries. This explains the relatively low equatorial column density of about 1016 cm−2 reported by previous studies using the Ly-α images (e.g., Feldman et al., 2000; Feaga et al., 2009) compared to other studies (e.g., Spencer et al., 2005; Tsang et al., 2013; Jessup and Spencer, 2015; Lellouch et al., 2015), where the obtained column density is often 1017 cm−2. By assuming a log-normal probability distribution function for the column density, a new estimate of the SO2 column density is then fitted, indirectly accounting for abundances beyond the detectability limits. This method suggests slightly higher equatorial SO2 abundances and much larger upper-limits, revealing that the Ly-α observations are in fact consistent with the higher abundances found in other studies. We then investigate the SO2 abundances at three volcanic sites (Loki, Marduk, Thor), where plumes were observed before and where the sensitivity in our images is comparably high. The observations did not reveal transient changes due to local outgassing at any of the three sites. Finally, the heliocentric distance of Io changed from 4.95 AU to 5.45 AU between the observation dates, potentially allowing us to investigate the influence of solar intensity changes on the SO2 column density via surface frost sublimation. However, the derived error bars are significantly larger than the derived variability, preventing any firm conclusion on seasonal changes and local volcanic outgassing.

Assessment of Building Vulnerability Curve Subjected to Debris-Flow

In this study, the vulnerability curves for masonry and concrete frame buildings are assessed based on building fragility curves for the debris-flow caused by landslides on mountain slopes. The First-Order Second-Moment (FOSM) method is used to estimate the building fragility curve (expressed as probability of damage exceedance) subjected to debris-flow. In this method, the horizontal displacement of a building impacted by debris-flow and the statistics of resistance (i.e., building displacement) following four different damage states (i.e., slight, moderate, extensive, and complete) are utilized to estimate the building fragility curve. The building vulnerability curves (expressed as mean probability of damage) were evaluated based on the estimated building fragility curve and corresponding mean damage ratio for each damage state and were verified by calculating the root mean square error with datasets obtained from post-disaster damage assessment. In this study, the effects of structural material, type, and height on the building vulnerability curves were also studied. All vulnerability curves of buildings estimated in this study were fitted and databased using parameters of the log-normal cumulative distribution function and can be used to measure the performance of buildings in debris-flow prone areas as well as to provide information for risk and loss assessment.

Dynamic Modeling of a Ball-Screw Drive and Identification of Its Installation Parameters

Abstract Parametric expressions of equivalent stiffnesses of a ball-screw shaft are obtained by derivation of its geometric parameters, the finite element method (FEM), and data fitting based on a modified probability density function of log-normal distribution. A dynamic model of a ball-screw drive that considers effects of bearing stiffnesses, the mass of the nut, and the axial pretension is established based on equivalent stiffnesses of its shaft. With the dynamic model and modal experimental results obtained by Bayesian operational modal analysis (BOMA), installation parameters of the ball-screw drive are identified by a genetic algorithm (GA) with a new comprehensive objective function that considers natural frequencies, mode shapes, and flexibility of the ball-screw drive. The effectiveness of the methodology is experimentally validated.

Pre-weakening behavior of magnetite quartzite based on high-voltage pulse discharge

To ascertain the mechanism that the ore grinding characteristics were improved by high-voltage pulse discharge (HVPD) pre-treatment, an innovative experiment system was performed on magnetite quartzite. The HVPD pre-treatment improved the −0.074 mm mass fraction in ground products, and the increase in pulse number effectively enhanced the mass fraction. The values of relative grindability (K1 and K2) increased with the pulse number significantly, whereas their value reduced as the grinding fineness and grinding time extended. A laser particle size analysis showed that the distribution of HVPD pre-treatment products was uniform. The particle size distribution and cumulative distribution curves satisfied the lognormal distribution function and power function, respectively. The Brunauer–Emmett–Teller (BET) analysis indicated that the specific surface area, total pore volume, and the porosity of crushed products were improved effectively by the HVPD pre-treatment. The internal ore structure became loosened, resulting in the decline in the mechanical properties of the ore; this is conducive to improve the grinding efficiency. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) analyses indicated that the grain-boundary breakage was obtained via the HVPD pre-treatment selectivity.

Framework for calculating seismic fragility function of urban road networks: A case study on Tangshan City, China

The aim of this work is to present a method for calculating seismic fragility function of urban road network. In this paper, urban road system is simplified to a planar network. The spatial correlation of seismic ground motions is considered. The damage probability of network edge is determined by the fragility function of single road section. By repeating simulation, a large number of samples of post-earthquake road network are obtained. Their damage states are classified as minor, moderate, extensive and complete by piece number and diameter of the maximal piece. The seismic fragility function of road network is assumed in the form of lognormal cumulative distribution function and its parameters are identified by fitting the fragility function to the exceeding probability of the damage states. To demonstrate the practicality of the proposed method, an application to the urban road network of Tangshan City is performed. The case study indicates that the rare earthquake may cause the disconnection and fragmentation of the road network with high probability. The proposed framework is a valuable contribution to the seismic performance evaluation of urban road system and provides engineers and practitioners with a tool to design road network in high seismic hazard zone.

