Exponential Correlation Function Research Articles

Probability Characteristics of Gompertz Model with Different Kinds of Colored Noise Excitation (invited talk)

We explore the steady-state probability distribution of Gompertz model in tumor growth rate for two different kinds of colored noise with exponential correlation functions, namely, for Ornstein–Uhlenbeck process and Markovian dichotomous noise. Comparing the behavior of the steady-state distributions depending on the correlation time of these noises with the same power, we establish the influence of the probability characteristics of fluctuations on the original system.

Study the effect of generating randomly rough interfaces on electron transport properties across the heterostructures

In the present paper, generating randomly rough interfaces -with two different types of correlation functions and dissimilar characteristics and morphologies- have been considered. The correlation functions of generated interfaces have Gaussian and exponential forms and they have been used in heterostructures as the rough interfaces. The main purpose of the present research is to study the effect of interfaces roughness types on the coherent electron transport through heterostructures. In order to better evaluation, the transport properties of heterostructures have been obtained for both planar and rough interfaces. The results show that the transmission probability and current density have the lower values with considering the rough interfaces, in comparison with the planar ones. Moreover, it is found that the generated interfaces by exponential correlation function were rougher than that Gaussian ones.

Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations

This article discusses an alternative method for estimating marginal probability densities of the solution to stochastic differential equations (SDEs). Two algorithms for calculating the numerical–statistical projection estimate for distributions of solutions to SDEs using Legendre polynomials are proposed. The root-mean-square error of this estimate is studied as a function of the projection expansion length, while the step of a numerical method for solving SDE and the sample size for expansion coefficients are fixed. The proposed technique is successfully verified on three one-dimensional SDEs that have stationary solutions with given one-dimensional distributions and exponential correlation functions. A comparative analysis of the proposed method for calculating the numerical–statistical projection estimate and the method for constructing the histogram is carried out.

Exponential vs Gaussian Correlation Functions in the Characterization of Block Copolymer Grain Structure by Depolarized Light Scattering.

Block copolymer (BCP) grain structure affects the mechanical, optical, and electrical properties of BCP materials, making the accurate characterization of this grain structure an important goal. In this study, improved BCP grain parameters were obtained by employing an exponentially decaying correlation function within the ellipsoidal grain model, instead of the Gaussian correlation function that was used in previous work. The exponential correlation function provides a better fit to the experimental depolarized light scattering data, which outweighs the disadvantage that it requires numerical integration to obtain the model scattered intensity.

Optimal grid size for site‐specific nutrient application

AbstractThis article develops a theoretical framework to determine the economically optimal grid size when sampling to guide precision application of inputs. Our theoretical model shows that a finer grid is optimal with increases in output price. A coarser grid is optimal with increased sampling costs and increased spatial correlation. With an exponential variogram, for example, the optimal grid size increases as the range increases. An applied example of lime application for winter wheat is used to demonstrate the framework. Spatial variograms for pH and Buffer pH were estimated using data from nine farmer fields. At the average spatial variability from these fields and using typical Oklahoma wheat yields of 40 bu/ac, grid sampling was economical when prices were above $5.43/bu. The optimal grid sizes were slightly larger than the 2.5‐acre sizes that are typically used by producers. The empirical example verified the theory in that it found that optimal grid size decreased with higher output prices and crop yields and increased with greater spatial correlation. For example, optimal grid size approximately doubled as the range of the exponential correlation function doubled.

Extreme Rainfall Analysis Of The West Papua Province Using Schlather’s Model Of Max Stable Process

