Probability Distribution Function Research Articles

Energetic and Entropic Motifs in Vesicle Morphogenesis in Amphiphilic Diblock Copolymer Solutions

Coarse-grained molecular dynamic simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) via self-assembly of randomly distributed amphiphilic diblock copolymers PB-PEO (Poly(Butadiene)-b-Poly(Ethylene Oxide)) in water. The vesiculation pathway consists of several intermediate structures, such as spherical/rodlike aggregates, wormlike micelles, lamellae, and cavities. The lamella-to-vesicle transition occurs at a constant aggregation number and is accompanied by a reduction in the solvent-accessible surface area. Simulation predictions are in qualitative agreement with the mechanism of vesicle formation in which the unfavorable hydrophobic interactions between water molecules and polymer segments, along the edge of the lamella, are eliminated at the expense of gaining curvature energy. However, rod–lamella–vesicle transition is accompanied by an increase in copolymer packing density. Hence, the change in the surface area accompanying vesiculation predicted by the simulations is significantly lower than theoretical estimates. Changes in information entropy, quantified by the expectation of the logarithm of the probability distribution function of the segmental stretch parameter s, defined as the difference between the maximum and instantaneous segmental extension, are statistically insignificant along the vesiculation pathway. For rods, lamellae, and polymersomes, s follows a log normal distribution. This is explained based on the configurational dynamics of a single diblock chain in water.

Effects of electrostatic interaction on clustering and collision of bidispersed inertial particles in homogeneous and isotropic turbulence

In sandstorms and thunderclouds, turbulence-induced collisions between solid particles and ice crystals lead to inevitable triboelectrification. The charge segregation is usually size dependent, with small particles charged negatively and large particles charged positively. In this work, we perform numerical simulations to study the influence of charge segregation on the dynamics of bidispersed inertial particles in turbulence. Direct numerical simulations of homogeneous isotropic turbulence are performed with the Taylor Reynolds number ${Re}_{\lambda }=147.5$ , while particles are subjected to both electrostatic interactions and fluid drag, with Stokes numbers of 1 and 10 for small and large particles, respectively. Coulomb repulsion/attraction is shown to effectively inhibit/enhance particle clustering within a short range. Besides, the mean relative velocity between same-size particles is found to rise as the particle charge increases because of the exclusion of low-velocity pairs, while the relative velocity between different-size particles is almost unaffected, emphasizing the dominant roles of differential inertia. The mean Coulomb-turbulence parameter, ${Ct}_0$ , is then defined to characterize the competition between the Coulomb potential energy and the mean relative kinetic energy. In addition, a model is proposed to quantify the rate at which charged particles approach each other and to capture the transition of the particle relative motion from the turbulence-dominated regime to the electrostatic-dominated regime. Finally, the probability distribution function of the approach rate between particle pairs is examined, and its dependence on the Coulomb force is further discussed using the extended Coulomb-turbulence parameter.

Riemannian Manifold-Based Feature Space and Corresponding Image Clustering Algorithms.

Image feature representation is a key factor influencing the accuracy of clustering. Traditional point-based feature spaces represent spectral features of an image independently and introduce spatial relationships of pixels in the image domain to enhance the contextual information expression ability. Mapping-based feature spaces aim to preserve the structure information, but the complex computation and the unexplainability of image features have a great impact on their applications. To this end, we propose an explicit feature space called Riemannian manifold feature space (RMFS) to present the contextual information in a unified way. First, the Gaussian probability distribution function (pdf) is introduced to characterize the features of a pixel in its neighborhood system in the image domain. Then, the feature-related pdfs are mapped to a Riemannian manifold, which constructs the proposed RMFS. In RMFS, a point can express the complex contextual information of corresponding pixel in the image domain, and pixels representing the same object are linearly distributed. This gives us a chance to convert nonlinear image segmentation problems to linear computation. To verify the superiority of the expression ability of the proposed RMFS, a linear clustering algorithm and a fuzzy linear clustering algorithm are proposed. Experimental results show that the proposed RMFS-based algorithms outperform their counterparts in the spectral feature space and the RMFS-based ones without the linear distribution characteristics. This indicates that the RMFS can better express features of an image than spectral feature space, and the expressed features can be easily used to construct linear segmentation models.

