Probability Distribution Analysis Research Articles

Limited Preservation of Strike‐Slip Surface Displacement in the Geomorphic Record

AbstractOffset geomorphic markers are commonly used to interpret slip history of strike‐slip faults and have played an important role in forming earthquake recurrence models. These data sets are typically analyzed using cumulative probability methods to interpret average amounts of slip in past earthquakes. However, interpretation of the geomorphic record to infer surface slip history is complicated by slip variability, measurement uncertainty, and modification of offset features in the landscape. To investigate how well geomorphic data record surface slip, we use offset measurements from recent strike‐slip surface ruptures (n = 39), faults with geomorphic evidence of multiple strike‐slip earthquakes (n = 29), and synthetic slip distributions with added noise (n10,000) to examine the constraints of the geomorphic record and the underlying assumptions of the cumulative offset probability distribution analysis method. We find that the geomorphic record is unlikely to resolve more than two paleo‐slip distributions, except in specific cases with low slip variability, high slip‐per‐event, and semiarid climate. In cases where site‐specific conditions allow for interpretation of more than two earthquakes, lateral extrapolation along a fault is not straightforward because on‐fault displacement and distributed deformation may be spatially variable in each earthquake. We also find that average slip in modern earthquakes is adequately recovered by probability methods, but the reported prevalence of strike‐slip faults with characteristic slip history is not supported by geomorphic data. We also propose updated methods to interpret slip history and construct uncertainty bounds for paleo‐slip distributions.

Preprocessing and postprocessing analysis for hot-mix asphalt dynamic modulus experimental data

Dynamic modulus (|E*|) measurements of hot-mix asphalt (HMA) mixtures are critical for understanding material behavior but present significant challenges due to the complex testing procedures and precision required. While substantial efforts have focused on developing predictive models for |E*|, the critical role of experimental data preprocessing has been largely overlooked in the existing literature. This study addresses this gap by proposing a novel, comprehensive framework for both preprocessing and post-processing of dynamic modulus data. Leveraging the well-established ASU |E*| database and the NCHRP 1–40D Witczak prediction model as benchmarks, we introduce advanced empirical techniques, including probability distribution analysis, scatter and box plots, correlation coefficients, and mutual information metrics, to refine data quality and enhance the interpretability of predictive models. Our approach reveals new insights into the interaction of various input factors and |E*| values, leading to improved model robustness and reliability. The post-processing techniques further substantiate the predictive power of the Witczak model, yielding significant enhancements in accuracy and reliability. This research pioneers a standardized data preparation methodology that sets a new precedent in asphalt material engineering, offering a robust foundation for future |E*| modeling and analysis.

Gas hydrate inhibition by urea and its blends with vinyl lactam polymer: Paving the way to green hybrid inhibitors

Urea is an environmentally benign substance considered a promising gas hydrate inhibitor in flow assurance. Nevertheless, its effect on gas hydrate formation kinetics remains poorly understood. This study investigates the impact of urea and hybrid urea/polymer KHI samples on the nucleation and growth kinetics of sII natural gas hydrates. Hydrate formation was observed at a lower onset temperature with increasing urea and polymer concentration. The nucleation of sII hydrate in aqueous urea solutions occurred at a higher subcooling (7.50 ± 0.58 K at 30 mass%) than in pure water (5.17 ± 0.69 K). These findings indicate that urea acts as a nucleation inhibitor of sII hydrates, although its capacity is not as potent as that of polymer KHI.The analysis of the hydrate nucleation probability distributions revealed that the sII hydrate nucleation rate exhibited a significant decline, approximately one order of magnitude, at subcooling of 5.3–6 K for 20 mass% urea compared to water. A similar behavior was noticed in an aqueous solution of polymer KHI. Urea has succeeded in providing a total benefit of up to 10 K in hydrate onset temperature due to a shift in the hydrate stability zone and nucleation retardation.Consequently, urea is a green dual-acting anti-hydrate chemical that inhibits the formation of sII hydrates by thermodynamic and kinetic mechanisms. Besides, adding 10 mass% urea increases the cloud point temperature of vinyl lactam polymer Luvicap 55W by 14 K. Urea is an additive that considerably augments the stability of the polymer in aqueous solutions at elevated temperatures. These findings make urea an effective and environmentally friendly top-up inhibitor that significantly enhances the anti-hydrate properties of polymer KHI.