Statistical model for filamentary structures of molecular clouds

We propose a new statistical model that can reproduce the hierarchical nature of the ubiquitous filamentary structures of molecular clouds. This model is based on the multiplicative random cascade, which is designed to replicate the multifractal nature of intermittency in developed turbulence. We present a modified version of the multiplicative process where the spatial fluctuations as a function of scales are produced with the wavelet transforms of a fractional Brownian motion realisation. This simple approach produces naturally a log-normal distribution function and hierarchical coherent structures. Despite the highly contrasted aspect of these coherent structures against a smoother background, their Fourier power spectrum can be fitted by a single power law. As reported in previous works using the multiscale non-Gaussian segmentation (MnGSeg) technique, it is proven that the fit of a single power law reflects the inability of the Fourier power spectrum to detect the progressive non-Gaussian contributions that are at the origin of these structures across the inertial range of the power spectrum. The mutifractal nature of these coherent structures is discussed, and an extension of the MnGSeg technique is proposed to calculate the multifractal spectrum that is associated with them. Using directional wavelets, we show that filamentary structures can easily be produced without changing the general shape of the power spectrum. The cumulative effect of random multiplicative sequences succeeds in producing the general aspect of filamentary structures similar to those associated with star-forming regions. The filamentary structures are formed through the product of a large number of random-phase linear waves at different spatial wavelengths. Dynamically, this effect might be associated with the collection of compressive processes that occur in the interstellar medium.

Spectral induced polarization study on enzyme induced carbonate precipitations: influences of size and content on stiffness of a fine sand

Heterogeneity in either chemically or microbiologically induced carbonate-based ground improvement methods is a major obstacle in engineering application. Spectral induced polarization (SIP), an innovative and nondestructive method, which has demonstrated promise in monitoring microbial activity, was used in this study to monitor enzyme induced carbonate precipitation (EICP). The complex conductivities, together with the shear wave velocities (Vs), of an EICP modified sand were monitored using a self-developed spectral induced polarization–bender element column. The mean precipitate size was calculated by relaxation time (τ) and the Schwarz equation. The precipitate contents were calculated by cumulative gamma distribution function on the global polarization magnitude (mn) with R2 = 0.989. The stiffness of the enhanced geomaterial, in terms of Vs, correlates to mn with a cumulative lognormal distribution function with R2 = 0.967. Contact cementation was postulated as the dominant association pattern. The possible mechanism for this may be the formation of eddies and the nucleation of CaCO3 crystals during precipitation. The results suggest that SIP can be used as an effective nondestructive monitoring tool to assess the stiffness of geomaterials.

PARAMETERIZATION OF MAGNETIC NANOPARTICLES MATHEMATICAL MODEL USING EVOLUTIONARY ALGORITHMS

In this paper, the evolutionary algorithms approach is applied to the parameterization of a mathematical model describing the Mössbauer spectra of nanogranular (or nanoparticle) magnetic systems. These systems exhibit physical properties very different from bulk specimens being of great interest for material science and its use as biosensors, magneto sensors, data storage, and magnetic fluids. The purpose of this work is to compare the performance between the Differential Evolution and the Evolutionary Strategies algorithms to optimize the model parameters which best fit the experimental Mössbauer spectra of nanoscale magnetic particles. Spectra of two samples (??iron foil and NiFe2O4 nanoparticles) were recorded, at room temperature, by a conventional Mössbauer spectrometer using a scintillation detector in transmission geometry with a 57Co/Rh source. Fits to Mössbauer spectra were done using spin hamiltonians to describe both the electronic and nuclear interactions; a model of superparamagnetic relaxation of two levels (spin ½) and stochastic theory; a lognormal particle size distribution function as well as a dependency of the magnetic transition temperature and the anisotropy constant on particle diameter. The evolutionary algorithms have been implemented using Python programming language. For comparison, the two algorithms obey the termination criterion of 6,000 evaluations of the objective function. The results presented show the efficiency of these algorithms in the optimization of the parameters and on the fits of the spectra.

ON SPIN HAMILTONIAN FITS TO MÖSSBAUER SPECTRA OF NiFe2O4 NANOPARTICLES SYNTHESIZED BY CO-PRECIPITATION

Nanocrystalline NiFe2O4 particles prepared by chemical co-precipitation method were studied using magnetic measurements, 57Fe Mössbauer spectroscopy, X-ray diffraction, and transmission electron microscopy. Fits to Mössbauer spectra, in the range of 4.2 K – 300 K, were done using spin hamiltonians to describe both the electronic and nuclear interactions, a model of superparamagnetic relaxation of two levels (spin ½) and stochastic theory, a log-normal particle size distribution function as well as a dependency of the magnetic transition temperature and the anisotropy constant on particle diameter. We have used evolutionary strategies to fit the more complex Mössbauer spectra line shapes. The nanoparticles have an average size of 7 nm and exhibit superparamagnetism at room temperature. The saturation magnetization (Ms) at 4.2 K was determined from M vs. 1/H plots by extrapolating the value of magnetizations to infinite fields, to 24.21 emu/g and coercivity to 3.15 kOe. A magnetic anisotropy energy constant (K) 1.9´105 J/m3, at 4.2 K, were calculated from magnetization measurements. The synthesis, characterization, and functionalization of magnetic nanoparticles is a highly active area of current research located at the interface between materials science, biotechnology, and medicine. Superparamagnetic iron oxides nanoparticles have unique physical properties and have emerged as a new class of diagnostic probes for multimodal tracking and as contrast agents for magnetic resonance imaging (MRI).