Random Function Research Articles

Permeability of large‐scale fractures with ununiform proppant distributions in coalbed methane development

AbstractThe coalbed methane (CBM) productivity is directly determined by the fracture permeability during hydraulic fracturing, which is regulated by the distribution of proppants. The proppant may be unevenly distributed in the fracture because of variables like the architecture of the fracture and the characteristics of the sand‐carrying fluid. This study used two types of random functions to produce different ununiform distributions of proppant clusters in large‐scale fractures, with the aim of investigating the effect of these distributions on the overall permeability of the fracture. A model of fluid‐structure coupling is proposed. The closure of large‐scale fractures under in‐situ stress is analyzed using solid mechanics and the penalty function; the CBM flowing in proppant clusters and the high‐speed channel between them is simulated using Darcy's law and the Navier–Stokes equation, respectively; and the overall permeability of fractures is computed using the fluid pressure drop throughout the fracture and the fluid flowing velocity in the fracture's outlet. Since most CBM flows along high‐speed channels between the proppant clusters, the simulated findings show that the overall permeability of fractures with an uneven distribution of proppant clusters is significantly higher than that of the proppant cluster itself. As CBM becomes more discretely distributed, the proportion of CBM flowing within the proppant cluster continuously drops. As the permeability of the proppant cluster increases, the volume ratio of proppant clusters decreases, and the distribution of proppant clusters becomes more discrete, the overall permeability of the fracture continuously increases.

Dynamics of large oscillator populations with random interactions.

We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence of the phases and the couplings, we derive reduced averaged equations with effective non-random coupling terms. As a particular example, we study interactions defined via the coupling functions that have the same shape but possess random coupling strengths and random phase shifts. While randomness in coupling strengths just renormalizes the interaction, a distribution of the phase shifts in coupling reshapes the coupling function.

Time-domain dimension-reduction representation for stochastic ground motion utilizing filtered white noise

A method is proposed for characterizing and simulating both stationary and fully non-stationary stochastic ground motions. This method is based on discrete filtered white noise models, including single and double filtered, with the latter is introduced to suppress low-frequency components. Specifically, the proposed method expresses seismic ground motion as a linear combination of products involving orthogonal random variables and deterministic functions. Further, by defining high-dimensional orthogonal random variables as orthogonal functions of extremely low dimensional elementary random variables, efficient dimension-reduction (DR) of primitive ground motion process can be achieved. To illustrate this concept, three distinct categories of random orthogonal functions involving only one or two elementary random variables are examined, employing filtered white noise models to simulate ground motion acceleration processes, thereby demonstrating the accuracy and efficiency of the proposed method. Simultaneously, recommendations for employing the proposed method in simulations are provided based on an analysis of the impacts of various parameters on random ground motion processes. Case studies demonstrate the accuracy and robustness of the proposed method compared to Monte Carlo (MC) methods. Furthermore, case studies on fully non-stationary ground motion highlight the practical applicability of the proposed method in engineering.

STATISTICAL EVALUATION OF PERFORMANCE INDICATORS OF PHOTOVOLTAIC PLANTS AS A SOURCE OF ENERGY FOR WATER DESALINATION IN THE AZOV-BLACK SEA REGION OF UKRAINE

The application of statistical methods for the analysis of random processes to obtain quantitative estimates for the performance indicators of photovoltaic plants as a stochastic energy source is considered. The power generation process is represented by a set of daily random functions with their respective trends and stochastic components. One hour was taken as the minimum stationari-ty interval of trend’s statistical characteristics. A time period of 16 years was studied to obtain statistically stable estimates. The meteorological database SARAH2 was used as a source of hourly data on the density of solar irradiance, ambient temperature and wind speed in the middle part of the Azov-Black Sea region of Ukraine. For mathematical modelling of power generation and electricity production processes, specialized software PVGIS version 5.2 of the European Commission was used. Hourly quantitative estimates of expected daily power generation trends for each month of the year, as well as their correlation functions, were computed. Algorithms were developed and levels of probabilistic assurance for hourly generated power were evaluated. Statistical estimates of the expected daily, monthly, and annual volumes of electricity production by photovoltaic power plants were studied, taking into account the meteorological conditions in the said region.

Obfuscating Verifiable Random Functions for Proof-of-Stake Blockchains

Obfuscating Verifiable Random Functions for Proof-of-Stake Blockchains

Taking into account the random function of parameter deviation in predicting the reliability of equipment

In article the question on forecasting of reliability of the equipment is considered. The characteristics infl uencing change of technical condition and reliability of the car (system) are analysed. Infl uence of stochastic function on a deviation of the actual values of parameter of technical condition is considered and the solution on her account is proposed.