Understanding the Size‐Dependent Photostability and Photoluminescence Intermittency of Blue‐Emitting Core/Graded Alloy/Shell “giant”‐Quantum Dots

AbstractRecently, giant quantum dots (g‐QDs) with a core/interface graded alloy shell/shell structure have shown promise in reducing photoluminescence (PL) intermittency and improving photostability. However, this approach has been mainly demonstrated with red and green emitting g‐QDs but the blue‐emitting graded alloy QDs has remained less explored. To tackle this challenge, a composition gradient method is employed to create three blue‐emitting CdZnS/CdxZn1–xS/ZnS core/interface graded alloy shell/shell (C/A/S) quantum dots (QDs) with different diameters. The sample with the largest diameter (gQD‐3) exhibits superior optical characteristics, with a photoluminescence quantum yield (PLQY) of approximately 62% and around 80% ON/radiative events at the single‐particle level. Conversely, the smallest diameter (gQD‐1) sample shows lower PLQY and only 30% radiative events with longer OFF/nonradiative events. Probability distribution analysis of PL trajectories, fitted with a truncated power law, reveals a significantly higher carrier de‐trapping rate in gQD‐3 compared to gQD‐1, attributed to its proximity to band edge trap states. Additionally, the largest diameter sample retains remarkable optical performance during 48 h of continuous UV irradiation in colloidal suspension and single‐particle levels. These findings show optimized core/shell structures, gradual alloy interfaces, and outer shell coatings can stabilize blue‐emitting quantum dots, advancing next‐gen optoelectronics.

Statistical Analysis of Characteristic Parameters and Probability Distribution of Near-Fault Velocity Pulses—A Case Study on the 1999 Mw 7.6 Chi-Chi Earthquake

Abstract The 1999 Mw 7.6 Chi-Chi earthquake in the Taiwan region generated valuable ground motions, providing an opportunity for studying the characteristic parameters and distribution of near-fault velocity pulses. Using the finite-difference method, we built a source model, simulated the 1999 Mw 7.6 Chi-Chi earthquake ground motions, and obtained synthetic velocity waveforms consistent with the observed waveforms. On this basis, we analyzed the distribution of velocity pulses in the near-fault region and compared it with the pulse probability distribution (PPD) curve of the near-fault velocity pulse. We found that the complex rupture process of the Mw 7.6 Chi-Chi earthquake resulted in velocity pulses still being recorded in Miaoli and Xinzhu. In addition, we analyzed the relationship between pulse period, pulse peak, and fault distance. The pulse peak indicates a clear attenuation trend with increasing fault distance (Rrup) and no statistical relationship between the pulse period and Rrup. More velocity pulses in normal-fault components reveal the reverse fault of the Chi-Chi earthquake. Finally, structures with natural periods within the 1–7 s are more susceptible to resonance from near-fault velocity pulses, and it is necessary to take appropriate seismic measures. This study lays the foundation for a deeper understanding of the ground motion and pulse characteristics caused by earthquakes and contributes to sustained efforts in seismic hazard assessment.

Probability Distribution Analysis of Annual Maximum Precipitation in the Niger Delta: A Critical Step towards Effective Flood Risk Management