Data from Badan Pusat Statistik (BPS) in 2021 notes the province of West Papua as the province with the 5th highest rainfall in Indonesia with a rainfall of 3,811 mm. The province also recorded 268 rainy days, the most amongst all provinces in the country. The excess amount of rain is one of the causes of disasters such as floods. This research uses rainfall data from the Regencies of Manokwari, Fakfak, and Kaimana. The method used is Spatial Extreme Value particularly Schlather's Model of the Max Stable Process. The data used is hourly rainfall for the period of 13 March 2022 to 17 October 2022 with the proportion of training and testing data respectively 85.84% and 14.16%. Extreme data collection was carried out using the Block Maxima method with a fitting to the Generalized Extreme Value (GEV) distribution before being transformed into the Frechet Z margin units. The calculation of the extreme coefficient resulted in a value between 1.4 to 1.85, indicating a relationship between the locations. Next, the best trend surface model was determined, which involves latitude coordinates for the calculation of the location parameter and both longitude and latitude coordinates for the calculation of the scale parameter. The spatial parameter estimation is carried using the powered exponential correlation function. Then, model validation was carried out using MAPE based on a comparison of return levels and testing data. The MAPE values obtained was 22.61% for the BFGS iteration method. The final step is to calculate return levels for periods of 2, 4, 6, 8, and 10 years ahead. All the results were categorized under very heavy rain. These results can be used by related parties to carry out disaster mitigation efforts.

Monte Carlo estimates of extremes of stationary/nonstationary Gaussian processes

Abstract Finite-dimensional (FD) models X d ⁢ ( t ) X_{d}(t) , i.e., deterministic functions of time and finite sets of 𝑑 random variables, are constructed for stationary and nonstationary Gaussian processes X ⁢ ( t ) X(t) with continuous samples defined on a bounded time interval [ 0 , τ ] [0,\tau] . The basis functions of these FD models are finite sets of eigenfunctions of the correlation functions of X ⁢ ( t ) X(t) and of trigonometric functions. Numerical illustrations are presented for a stationary Gaussian process X ⁢ ( t ) X(t) with exponential correlation function and a nonstationary version of this process obtained by time distortion. It was found that the FD models are consistent with the theoretical results in the sense that their samples approach the target samples as the stochastic dimension is increased.

Electromagnetic Scattering and Doppler Spectrum Simulation of Land–Sea Junction Composite Rough Surface

In this paper, a weighted arctangent function is used in conjunction with the spectral method to generate a land–sea junction composite rough surface under the spatially homogeneous and time-stationary hypotheses. The exponential correlation function and the Joint North Sea Wave Project (JONSWAP) spectrum, combined with an experiment-verified shoaling coefficient, are applied to model the land surfaces and the time-varying sea surfaces separately. The second-order small slope approximation (SSA-II) with tapered wave incidence is utilized for evaluating the electromagnetic scattering characteristics and Doppler characteristics of the generated composite rough surface. The influence of land–sea interface factors on radar cross-section (RCS) and Doppler shift of radar echoes is investigated in detail by comparing the RCS and Doppler spectra of the land–sea junction composite rough surfaces with those of finite-depth sea surfaces. It can be found that the Doppler spectra of the land–sea junction composite rough surface is narrower than that of the finite-depth sea surface under upwind directions and wider than that of the finite-depth sea surface under crosswind directions.

Super-resolution time delay estimation using exponential kernel correlation in impulsive noise and multipath environments

The time delay estimation (TDE) is an important and fundamental part in wireless communication signal processing, which has been widely used in localization, intelligent navigation, and radio monitoring. However, it remains a challenging task to support such TDE mechanisms with super-resolution in impulsive noise and multipath environments. Aiming at improving the TDE performance in both impulsive noise and multipath environments, in this paper, a novel super-resolution TDE method is proposed by using the defined exponential kernel correlation (EKC) function. In the proposed TDE method, EKC function is defined to suppress the non-Gaussian impulsive noise. Specifically, the theoretical analysis is also given to prove its boundedness and its effectiveness in non-Gaussian impulsive noise suppression. Further, a novel super-resolution TDE method is proposed by combining EKC function and multiple signal classification (MUSIC) method, which can significantly improve the estimation performance in terms of resolution and accuracy with both non-Gaussian impulsive noise and multipath environments. Finally, simulation experiments demonstrate that the proposed super-resolution TDE method maintains good performance even with a low characteristic exponent and low generalized signal-to-noise ratio (GSNR).