An analysis of the effect of agriculture subsidies on technical efficiency: Evidence from rapeseed production in China

This study was conducted to examine the effects of agricultural subsidies on the technical efficiency of agricultural production technology and on factor input. It utilized a random frontier production function, instrumental variable method, and threshold regression model. The data used for this analysis consisted of 609 field yield measurements from the National Rapeseed Industry Technology System in 2020. The findings indicate that agricultural subsidies have a substantial impacts and it increases the technical efficiency of production process. Specifically, these subsidies encourage the use of land resources while inhibiting the use of chemical fertilizers. However, this does not have a significant effect on the utilization of labor and capital resources. Furthermore, the impact of agricultural subsidies on production technology efficiency varies depending on the scale of the farming operation. The subsidies significantly enhance the production technology efficiency of farmers with a business scale of less than 0.67 ha, but do not significantly improve the production technology efficiency of farmers with a business scale exceeding 0.67 ha. To optimize the effectiveness of agricultural subsidy policy, three methods and recommendations are proposed: increasing the overall amount of subsidies, expanding and diversifying the types of subsidies, and refining the process of disbursing subsidies.

Characterization of supercritical CO2 heat transfer in microporous media under (T/p)-mutability and integrated random function

The thermophysical properties of supercritical carbon dioxide (sCO2) undergo drastic changes under reservoir conditions, which significantly affects transfer characteristics and the storage efficiency. The present work seeks to identity of the heat transfer response of a mutable sCO2 in porous micromodels with integrated Boolean stochastic models. An upgraded variant of Lattice Boltzmann model is used after a thorough validation with literature experiments. The injection conditions of sCO2 are ranged from 295 to 333 K and 8–10 MPa, with a mass flow rate of 0.05–0.20 kg/min. The thermodynamic instabilities are discussed through the joint bonds between temperature and density, local and overall heat transfer, and pressure drop coefficient, under a series of pore-throats dimension from 7.5 to 401.3 μm. The results showed: (i) the remarkable (T/p)-nature of heat transfer capacity of sCO2 to lead the transfer coefficients with a subordinate impact of thermal conductivity near the Widom line, as long as the convective mode primes with increased temperature and pressure; (ii) The heterogeneity of the microporous media promoted the decrease of the transfer capacity while adjusting the spatiotemporal density and the heat transfer orientations inside the pore bodies; (iii) the growth of the pressure drop under increasing temperature has revealed an equilibrium stage where, neither the mutability of sCO2 properties nor the injection intensity can significantly affect the heat transfer of the integrated microporous.

Change-Point Detection in Functional First-Order Auto-Regressive Models

A sample of continuous random functions with auto-regressive structures and possible change-point of the means are considered. We present test statistics for the change-point based on a functional of partial sums. To study their asymptotic behavior, we prove functional limit theorems for polygonal line processes in the space of continuous functions. For some situations, we use a block bootstrap procedure to construct the critical region and provide applications. We also study the finite sample behavior via simulations. Eventually, we apply the statistics to a telecommunications data sample.

A Framework for Developing Systematic Testbeds for Multi-Fidelity Optimization Techniques

Abstract Multi-fidelity (MF) models abound in simulation-based engineering fields. Many MF strategies have been proposed to improve the efficiency in engineering processes, especially in design optimization. When it comes to assessing the performance of MF optimization techniques, existing practice usually relies on test cases involving contrived MF models of seemingly random math functions, due to limited access to real-world MF models. While it is acceptable to use contrived MF models, these models are often manually written up rather than created in a systematic manner. This gives rise to the potential pitfall that the test MF models may be not representative of general scenarios. We propose a framework to generate test MF models systematically and characterize tested MF optimization methods' performances comprehensively. In our framework, the MF models are generated based on given high-fidelity (HF) model and come with two parameters to control their fidelity levels and allow model randomization. In our testing process, MF case problems are systematically formulated using our model creation method. Running the given MF optimization technique on these problems produces what we call “savings curve” that characterizes the method's performance similarly to how ROC curves characterize machine learning classifiers. Our test results also allow plotting “optimality curves” that serve similar functionality to savings curves in certain types of problems. The flexibility of our MF model creation facilitates the development of testing processes for general MF problem scenarios, and our framework can be easily extended to other MF applications than optimization.

Density estimation for time-dependent PDE with random input by a Legendre-based multi-element probabilistic collocation method

This paper proposed a Legendre-based multi-element probabilistic collocation method for time-dependent stochastic differential equations, used for density estimation of unknown functions. This method involves discretizing the stochastic space, and on each element, constructing Lagrange interpolation basis functions based on Legendre–Gauss–Lobatto collocation/quadrature nodes. The proposed method is applied to approximate one-dimensional/two-dimensional smooth/non-smooth functions and is tested for accuracy in approximating random function values, density estimations, and mathematical expectations. This method is applied to stochastic nonlinear Schrödinger equations and coupled stochastic nonlinear Schrödinger equations, and all numerical results are compared with Monte Carlo simulation.

Improved vigenere using affine functions surrounded by two genetic crossovers for image encryption

This paper presents an improved method for encrypting color images, surpassing the effectiveness of genetic crossover and substitution operations. The technique incorporates dynamic random functions to enhance the integrity of the resulting vector, increasing temporal complexity to thwart potential attacks. The improvement involves integrating genetic crossover and utilizing two extensive pseudorandom replacement tables derived from established chaotic maps in cryptography. Following the controlled vectorization of the original image, our approach initiates with a first genetic crossover inspired by deoxyribonucleic acid (DNA) behavior at the pixel level. This genetic crossover is succeeded by a confusion-diffusion lap, reinforcing the connection between encrypted pixels and their neighboring counterparts. The confusion-diffusion process employs dynamic pseudorandom affine functions at the pixel level. Then a second genetic crossover operator is applied. Simulations conducted on a diverse set of images with varying sizes and formats showcase the robustness of our method against statistical, brute-force, and differential attacks.