Aims: The study aimed to analyze historical maximum precipitation data from seven cities in the Niger Delta to assess vulnerability to extreme rainfall events, identify optimal probability distribution models for future predictions, and provide insights for flood risk management strategies. Study Design: This is a retrospective analytical study based on historical precipitation data. Place and Duration of Study: The study was conducted across seven major cities in the Niger Delta region of Nigeria, utilizing data collected over several decades. Methodology: Historical maximum precipitation data were statistically analyzed to determine the best-fit probability distribution models. The Kolmogorov-Smirnov (KS) test and Mean Squared Prediction Error (MSPE) were used to validate the suitability of distributions, including Log-Normal, Normal, Log-Pearson III, and Generalized Extreme Value (GEV) for each city. Return periods of 10, 25, 50, and 100 years were calculated to predict future precipitation trends and assess flood risks. Results: Significant variations in annual maximum precipitation were observed across the cities, with Calabar recording the highest peak at 4062.7mm. The Log-Normal distribution was the best fit for Akure and Calabar, while the Normal distribution best described rainfall in Benin City. Log-Pearson III was optimal for Owerri, Umuahia, and Uyo, and GEV best fitted Port Harcourt’s data. High P-values (>0.87) indicated good model fits across the cities. Return period analysis suggested greater risks of extreme precipitation events in coastal cities like Calabar and Port Harcourt. Conclusion: The study underscores the importance of tailored, city-specific flood management strategies in the Niger Delta to mitigate the impact of extreme rainfall events, particularly in the face of climate change.

Theoretical insights into size and dielectric confinement: Unraveling real and imaginary parts of the effective complex dielectric function in spherical multilayered quantum dots with oxide interfaces

A quantitative numerical exploration is conducted to scrutinize the combined effects of size and dielectric confinement consequences on the electronic and optical characteristics of spherical multilayered quantum dot CdSe/ZnS/CdSe/ZnS (SMLQD) and its inverted configuration ZnS/CdSe/ZnS/CdSe (ISMLQD) buried into two oxides: HfO2 and SiO2. By employing the effective mass approximation (EMA) and the density matrix approach (DMA), the derived quantized electron energy states and their associated wave functions were obtained by solving the Schrödinger equation in a spherical coordinates. The dipole transition element, both real and imaginary parts of the effective complex dielectric function (ECDF) as well as its linear, nonlinear and total counterparts are brought out for various values of inner core radii, number density of QDs and incident photon intensity. In addition, a specific analysis of electron probability distributions is provided to gain a clearer understanding of the underlying physical factors. Our findings point to a notable influence of these mentionned factors on the computed coefficients. The study unveils that the dielectric mismatch occurring at the system/oxide interfaces plays a crucial role in modifying the electronic structure and a substantial impact on both linear and third-order nonlinear components is witnessed.

Verification Test and Research on Fitting Curve of Shear and Tensile Synthesis Method

Based on the recommended curve of concrete compressive strength tested by shear and tensile composite method, this paper combined with concrete specimens of different strength grades, ages and batches produced by several test verification units, adopted the in vitro shear and tensile test method introduced by the regulations, and used basically the same test equipment to collect the single shear and tensile strength and the compressive strength of cube specimens under the same conditions. Each batch was divided into 15 or 30 specimens. Through the collected test data, the conversion strength of the single shear, pull-out and shear tensile composite methods were calculated respectively. The relative error of a single specimen was calculated based on the average strength of each batch of concrete. The error distribution types and errors of each company were systematically studied, and finally the relative error data of each company were summarized, and the probability distribution parameters of the error of the Shear and tensile synthesis method were understood through probability distribution analysis, and the relationship between the error of the shear and tensile synthesis method, the single shear method and the pull method, and the influence degree on the conversion strength of the shear and tensile synthesis method were shown by using three-dimensional coordinates. Using the test data of "shear and tensile synthesis method", "single shear method" and "pull-out method", the scatter plot is drawn, and the error size is compared to explore the direction of further improving the detection accuracy of "shear and tensile synthesis method".

Analysis of Probability Distributions for Modelling Extreme Rainfall Events and Detecting Climate Change: Insights from Mathematical and Statistical Methods

Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions—to assess annual maximum 24 h rainfall series obtained over a long period (1972–2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov–Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience.