Characterization and evolution of local streamline geometry in an incompressible turbulent channel flow

We investigated the statistical characterization and time evolution of local streamline geometry in typical regions of an incompressible turbulent channel flow at the friction Reynolds number Reτ∼1000. Local streamline structure is completely and uniquely determined by one magnitude factor—the magnitude of velocity gradient tensor (VGT) A—and four shape parameters—the second and third invariants of normalized VGT q and r, the intermediate eigenvalue of normalized strain-rate tensor a2, and the cosine of the angle between vorticity and the intermediate eigendirection of normalized strain-rate tensor | cos β|. As the distance to the wall decreases, the joint probability distribution function of q and r becomes more symmetrical and concentrated, while outside the viscous sublayer, the distribution of A in q–r plane gets dispersed. Interestingly, the inertial conditional mean trajectories (CMTs) exhibit a symmetrical picture only in the buffer layer, and outside the viscous sublayer, the pressure CMTs contributing to slow evolution from unstable focus compression geometry to stable focus stretching geometry tend to dominate the q–r plane as getting closer to the wall. Due to combined effects of inertia and pressure, the origin of the q–r plane (pure-shear geometry) acts as an attractor in the central region, the logarithmic region, and the upper part of the buffer layer while acts as a repeller in the lower part of the buffer layer and the viscous sublayer.

Field-level Lyman-α forest modeling in redshift space via augmented nonlocal Fluctuating Gunn-Peterson Approximation

Context. Devising fast and accurate methods of predicting the Lyman-α forest at the field level, avoiding the computational burden of running large-volume cosmological hydrodynamic simulations, is of fundamental importance to quickly generate the massive set of simulations needed by the state-of-the-art galaxy and Lyα forest spectroscopic surveys. Aims. We present an improved analytical model to predict the Lyα forest at the field level in redshift space from the dark matter field, expanding upon the widely used Fluctuating Gunn-Peterson Approximation (FGPA). Instead of assuming a unique universal relation over the whole considered cosmic volume, we introduce a dependence on the cosmic web environment (knots, filaments, sheets, and voids) in the model, thereby effectively accounting for nonlocal bias. Furthermore, we include a detailed treatment of velocity bias in the redshift space distortion modeling, allowing the velocity bias to be cosmic-web-dependent. Methods. We first mapped the dark matter field from real to redshift space through a particle-based relation including velocity bias, depending on the cosmic web classification of the dark matter field in real space. We then formalized an appropriate functional form for our model, building upon the traditional FGPA and including a cutoff and a boosting factor mimicking a threshold and inverse-threshold bias effect, respectively, with model parameters depending on the cosmic web classification in redshift space. Eventually, we fit the coefficients of the model via an efficient Markov chain Monte Carlo scheme. Results. We find evidence for a significant difference between the same model parameters in different environments, suggesting that for the investigated setup the simple standard FGPA is not able to adequately predict the Lyα forest in the different cosmic web regimes. We reproduce the summary statistics of the reference cosmological hydrodynamic simulation that we use for comparison, yielding an accurate mean transmitted flux, probability distribution function, 3D power spectrum, and bispectrum. In particular, we achieve maximum deviation and average deviation accuracy in the Lyα forest 3D power spectrum of ∼3% and ∼0.1% up to k ∼ 0.4 h Mpc−1, and ∼5% and ∼1.8% up to k ∼ 1.4 h Mpc−1. Conclusions. Our new model outperforms previous analytical efforts to predict the Lyα forest at the field level in all the probed summary statistics, and has the potential to become instrumental in the generation of fast accurate mocks for covariance matrices estimation in the context of current and forthcoming Lyα forest surveys.

Analytical results and universal behavior in fast thermal equilibration protocols.