A 3D random porous media model for cement mortar based on X-ray computed tomography

Cement-based materials are typical porous media in which the spatial pores are of vital importance to flow problems, such as chloride ion penetration. This study proposes a three-dimensional (3D) random porous media model to characterize the spatial distribution associated with the porosity in cement mortar. The proposed model addresses the random heterogeneity in material properties using a Weibull random field and an exponential correlation function. The spatial distribution data associated with the porosity of the cement mortar, including the marginal distribution of the porosity and correlation structure of the Weibull random field, are obtained via X-ray computed tomography (XCT). The results indicate that the isotropic exponential correlation function is adequate for characterizing the correlation structure of the Weibull field with a maximum correlation length of 5.7515 mm. Moreover, a comparison of the simulated and measured porosity fields suggests that the proposed model can capture the characteristics of the porosity distribution in cement mortar. Considering the correlation in the porosity leads to a larger variance in the mean porosity of the mortar in the Monte Carlo simulation (MCS). In the example, the chloride diffusion in the cement mortar is illustrated using the proposed 3D random porous media model coupled with finite element (FE) analysis. The effect of the spatial correlation of the porosity on chloride diffusion in cement mortar was discussed from a probabilistic perspective. The proposed model provides insights into considering the properties of heterogeneous materials.

Growth of Turbulent Boundary Layer with Varying Inlet ‎Length Scales‎

This study aims to generate a fully developed turbulent boundary layer in the channel domain using ‎LES (Large Eddy Simulation), suitable inflow conditions along with statistically reliable turbulent ‎characteristics are required. This study clarifies the effect of the integral length scale from the ‎existing data on the generation of turbulent boundary layers. In order to justify the work, an ‎artificially created boundary layer is imposed on the inlet section, which gradually evolves into a ‎fully developed turbulent boundary layer flow inside the numerical domain. In this study, the ‎synthetic inflow method, which is based on an exponential correlation function, is used by ‎imposing the spatial and temporal correlation between two different points on the inlet section. In ‎addition, we conducted parametric length scale studies on the inlet section and compare our results ‎with existing data. The results indicated that the cases of larger length scale in the span-wise ‎direction were not only effective in achieving the target shape of a fully developed turbulent ‎boundary layer, but also developed it faster than the smaller-length scales.‎

COMPARISON OF EXPONENTIAL COVARIANCE FUNCTIONS FOR BIVARIATE GEOSTATISTICAL DATA

In the analysis of multivariate spatial random elds, it is essential to dene a covariance structure that adequately models the relationship between the variables under study. We propose a covariance structure with exponential correlation function for bivariate random elds, the SEC model. We compare the SEC model fits with the bivariate separable exponential model and the bivariate exponential model with constraints, which are particular cases of the full bivariate Matern model, presented in the literature. A simulation study assess characteristics of the proposed model. The model is tted to a weather data set from Brazil, bearing in mind the importance of analyzing climate data to predict adverse environmental conditions. Predictive measures are used to compare the models under study. The satisfactory results compared to the models considered and the simpler structure makes the SEC model an alternative for the analysis of bivariate spatial elds.

Entanglement Dynamics of Random GUE Hamiltonians

In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential n-point correlation functions in the gas of GUE eigenvalues.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

Implementation of a synthetic inflow turbulence generator in idealised WRF v3.6.1 large eddy simulations under neutral atmospheric conditions

Abstract. A synthetic inflow turbulence generator was implemented in the idealised Weather Research and Forecasting large eddy simulation (WRF-LES v3.6.1) model under neutral atmospheric conditions. This method is based on an exponential correlation function and generates a series of two-dimensional slices of data which are correlated both in space and in time. These data satisfy a spectrum with a near “-5/3” inertial subrange, suggesting its excellent capability for high Reynolds number atmospheric flows. It is more computationally efficient than other synthetic turbulence generation approaches, such as three-dimensional digital filter methods. A WRF-LES simulation with periodic boundary conditions was conducted to provide prior mean profiles of first and second moments of turbulence for the synthetic turbulence generation method, and the results of the periodic case were also used to evaluate the inflow case. The inflow case generated similar turbulence structures to those of the periodic case after a short adjustment distance. The inflow case yielded a mean velocity profile and second-moment profiles that agreed well with those generated using periodic boundary conditions, after a short adjustment distance. For the range of the integral length scales of the inflow turbulence (±40 %), its effect on the mean velocity profiles is negligible, whereas its influence on the second-moment profiles is more visible, in particular for the smallest integral length scales, e.g. those with the friction velocity of less than 4 % error of the reference data at x/H=7. This implementation enables a WRF-LES simulation of a horizontally inhomogeneous case with non-repeated surface land-use patterns and can be extended so as to conduct a multi-scale seamless nesting simulation from a meso-scale domain with a kilometre-scale resolution down to LES domains with metre-scale resolutions.

Analysis of discriminatory characteristics of a video sensor with an exponential correlation function

This article presents an analysis of the characteristics of the video sensors functioning both in the visible and “thermal” regions of the spectrum. The influence of errors caused by the non-linearity of the discriminatory characteristic (DC) in the idealized model is studied. The article is devoted to the refinement of the model, taking into account the constant exponent parameter and introducing its value into the algorithm implemented by the onboard video sensor.

Fully Coherent Electromagnetic Scattering Computation for Snowpacks Based on Statistical S-Matrix Approach

Electromagnetic scattering model from 3-D snowpack with arbitrary thickness is considered. A fully coherent model is presented through the usage of the Statistical S-Matrix Wave Propagation in Spectral Domain approach (SSWaP-SD). The computer-generated snow media is constructed using 3-D spatial exponential correlation function along with Lineal-Path function to preserve the connectivity of the snow particles as well. The SSWaP-SD in conjunction with a Method of Moments (MoM) code based on the discrete-dipole approximation (DDA) is chosen to leverage both the time-efficient computations of the DDA and the full-coherency of the SSWaP-SD method simultaneously. The SSWaP-SD depends on the discretization of the medium into thin slabs. Several realizations of a thin snow slab are solved numerically to form the statistics of the scattering matrix representing such a thin snow layer. For an arbitrarily thick snow layer, thin slabs of a snowpack are analyzed and a corresponding polarimetric N-port (representing different directions of scattering) S-matrix is generated. These S-matrices are cascaded using SSWaP-SD method to calculate the total forward and backward bistatic scattered fields in a fully coherent way. The simulation results of the backscattering from an arbitrary thick snow layer are presented and validated with measurements.

Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos.

Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem.

Households Health Status in Saudi Arabia: Spatial Distribution and Association With Socioeconomic Factors

This paper examines the spatial relationship between Saudi and non-Saudi people's health status and the socioeconomic composition of the neighbourhoods in which they live. Data were recorded from the National Population Health Survey (NPHS) performed by the Saudi General Authority for Statistics (GAS) in 2018. The survey counts 23,980,846 inhabitants grouped into 24,012 households who assessed their health status by gender and administrative region. Only people who are fifteen years of age and over and claiming poor health status were retained in the analysis. We used a Generalized Linear Spatial Model (GLSM) to study the relationship between Saudi and non-Saudi household’s health status and socioeconomic factors. A Gaussian process with a powered exponential spatial correlation function was introduced on the right-hand side of the model to consider the unexplained spatial variation in the data. The statistical results show the progressive increase in the number of Saudi and non-Saudi households claiming poor health status with the high Saudi unemployment rate, low average monthly income and high current daily smokers. The results of the statistical analyses show the wider potential of GLSM for analyzing data of this kind and the important risk of misleading interpretations when the non-spatial analysis is used on spatially structured data. The method of inference was Bayesian using Markov Chain Monte Carlo Implementation.

The Method of Unambiguous Determination of the Design Electrical Load According to the Heating Condition

A problem of checking conductors for heating condition in power supply systems in case of random electrical load is considered. A probabilistic model of current is used. The current is considered as a random process with a normal distribution law. It is shown that the existing practice of determining the design load from a ten-minute heating time constant does not provide a reliable solution. It is proposed to use the curve of the effective inertial current versus the heating time constant. Methods to obtain this dependence with a random electrical load are identified. The exact solution is found at the intersection of this curve with the curve of the long-term permissible conductor load versus the heating time constant. The calculations took into account that the scale of standard cross-sections of conductors is discrete. Errors of existing method are evaluated with example of random electrical load with exponential correlation function. It is shown that the error in determining the design electric load and the error in selecting the cross-section of the conductors are different.