A GPU-accelerated computational fluid dynamics solver for assessing shear-driven indoor airflow and virus transmission by scale-resolved simulations

We explore the applicability of MATLAB for 3D computational fluid dynamics (CFD) of shear-driven indoor airflows. A new scale-resolving, large-eddy simulation (LES) solver titled DNSLABIB is proposed for MATLAB utilizing graphics processing units (GPUs). In DNSLABIB, the finite difference method is applied for the convection and diffusion terms while a Poisson equation solver based on the fast Fourier transform (FFT) is employed for the pressure. The immersed boundary method (IBM) for Cartesian grids is proposed to model solid walls and objects, doorways, and air ducts by binary masking of the solid/fluid domains. The solver is validated in two canonical reference cases and against experimental data. Then, we demonstrate the validity of DNSLABIB in a room geometry by comparing the results against another CFD software (OpenFOAM). Next, we demonstrate the solver performance in several isothermal indoor ventilation configurations and the implications of the results are discussed in the context of airborne transmission of COVID-19. The novel numerical findings using the new CFD solver are as follows. First, a linear scaling of DNSLABIB is demonstrated and a speed-up by a factor of 3-4 is also noted in comparison to similar OpenFOAM simulations. Second, ventilation in three different indoor geometries are studied at both low (0.1 m/s) and high (1 m/s) airflow rates corresponding to Re=5000 and Re=50000. An analysis of the indoor CO2 concentration is carried out as the room is emptied from stale, high CO2 content air. We estimate the air changes per hour (ACH) values for three different room geometries and show that the numerical estimates from 3D CFD simulations differ by 80%–150% (Re=50000) and 75%–140% (Re=5000) from the theoretical ACH value based on the perfect mixing assumption. Third, the analysis of the CO2 probability distributions (PDFs) indicates a relatively non-uniform distribution of fresh air indoors. Fourth, utilizing a time-dependent Wells-Riley analysis, an example is provided on the growth of the cumulative infection risk which is shown to reduce rapidly after the ventilation is started. The average infection risk is shown to reduce by a factor of 2 for lower ventilation rates (ACH=3.4-6.3) and 10 for the higher ventilation rates (ACH=37-64). Finally, we utilize the new solver to comment on respiratory particle transport indoors. A key contribution of the paper is to provide an efficient, GPU compatible CFD solver environment enabling scale-resolved simulations (LES/DNS) of airflow in large indoor geometries on a single GPU designed for high-performance computing. The demonstrated efficacy of MATLAB for GPU computing indicates a high potential of DNSLABIB for various future developments on airflow prediction.

Fault Diagnostics Based on the Analysis of Probability Distributions Estimated Using a Particle Filter

This paper proposes a monitoring procedure based on characterizing state probability distributions estimated using particle filters. The work highlights what types of information can be obtained during state estimation and how the revealed information helps to solve fault diagnosis tasks. If a failure is present in the system, the output predicted by the model is inconsistent with the actual output, which affects the operation of the estimator. The heterogeneity of the probability distribution of states increases, and a large proportion of the particles lose their information content. The correlation structure of the posterior probability density can also be altered by failures. The proposed method uses various indicators that characterize the heterogeneity and correlation structure of the state distribution, as well as the consistency between model predictions and observed behavior, to identify the effects of failures.The applicability of the utilized measures is demonstrated through a dynamic vehicle model, where actuator and sensor failure scenarios are investigated.

Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatiotemporal Forecasting.

Graph neural networks (GNNs), especially dynamic GNNs, have become a research hotspot in spatiotemporal forecasting problems. While many dynamic graph construction methods have been developed, relatively few of them explore the causal relationship between neighbor nodes. Thus, the resulting models lack strong explainability for the causal relationship between the neighbor nodes of the dynamically generated graphs, which can easily lead to a risk in subsequent decisions. Moreover, few of them consider the uncertainty and noise of dynamic graphs based on the time series datasets, which are ubiquitous in real-world graph structure networks. In this article, we propose a novel dynamic diffusion-variational GNN (DVGNN) for spatiotemporal forecasting. For dynamic graph construction, an unsupervised generative model is devised. Two layers of graph convolutional network (GCN) are applied to calculate the posterior distribution of the latent node embeddings in the encoder stage. Then, a diffusion model is used to infer the dynamic link probability and reconstruct causal graphs (CGs) in the decoder stage adaptively. The new loss function is derived theoretically, and the reparameterization trick is adopted in estimating the probability distribution of the dynamic graphs by evidence lower bound (ELBO) during the backpropagation period. After obtaining the generated graphs, dynamic GCN and temporal attention are applied to predict future states. Experiments are conducted on four real-world datasets of different graph structures in different domains. The results demonstrate that the proposed DVGNN model outperforms state-of-the-art approaches and achieves outstanding root mean square error (RMSE) results while exhibiting higher robustness. Also, by F1-score and probability distribution analysis, we demonstrate that DVGNN better reflects the causal relationship and uncertainty of dynamic graphs. The website of the code is https://github.com/gorgen2020/DVGNN.

Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways

We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of diseases spreading (Susceptible-Infected-Refractory-Susceptible (SIRS)) on a regular one-dimensional lattice. In this model, particles of three species (S, I, and R) on a lattice react as follows: S+I→2I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S+I\\rightarrow 2I$$\\end{document} with probability λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}, I→R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$I\\rightarrow R$$\\end{document} after infection time τI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _I$$\\end{document} and R→I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R\\rightarrow I$$\\end{document} after recovery time τR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _R$$\\end{document}. In the case of τR>τI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _R>\ au _I$$\\end{document}, this model has been found to have two critical thresholds separating the active phase from absorbing phases. The first critical threshold λc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c1}$$\\end{document} corresponds to a low infection probability and the second critical threshold λc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c2}$$\\end{document} corresponds to a high infection probability. At the first critical threshold λc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c1}$$\\end{document}, our Monte Carlo simulations of this model suggest the phase transition to be of directed percolation class (DP). However, at the second critical threshold λc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c2}$$\\end{document} we observe that the system becomes so sensitive to initial values conditions which suggest the phase transition to be a discontinuous transition. We confirm this result using order parameter quasistationary probability distribution and finite-size analysis for this model at λc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c2}$$\\end{document}.

Asphalt pavement surface repair area detection based on smartphone sensors

Asphalt pavement repair areas affect pavement performance and service levels. It is necessary to distinguish the repair areas from normal sections. Based on vehicle vibration signals, this study identified ten pavement repair areas and divided them into four cases by factors including length and form in conjunction with the driving approach. Additionally, time domain analysis, frequency analysis, and probability distribution analysis were used to form the characteristics of the repair cases as well as the normal sections. It was found that the maximum value, extreme deviation, standard deviation in the time domain, maximum amplitude in the frequency domain, and peak of the probability density curve would serve as judgment indexes. A framework for identifying the repair areas was also established based on the five indexes. By validation, the overall accuracy can reach 95.0%, demonstrating a strong generalization capability.

Analisis Kapasitas Saluran Drainase pada Wilayah Padat Penduduk dengan Menggunakan Rational Modification Method

Merauke City, as a city in a growth and development period, cannot be separated from various problems. The provision of inadequate city facilities and infrastructure is one of the factors in the situation, drainage, for example. Generally, drainage handling in Merauke City is not comprehensive, so it has yet to handle the problem of inundation or flooding entirely. In residential areas around Estuary 3, puddles or floods are often found whenever rain is high enough intensity. Given that the city of Merauke, including in a flat area or the absence of elevation differences, makes one of the causes of waterlogging or flooding. This study aims to determine the capacity of estuary drainage channels in 3 Merauke Regency to accommodate or drain planned flood discharge. The research method used in this study is the rational method. This study uses two analyses, namely hydrological analysis and hydraulics analysis, where hydrological analysis a carried out to determine planned flood discharge by calculating daily rainfall using probability distribution and hydraulics analysis to determine channel capacity discharge by calculating cross-sectional dimensions. Based on the results of the study shows that segment 1 to segment 10 has different capacity discharge (Qs) and flood discharge (Qr). Segment 1 is one of the channel segments capable of accommodating or draining planned flood discharge with a capacity discharge of 5.51"m" ^"3" "/sec" and flood discharge of 2.07 "m" ^"3" "/sec" (Qs>Qr). In segment 7, which is the segment with the minor channel discharge, namely channel capacity discharge (Qs) of 0.004 "m" ^"3" "/sec" and plan flood discharge (Qr) of 0.78"m" ^"3" "/sec" then, the channel is unable to accommodate or drain plan flood discharge (Qr > Qs). And for other segments, the track cannot adjust or drain the planned flood discharge (Qs<Qr) with a capacity discharge between 0.003-0.05 "m" ^"3" "/sec" with a deliberate flood discharge of 0.21-1.19 "m" ^"3" "/sec" .

Computational analysis on mechanostructural properties of hydroxyapatite–alumina–titanium nanocomposite

AbstractIn this research, Taguchi–grey relational analysis has been applied to mitigate the insufficient assumptions made on the optimization of mechanical and structural (mechanostructural) properties of synthesized hydroxyapatite (HAp)–alumina–titanium nanocomposite. This nanocomposite has already been developed and studied in the previous study. This paper employs the L9 (3**3) orthogonal array, including displaying factors and levels of 3, 5, 7 wt % for alumina, 5, 10, 15 wt % for titanium, and 1100, 1150, 1200 °C sintering temperature. The computational analysis presents the predicted mechanostructural grey relational response as 0.7271, higher than the highest response shown in the ninth experimental run. The optimal control factors are analyzed to be 7 wt % alumina, 15 wt % titanium, and 1200 °C sintering temperature. The obtained result elucidates the hypothesis that a singular response optimization is not enough in the fabrication of biomedical material, disproving the assumption made in the previous literature. Importantly, to fabricate a high clinical grade HAp–alumina–titanium nanocomposite, titanium is the most invaluable contributor with a contribution of 49.11%, followed by alumina (45.52%), and then sintering temperature (3.2%). Although the confidence level and probability distribution analysis show that all the experimental mechanostructural responses were within the 95% confidence level, the employment of the predicted optimal factors is strongly recommended for experimentation.

An in-depth analysis of parameter settings and probability distributions of specific ordinal patterns in the Shannon permutation entropy during different states of consciousness in humans

As electrical activity in the brain has complex and dynamic properties, the complexity measure permutation entropy (PeEn) has proven itself to reliably distinguish consciousness states recorded by the EEG. However, it has been shown that the focus on specific ordinal patterns instead of all of them produced similar results. Moreover, parameter settings influence the resulting PeEn value. We evaluated the impact of the embedding dimension m and the length of the EEG segment on the resulting PeEn. Moreover, we analysed the probability distributions of monotonous and non-occurring ordinal patterns in different parameter settings. We based our analyses on simulated data as well as on EEG recordings from volunteers, obtained during stable anaesthesia levels at defined, individualised concentrations. The results of the analysis on the simulated data show a dependence of PeEn on different influencing factors such as window length and embedding dimension. With the EEG data, we demonstrated that the probability P of monotonous patterns performs like PeEn in lower embedding dimension (m = 3, AUC = 0.88, [0.7, 1] in both), whereas the probability P of non-occurring patterns outperforms both methods in higher embedding dimensions (m = 5, PeEn: AUC = 0.91, [0.77, 1]; P(non-occurring patterns): AUC = 1, [1, 1]). We showed that the accuracy of PeEn in distinguishing consciousness states changes with different parameter settings. Furthermore, we demonstrated that for the purpose of separating wake from anaesthesia EEG solely pieces of information used for PeEn calculation, i.e., the probability of monotonous patterns or the number of non-occurring patterns may be equally functional.

Electrical Response Estimation of Vibratory Energy Harvesters via Hilbert Transform Based Stochastic Averaging

Abstract Converting mechanical vibrations into electrical power with vibratory energy harvesters can ensure the portability, efficiency, and sustainability of electronic devices and batteries. Vibratory energy harvesters are typically modeled as nonlinear oscillators subject to random excitation, and their design requires a complete characterization of their probabilistic responses. However, simulation techniques such as Monte Carlo are computationally prohibitive when the accurate estimation of the response probability distribution is needed. Alternatively, approximate methods such as stochastic averaging can estimate the probabilistic response of such systems at a reduced computational cost. In this paper, the Hilbert transform based stochastic averaging is used to model the output voltage amplitude as a Markovian stochastic process with dynamics governed by a stochastic differential equation with nonlinear drift and diffusion terms. Moreover, the voltage amplitude dependent damping and stiffness terms are determined via an appropriate equivalent linearization, and the stationary probability distribution of the output voltage amplitude is obtained analytically by solving the corresponding Fokker–Plank equation. Two examples are used to demonstrate the accuracy of the obtained analytical probability distributions via comparisons with Monte Carlo simulation data.

Construction of a mathematical model and approximate analytical solution to the problem of energy exchange in the «sun ‒ paraboloid concentrator ‒ heat receiver» system

The object of research is the processes of radiation transfer in the «Sun – paraboloid concentrator – heat receiver» system. There are many factors that affect the value of the density of the concentrated heat flux that reaches the surface of the heat sink. The study of the influence of these factors on the overall energy indicators of the system is an important scientific problem that was solved in this work. To solve this problem, a generalized mathematical model of the radiation transfer process in the «Sun – concentrator – heat receiver» system was built, which was adapted for a paraboloid concentrator. The constructed mathematical model was solved by an approximate analytical method, which took into account the integral and discrete parameters of the system, as well as the probability distribution of aberrations of the concentrator surface, its defocusing, and other random influences. The dimensionless density of the heat flux on the surface of the heat sink for a mathematically ideal and real paraboloid concentrator of a fixed geometry was determined. Using the found analytical solution, the results obtained on the basis of the Monte Carlo method were verified. Analytical and numerical results for a mathematically ideal and a real concentrator with minor aberrations and a clear orientation to the Sun agree within the permissible error. For a real concentrator with defocusing, a deviation of numerical data from analytical data was observed. The presence of deviations is associated with a simplification in the interpretation of the analytical probability distribution, in which it is impossible to take into account each influence separately. The obtained analytical results will be useful in the development of real power plants and can be used practically at the stage of checking the adequacy of the system model

Testing a numerically-analytical method for prediction design maxima discharges of floods using plotting position formulas: the river Uzh case, the “Uzhhorod” gauging station data

There are a lot of analytical probability distributions that might be used to predict peak discharges of floods. However, there is no proper theoretical or another similar justification for choosing an appropriate parametric probability distribution to predict peak discharges of floods by using observed data. As a permissible hypothesis, any of recommended probability distributions can be considered providing it meets the given statistical criteria and other considerations for the adequacy of simulation are taken into account. In turn, more than seventeen plotting position formulas have been proposed. They provide a non-parametric means to estimate the observed data probability distribution. Using a plotting position formula, a plot of the estimated values from a theoretical parametric probability distribution can be compared with the observed data.The choice of a better plotting position formula for fitting the different probability distributions has been discussed many times in hydrology and statistical literature. However, no specific criterion for choosing these formulas has been proposed yet. Perhaps there is no need for such a criterion. Maybe, the diversity of estimates that can be obtained due to these formulas matters more. Due to the diversity of the different plotting position estimates, from the point of view of informational entropy, different plotting position formulas enable revealing epistemic (non-stochastic or subjective) uncertainty in predictions of hydrological extremes.Results of calculating empirical annual probabilities of exceedance observed maxima discharge employing various plotting position formulas show that increasing the predicting horizon toward low probable and more extreme events increases the divergence between the estimates obtained using the different plotting position formulas. Therefore, it is reasonable to assume that this divergence may be extrapolated to predict design maxima discharges of floods based on empirical estimates of plotting position probabilities.This paper proposes a numerically-analytical method using such an extrapolation. It is based on using different plotting position formulas, numerical calculations of plotting position probabilities, and extrapolation of the divergence between the obtained estimates. The method is tested in predicting the maxima discharges of 0.5% and 1% annual probability of exceedance for the Uzh River flowing in the Transcarpathia region, the hydrological station “Uzhhorod” data.