When a system deviates from equilibrium, it is possible to manipulate and control it to drive it towards equilibrium within finite time t_{f}, even by reducing its natural relaxation timescale τ_{relax}. Although numerous theoretical and experimental studies have explored these shortcut protocols, few have yielded analytical results for the probability distribution of the work, heat, and produced entropy. In this study, we propose a two-step protocol that captures the essential characteristics of more general protocols and provides an analytical solution for the relevant thermodynamic probability distributions. Additionally, we present evidence that for a very short protocol duration t_{f}≪τ_{relax}, all protocols exhibit universal behavior for the ratio of probability distribution functions of positive and negative work, heat, and the produced entropy.

Optimal Reactive Power Dispatch problem integrating probabilistic model of wind power for uncertainties in load using JAYA algorithm

The optimal reactive power dispatch (ORPD) is a method for optimising power system engineering to reduce power loss and voltage deviation. This work addresses the ORPD problem considering load uncertainty, where load is varied in ten different instances. The optimal conditions have been determined for the system with minimum power loss and minimum total voltage deviations for different loading instances. The problem has also been integrated with the probabilistic nature of wind power, calculated using the Weibull Probability Distribution Function (WPDF). The aim is to obtain the optimal values of wind power using the WPDF for two separate cases: overestimation and underestimation, integrate these power individually, and minimise both the power loss and voltage deviation for the ten different loading scenarios. This hybrid wind power integrated ORPD problem, considering load uncertainty, has been tested on the IEEE 30 and IEEE 57 bus systems using the JAYA algorithm and other optimisation techniques. This tuning-parameter-free JAYA algorithm has obtained the best solutions for power loss of 1.8641 MW and TVD of 0.123 p.u. for the overestimated wind power integration at the IEEE 30 bus system at 100% loading compared to the other algorithms. It also acquired the best power loss and TVD solutions of 1.9144 MW and 0.1245 p.u., respectively, for the underestimated wind power at the same bus system for 100% loading with the highest convergence rate. The overall study establishes the JAYA algorithm as a superior optimising technique for solving this hybrid ORPD problem compared to the other techniques.

Modeling forecast errors for microgrid operation using Gaussian process regression

Microgrids, denoting small-scale and self-sustaining grids, constitute a pivotal component in future power systems with a high penetration of renewable generators. The inherent uncertainty tied to renewable power generation, typified by photovoltaic and wind turbine systems, necessitates counterbalancing mechanisms. These mechanisms encompass Energy storage systems or conventional thermal fossil-fuel generators imbued with heightened flexibility. Addressing the uncertainty stemming from renewable generators mandates a cost-effective assessment and operational strategy for said compensatory devices. To this end, myriad uncertainty factors warrant scrutiny, conceivably concretized into a unified probability distribution function (PDF) that takes into account their temporal inter-dependencies. Diverse uncertainty factors, characterized by varying marginal distributions and scales, can be assimilated into a multivariate probability distribution through a conversion to normal distributions via rank correlation. However, with the escalation in the number of uncertainty factors embraced within a microgrid context, the endeavour becomes notably intricate when aiming to define conditional probability distributions originating from joint PDFs. This paper presents a method proposing the modelling of net-load forecast error distribution, considering the interplay among uncertainty factors. The approach introduces a data-driven Gaussian process regression technique for training and validating conditional PDFs among these uncertainty factors. Notably, this approach facilitates the transformation of said factors into normal distributions while preserving their inherent marginal characteristics. The resultant conditional density function, as per the proposed methodology, exhibits enhanced suitability for estimating net-load error distribution. Consequently, the conditional density function stemming from this proposed approach demonstrates superior aptitude in approximating the distribution of net load error.

Investment risk analysis of electricity generation from vinasse biodigestion in the Brazilian Regulated Market

This paper presents a methodology of investment risk analysis of the electricity generation by using biogas from biodigestion of sugarcane vinasse produced in sugarcane agroindustries. The methodology to be presented uses econometric models to generate synthetic time series of ethanol production, which is used to estimate the production of vinasse, biogas and electricity. The economic viability analysis will be done from the evaluation of the probability distribution functions of Net Present Value, Modified Internal Rate of Return and Discounted Payback, by considering that the electricity produced is commercialized in the Brazilian Regulated Contracting Environment. A case study is carried out using real data from a sugarcane plant located in the Midwest region of Brazil. The results indicate the economic viability of the project implementation.