SEMIPARAMETRIC BIVARIATE HIERARCHICAL STATE SPACE MODEL WITH APPLICATION TO HORMONE CIRCADIAN RELATIONSHIP.

The adrenocorticotropic hormone and cortisol play critical roles in stress regulation and the sleep-wake cycle. Most research has been focused on how the two hormones regulate each other in terms of short-term pulses. Few studies have been conducted on the circadian relationship between the two hormones and how it differs between normal and abnormal groups. The circadian patterns are difficult to model as parametric functions. Directly extending univariate functional mixed effects models would result in a large dimensional problem and a challenging nonparametric inference. In this article, we propose a semi-parametric bivariate hierarchical state space model, in which each hormone profile is modeled by a hierarchical state space model, with nonparametric population-average and subject-specific components. The bivariate relationship is constructed by concatenating two latent independent subject-specific random functions specified by a design matrix, leading to a parametric inference on the correlation. We propose a computationally efficient state-space EM algorithm for estimation and inference. We apply the proposed method to a study of chronic fatigue syndrome and fibromyalgia and discover an erratic regulation pattern in the patient group in contrast to a circadian regulation pattern conforming to the day-night cycle in the control group.

Modeling patchy saturation of fluids in nanoporous media probed by ultrasound and optics.

Nanoporous materials provide high surface area per unit mass and are capable of fluids adsorption. While the measurements of the overall amount of fluid adsorbed by a nanoporous sample are straightforward, probing the spatial distribution of fluids is nontrivial. We consider literature data on adsorption and desorption of fluids in nanoporous glasses reported along with the measurements of ultrasonic wave propagation. We analyze these using the so-called dynamic equivalent medium approach, which is based on Biot's theory of dynamic poroelasticity with coefficients that are continuous random functions of position. When further constrained by optical scattering data for similar systems, the calculations show that on adsorption the characteristic patch size is of the order of 100 pore diameters, while on desorption the patch size is comparable to the sample size. Our analysis suggests that one can employ ultrasound to probe the uniformity of the spatial distribution of fluids in nanoporous materials.

Paucity phenomena for polynomial products

AbstractLet be a polynomial with at least two distinct complex roots. We prove that the number of solutions to the equation (for any ) is asymptotically as . This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums match standard complex Gaussian moments as , where is the Steinhaus random multiplicative function.

A Plasmonic Optoelectronic Resistive Random-Access Memory for In-Sensor Color Image Cryptography.

The optoelectronic resistive random-access memory (RRAM) with the integrated function of perception, storage and intrinsic randomness displays promising applications in the hardware level in-sensor image cryptography. In this work, 2D hexagonal boron nitride based optoelectronic RRAM is fabricated with semitransparent noble metal (Ag or Au) as top electrodes, which can simultaneous capture color image and generate physically unclonable function (PUF) key for in-sensor color image cryptography. Surface plasmons of noble metals enable the strong light absorption to realize an efficient modulation of filament growth at nanoscale. Resistive switching curves show that the optical stimuli can impede the filament aggregation and promote the filament annihilation, which originates from photothermal effects and photogenerated hot electrons in localized surface plasmon resonance of noble metals. By selecting noble metals, the optoelectronic RRAM array can respond to distinct wavelengthsand mimic the biological dichromatic cone cells to perform the color perception. Due to the intrinsic and high-quality randomness, the optoelectronic RRAM can produce a PUF key in every exposure cycle, which can be applied in the reconfigurable cryptography. The findings demonstrate an effective strategy to build optoelectronic RRAM for in-sensor color image cryptography applications.

Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer

Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer

Littlewood-type theorems for Hardy spaces in infinitely many variables

Littlewood's theorem is one of the pioneering results in random analytic functions over the open unit disk. In this paper, we prove some analogues of this theorem for Hardy spaces in infinitely many variables. Our results not only cover finite-variable setting, but also apply in cases of Dirichlet series.

STATISTICAL ESTIMATES OF VARIABLES DETERMINING THE INTERVAL OF ELECTRIC POWER MONITORING

It is demonstrated that digital processing of information on electricity consumption is possible when transforming the studied process into a discrete form. The correct choice of the monitoring interval allows for the accurate reconstruction of the values of the studied function in the intervals between measurements. It is shown that when organizing the monitoring of average power, it is necessary to select a discretization interval that provides adequate representation of the current process. The proposed procedure for choosing the interval of electric power monitoring is based on determining the duration of the deviation of the random function of electric power change, subject to certain constraints. The justified number of monitoring studies is established to determine the optimal interval of electric power monitoring. It is shown that the most rational method of processing experimental data will be the method of joint estimation for correlation and standard deviation.

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions