Binary correlation function of a random field in a spatially inhomogeneous semiconductor

1984 ◽  
Vol 27 (11) ◽  
pp. 977-980
Author(s):  
V. D. Iskra
Keyword(s):  
Correlation Function ◽  
Random Field ◽  
Spatially Inhomogeneous ◽  
Inhomogeneous Semiconductor ◽  
Binary Correlation ◽  
Binary Correlation Function

BINARY CORRELATION FUNCTION FOR A HOMOGENEOUS PLASMA IN A UNIFORM MAGNETIC FIELD

1965 ◽  
Vol 43 (1) ◽  
pp. 122-130 ◽  
Author(s):  
M. J. Haggerty
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Velocity Distribution ◽  
Spatial Correlation ◽  
Particle Velocity ◽  
Uniform Magnetic Field ◽  
Spatial Correlation Function ◽  
Binary Correlation ◽  
Binary Correlation Function ◽  
The One

Previous work on the application of the theory of Prigogine and Balescu to a homogeneous single-species plasma in a static uniform magnetic field has been extended. An equation for the binary correlation function has been obtained in terms of the one-particle velocity distribution, which is in turn determined by the kinetic equation previously derived. Equations for the binary spatial correlation function and the binary correlation function for the guiding centers have also been obtained. It is demonstrated that the binary spatial correlation function represents the well-known Debye-screened equilibrium correlations when the one-particle velocity distribution is the equilibrium distribution.

scholarly journals CPT-Based Probabilistic Characterization of Undrained Shear Strength of Clay

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Mi Tian ◽  
Xiaotao Sheng
Keyword(s):  
Shear Strength ◽  
Correlation Function ◽  
Random Field ◽  
Site Investigation ◽  
Undrained Shear Strength ◽  
Bayesian Approaches ◽  
Probabilistic Characterization ◽  
Undrained Shear

Applying random field theory involves two important issues: the statistical homogeneity (or stationarity) and determination of random field parameters and correlation function. However, the profiles of soil properties are typically assumed to be statistically homogeneous or stationary without rigorous statistical verification. It is also a challenging task to simultaneously determine random field parameters and the correlation function due to a limited amount of direct test data and various uncertainties (e.g., transformation uncertainties) arising during site investigation. This paper presents Bayesian approaches for probabilistic characterization of undrained shear strength using cone penetration test (CPT) data and prior information. Homogeneous soil units are first identified using CPT data and subsequently assessed for weak stationarity by the modified Bartlett test to reject the null hypothesis of stationarity. Then, Bayesian approaches are developed to determine the random field parameters and simultaneously select the most probable correlation function among a pool of candidate correlation functions within the identified statistically homogeneous layers. The proposed approaches are illustrated using CPT data at a clay site in Shanghai, China. It is shown that Bayesian approaches provide a rational tool for proper determination of random field model for probabilistic characterization of undrained shear strength with consideration of transformation uncertainty.

scholarly journals Gaussian Random Particles with Flexible Hausdorff Dimension

2015 ◽  
Vol 47 (02) ◽  
pp. 307-327
Author(s):  
Linda V. Hansen ◽  
Thordis L. Thorarinsdottir ◽  
Evgeni Ovcharov ◽  
Tilmann Gneiting ◽  
Donald Richards
Keyword(s):  
Correlation Function ◽  
Hausdorff Dimension ◽  
Random Field ◽  
Kernel Smoothing ◽  
Three Dimensional ◽  
Random Sets ◽  
Closed Form Expression ◽  
Spherical Cap ◽  
Fractal Index ◽  
Von Mises

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

STATISTICAL SIMULATION OF RANDOM FIELD ON 2D AREA WITH WHITTLE-MATERN TYPECORRELATION FUNCTION IN THE GEOPHYSICAL PROBLEM OF ENVIRONMENT MONITORING

2019 ◽  
pp. 55-61
Author(s):  
Z. Vyzhva ◽  
V. Demidov ◽  
A. Vyzhva
Keyword(s):  
Correlation Function ◽  
Random Field ◽  
Monitoring System ◽  
Simulated Data ◽  
Simulation Method ◽  
Industrial Area ◽  
Statistical Simulation ◽  
Environment Monitoring ◽  
Geophysical Research ◽  
Monitoring Area

Due to the increasing number of natural and technogenic disasters the development of geological environment monitoring system is actual one using modern mathematical tools and information technology. The local monitoring of potentially dangerous objects is an important part of the overall environment monitoring system. The complex geophysical research was conducted on Rivne NPP area. The monitoring observations radioisotope study of soil density and humidity near the perimeter of buildings is of the greatest interest among these. In this case a problem occurred to supplement simulated data that were received at the control of chalky strata density changes at the research industrial area with use of radioisotope methods on a grid that included 29 wells. This problem was solved in this work by statistical simulation method that provides the ability to display values (the random field of a research object on a plane) in any point of the monitoring area. The chalk strata averaged density at the industrial area was simulated using the built model and the involvement optimal in the mean square sense Whittle-Matern type correlation function. In this paper the method is used and the model and procedure were developed with enough adequate data for Whittle-Matern type correlation function. The model and algorithm were developed and examples of karst-suffusion phenomena statistical simulation were given in the problem of density chalk strata monitoring at the Rivne NPP area. The statistical model of averaged density chalk strata distribution was built in the plane and statistical simulation algorithm was developed using Whittle-Matern type correlation function on the basis of spectral decomposition. The research subject realizations were obtained with required detail and regularity at the observation grid based on the developed software. Statistical analysis of the numerical simulation results was done and tested for its adequacy.

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