Sub-kpc scale gas density histogram of the galactic molecular gas: a new statistical method to characterise galactic-scale gas structures

Abstract To understand physical properties of the interstellar medium (ISM) on various scales, we investigate it at parsec resolution on the kiloparsec scale. Here, we report on the sub-kpc scale Gas Density Histogram (GDH) of the Milky Way. The GDH is a density probability distribution function (PDF) of the gas volume density. Using this method, we are free from an identification of individual molecular clouds and their spatial structures. We use survey data of 12CO and 13CO (J=1–0) emission in the Galactic plane (l = 10○–50○) obtained as a part of the FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45m telescope (FUGIN). We make a GDH for every channel map of 2○ × 2○ area including the blank sky component, and without setting cloud boundaries. This is a different approach from previous works for molecular clouds. The GDH fits well to a single or double log-normal distribution, which we name the low-density log-normal (L-LN) and high-density log-normal (H-LN) components, respectively. The multi-log-normal components suggest that the L-LN and H-LN components originate from two different stages of structure formation in the ISM. Moreover, we find that both the volume ratios of H-LN components to total (fH) and the width of the L-LN along the gas density axis (σL) show coherent structure in the Galactic-plane longitude-velocity diagram. It is possible that these GDH parameters are related to strong galactic shocks and other weak shocks in the Milky Way.

OAM mode-division multiplexing IM/DD transmission at 4.32 Tbit/s with a low-complexity adaptive-network-based fuzzy inference system nonlinear equalizer.

Stochastic nonlinear impairment is the primary factor that limits the transmission performance of high-speed orbital angular momentum (OAM) mode-division multiplexing (MDM) optical fiber communication systems. This Letter presents a low-complexity adaptive-network-based fuzzy inference system (LANFIS) nonlinear equalizer for OAM-MDM intensity-modulation direct-detection (IM/DD) transmission with three OAM modes and 15 wavelength division multiplex (WDM) channels. The LANFIS equalizer could adjust the probability distribution functions (PDFs) of the distorted pulse amplitude modulation (PAM) symbols to fit the statistical characteristics of the WDM-OAM-MDM transmission channel. Therefore, although the transmission symbols in the WDM-OAM-MDM system are subjected to a stochastic nonlinear impairment, the proposed LANFIS equalizer can effectively compensate the distorted signals. The proposed equalizer outperforms the Volterra equalizer with improvements in receiver sensitivity of 2, 1.5, and 1.3 dB for three OAM modes at a wavelength of 1550.12 nm, respectively. It also outperforms a CNN equalizer, with improvements in receiver sensitivity of 1, 0.5, and 0.3 dB, respectively. Moreover, complexity reductions of 67%, 74%, and 99.9% are achieved for the LANFIS equalizer compared with the Volterra, CNN, and ANFIS equalizers, respectively. The proposed equalizer has high performance and low complexity, making it a promising candidate for a high-speed WDM-OAM-MDM system.

Impacts of Nudged Sea Surface Temperature on Tropical Precipitation, Moisture, and Vertical Velocity in an Earth System Model

Abstract Understanding the effect of the nudged sea surface temperature (SST) on precipitation simulation is important in Earth system models. In this study, we analyzed the role of nudged SST and air–sea interaction in precipitation simulation by using the Chinese Academy of Sciences Earth System Model version 2 (CAS-ESM2). CAS-ESM2 fully coupled runs with and without nudged tropical SST to observations, and the atmosphere-only runs (AMIP) are comprehensively evaluated against observations and reanalysis over the tropical ocean from 1982 to 2015. The precipitation is affected by the nudged SST and air–sea interaction by means of changes in both thermodynamic and dynamic processes. Simulation with the nudged SST dramatically improves the climatological precipitation fields over the tropics and four regional areas. As the simulated SSTs are nudged toward the observations, CAS-ESM2 well reproduces the mean annual values in column water vapor (CWV), vertical structure of specific humidity, and large-scale circulation. The nudged SST run also captures a wide range of the complex interactions between SST, precipitation, moisture, and large-scale circulations, as measured by the monthly relationships and bivariate probability distribution function. The biases in heavy precipitation associated with the CWV induced under moist conditions are decreased by applying the nudging technique. In particular, the nudging run performs better in reproducing the SST–precipitation covariability than the control and AMIP runs. However, CAS-ESM2 with nudged tropical SST simulates the degradation of strong ascending motions, which is similar to the AMIP runs and reflects the deviation of the atmospheric model. Our results confirm that the fully coupled run using the nudged SST is a method for improving the precipitation simulation across the tropical oceans. Significance Statement Understanding the sources of precipitation errors in Earth system models is challenging because of the complex error compensation and air–sea interaction. When the simulated SST is nudged toward observations, few studies have focused on the changes in both thermodynamic and dynamic processes via atmospheric large-scale circulation, moisture, and changes in the SST–precipitation relationship at the same time. Here, we carry out two CMIP6 historical experiments (a fully coupled control run and an SST-nudged run) and the atmosphere-only runs by using CAS-ESM2 from 1982 to 2015. Then, we validate and analyze the climatology of SST, precipitation, moisture, large-scale circulation, and their complex interactions over the tropical oceans and different regional areas. The fully coupled nudged-SST run outperforms the fully free coupled run in reproducing the climatology and complex interactions between SST, precipitation, moisture, and large-scale circulations across the tropics. Moreover, the biases in the SST–precipitation covariability are significantly alleviated in the nudging experiments. We confirmed that the SST nudging method is a potential way to improve precipitation simulation in CAS-ESM2.

Prediction enhancement for surface water sodium adsorption ratio using limited inputs: Implementation of hybridized stacked ensemble model with feature selection algorithm

The Sodium Adsorption Ratio (SAR) is a widely used variable in water quality research, particularly in agriculture and environmental studies. In many cases, the key variables required for SAR calculation, namely Na+, Mg+2, and Ca+2, are not available. Consequently, the potential to calculate SAR using a limited number of water quality variables becomes critically important. The study implemented the Multilayer Perceptron Neural Network (MLPNN), Support Vector Regression (SVR), and K-Nearest Neighbors (KNN) models at level-0 for prediction purposes, along with the Boruta model for variable selection. A stacked ensemble learning model at level-1 enhanced the prediction accuracy. The discharge and water quality dataset from the Zarrin-Gol River in northern Iran was utilized to implement the modeling procedure. Results obtained from the variable selection process using the Boruta model revealed that using a limited number of water quality variables can effectively predict SAR even without the principal variables. Further investigation of the input combinations for the level-0 models demonstrated that, for the MLPNN, KNN, and SVR models, 4, 3, and 1 input variables, respectively, yielded optimal predictions. Among the level-0 models, the MLPNN model exhibited the highest accuracy, with RMSE = 0.54, MBE = 0.26, MAE = 0.44, R = 0.84, IA = 0.67, and KGE = 0.79. Implementing the stacked ensemble learning model at level-1 significantly improved the SAR prediction compared to the level-0 models. The ensemble-NN model yielded the best performance in estimating SAR within the range of recorded data, with RMSE = 0.53, MBE = 0.29, MAE = 0.41, R = 0.87, IA = 0.70, and KGE = 0.82. Residual analysis further confirmed the superior predictive capability of the level-1 models compared to the level-0 models. The generalized-logistic probability distribution function is used to estimate the extreme values data. The Ensemble-KNN model best predicted extreme values data, with RMSE = 0.69, MBE = −0.61, MAE = 0.61, R = 0.61, IA = 0.26, and KGE = 0.37. The findings underscore the substantial advancements achieved through stacked ensemble methods in enhancing the modeling of SAR across various aspects, including total data, extreme values, and models' residuals.

Charging management of electric vehicles with the presence of renewable resources

Considering the increasing use of electric vehicles, the establishment of charging stations to exchange power between the grid and electric devices, and the integration of charging stations with solar power generation sources, the optimal use of electric vehicle charging stations in the power system. The purpose of cost reduction in the presence of the intelligent environment is a challenge that must be investigated so that this platform is suitable for predicting the behaviour of vehicles and, as a result, optimizing their presence in the power network. This research presents a relatively complete radial distribution network development planning model in two scenarios. In the first scenario, the effects of electric vehicles are not considered, and only the effects of distributed production (renewable and dispatchable) are considered. Studies have been done on a sample 54-bus network, a common system in most Distribution expansion planning (DEP) articles for distribution networks. In addition, the real data of American highways have been used to create raw input data. Also, due to the distance limit, the information on vehicles under 100 miles has been received as electric vehicle information. The clustering method and Capiola multivariate probability distribution functions have created suitable vehicle scenarios during different planning years. Capiola’s method increases the accuracy of vehicle load forecasting according to a predetermined growth rate. The DEP problem in this research is modeled as an optimization problem based on scenario, dynamic, and in 5 one-year time frames (5-year time horizon and one-year accuracy). The results indicate that, in the presence of electric vehicles and distributed production sources, the technical characteristics of the network are improved.Similarly, the use of DGs, in addition to reducing the cost of equipment, has reduced undistributed energy in the system. But 10,000 vehicles, which have been applied to the network as an uncontrolled load, have caused an increase in undistributed energy. The cost of equipment required for the network development is almost as much as 5%.

Wind energy potential assessment: a case study in Central India

Access to sustainable energy is important for economic development and environmental protection. The shift towards renewable energy is essential for mitigating climate change and ensuring long-term energy sustainability. Though developing nations possess significant renewable energy capacity, transitioning to renewable sources remains a challenge. India's expanding wind energy sector has the potential to lower carbon dioxide emissions and produce energy in a sustainable manner. This research uses the Windographer software to conduct a comprehensive analysis of the wind energy potential at a distinct site in Nagpur, India. The assessment includes monthly average wind speeds, wind rose diagrams that show the prevailing wind directions, and wind power density (WPD) calculations. These factors together establish the site's classification. In this study, Weibull parameters are derived using four distinct methods to estimate the probability distribution function. The average WPD is found to be 13.63 and 71.08 W/m2 at heights of 10 and 100 m above ground level, respectively. Through wind turbine output analysis, numerous turbine models are assessed for suitability at the specified location. The Windtec DD 3000-125 model, interestingly, has a maximum capacity factor of 9.27%. The results highlight comparatively low wind potential in the studied region. Nevertheless, a wind turbine at this location can produce about 2 412 379 kW of electricity annually using the aforementioned wind turbine model.

Effect of Solute on Interfacial Properties and Micelle Structure of Dodecylbenzenesulfonate (DBS): Experimental and Molecular Dynamics Studies.

A combined experimental and molecular dynamic simulation approach was used to examine the structure and interfacial properties of solute-saturated micelles. The properties of dodecylbenzenesulfonate (DBS) micelles were examined in dodecane and benzene hydrocarbon systems. Pyrene fluorescence was used to determine the aggregation number of surfactant monomers in the micelle systems. Molecular dynamic (MD) simulations using energy minimization applying the CHARMm force field with the TIP3P model for water. Comparison of the DBS/benzene and DBS/Dodecane micelles equilibrium structures via radial distribution function (RDF) and probability distribution function (PDF) analysis indicates that the area per head group for the DBS/Benzene micelle interface is significantly larger than that of the DBS/Dodecane at the interface. It was also determined that benzene molecules can move freely within the micelle while dodecane is strictly confined in the core of the micelle. The increased interfacial area per monomer caused by the insertion of benzene also reduces the effectiveness of the surfactant, which has implications for use in various environmental applications. However, the DBS/benzene micelle can solubilize many more hydrocarbon molecules in one micelle with less surfactant monomer (i.e., lower aggregation number) per micelle due to the increased available packing positions within the micelle. This, in turn, increases the efficiency of the surfactant in real-world applications which is consistent with previous laboratory results. Understanding the differing solubilization characteristics of surfactants against various classes of hydrocarbons in single solute systems is a necessary step to beginning to understand their solubilization properties in the mixed waste systems prevalent in most surfactant enhanced remediation (SEAR) strategies.

Analysis of force-free fields in the solar corona at flare sites

Force-free magnetic fields can be used to compute the magnetic structure above active regions where the field strength is large. Using vector magnetograms for two active regions that gave rise to solar flares, the force-free fields are obtained for times before and after the flare. The current density in the upper atmosphere obtained from nonlinear force-free fields is analyzed using Singular Value Decomposition (SVD) methods to determine how it is distributed around the times of flare occurrence. Regions of localized and relatively intense currents are sought at the different scales since these are usually linked to magnetic reconnection. It is found that the probability distribution functions (PDF) for small scales exhibit long tails and they are compared for times before and after the flare. Previous to the flare they seem to be slightly wider but not significant enough to draw a definite conclusion. This is likely due to break down of the applicability of the Force-Free fields after the flare. The effect of having long-tailed PDFs is equivalent to the one found in temperature fluctuations about the flare occurrence (1) which could point to a correlation between electrical currents and temperature. It is also obtained that the energy content in the middle scales of the currents is larger before than after the flare which would point to a magnetic dissipation at those scales during the flare.

Uncertainty Quantification in Geostatistical Modelling of Saltwater Intrusion at a Coastal Aquifer System

Groundwater resources in Mediterranean coastal aquifers are under several threats including saltwater intrusion. This situation is exacerbated by the absence of sustainable management plans for groundwater resources. Management and monitoring of groundwater systems require an integrated approach and the joint interpretation of any available information. This work investigates how uncertainty can be integrated within the geo-modelling workflow when creating numerical three-dimensional aquifer models with electrical resistivity borehole logs, geostatistical simulation and Bayesian model averaging. Multiple geological scenarios of electrical resistivity are created with geostatistical simulation by removing one borehole at a time from the set of available boreholes. To account for the spatial uncertainty simultaneously reflected by the multiple geostatistical scenarios, Bayesian model averaging is used to combine the probability distribution functions of each scenario into a global one, thus providing more credible uncertainty intervals. The proposed methodology is applied to a water-stressed groundwater system located in Crete that is threatened by saltwater intrusion. The results obtained agree with the general knowledge of this complex environment and enable sustainable groundwater management policies to be devised considering optimistic and pessimistic scenarios.

Electric Vehicle and Photovoltaic Power Scenario Generation under Extreme High-Temperature Weather

In recent years, with the intensification of global warming, extreme weather has become more frequent, intensifying the uncertainty of new energy output and load power, and seriously affecting the safe operation of power systems. Scene generation is an effective method to solve the uncertainty problem of stochastic planning of integrated systems of new energy generation. Therefore, this paper proposes a scenario generation and scenario reduction model of photovoltaic (PV) output and electric vehicle (EV) load power under extreme weather based on the copula function. Firstly, the non-parametric kernel density estimation method is used to fit a large number of sample data. The kernel density estimation expressions of PV and EV powers under extreme weather conditions are obtained and the corresponding goodness of fit tests are carried out. Then, a variety of joint distribution models based on the copula function are established to judge the goodness of fit of each model, and the optimal copula function is selected as the joint probability distribution function by combining the Kendall and Spearman correlation coefficients of each model. Finally, the optimal copula joint probability distribution is used to generate PV and EV power scenarios. The data of extremely hot weather in a certain province were selected for an example analysis. The results show that the output scenario obtained conforms to the correlation under this extreme weather, and has higher accuracy in reflecting the actual PV output and load power in this province under this extreme weather, which can provide a reference for reliability analyses of power systems and power grid planning.

Describing geophysical turbulence with a Schrödinger–Coriolis equation in velocity space

In this paper, we examine the predictions of the scale-relativity approach for a turbulent fluid in rotation. We first show that the time derivative of the governing Navier–Stokes equation in the usual x-space can be transformed into a Schrödinger-like equation in velocity space with an external vectorial field to account for the rotation, together with a local velocity harmonic oscillator (VHO) potential in the v-space. The coefficients of this VHO are given by the second order x-derivatives of the pressure. We can then give formulas for the velocity and acceleration probability distribution functions (PDF). Using a simple model of anisotropic harmonic oscillator, we compare our predictions with relevant data from both direct numerical simulations (DNS) and oceanic drifter velocity measurements. We find a good agreement of the predicted acceleration PDF with that observed from drifters and some possible support in DNS for the existence of gaps in the local velocity PDF, expected in the presence of a Coriolis force.