Determination of correlation function of scattering potential of random medium by Gauss vortex beam

2013 ◽  
Vol 308 ◽  
pp. 164-168 ◽  
Author(s):  
Jia Li
Keyword(s):  
Correlation Function ◽  
Random Medium ◽  
Vortex Beam ◽  
Scattering Potential

The determination of energies and wavefunctions with full electronic correlation

1969 ◽  
Vol 310 (1500) ◽  
pp. 43-61 ◽  
Keyword(s):  
Correlation Function ◽  
Wave Equation ◽  
Variational Problems ◽  
Variation Theory ◽  
Electronic Correlation ◽  
Convergence Properties

It has been widely thought that the use of wavefunctions with full electronic correlation would involve integrals of 3 N dimensions, where N is the number of electrons. Here it is shown that by a method similar to that of variation theory a set of equations which determine the orbitals and correlation function can be derived so that they only involve integrals of up to nine dimensions. Even these nine-dimensional integrals have some special characteristics which make them equivalent to six-dimensional integrals in some methods of integration. The method is formulated for the particular canonical choice of correlation function that has been previously investigated by the authors and is based on a particular trans-correlated kind of wave equation and on some particular convergence properties recently shown for bi-variational problems. This appears to provide a solution to the problem of including all r ij - quantities in wavefunctions: a problem which has been variously discussed for the last thirty years.

scholarly journals A method of generating a random optical field using the Karhunen-Loeve expansion to simulate atmospheric turbulence

2020 ◽  
Vol 44 (1) ◽  
pp. 53-59
Author(s):  
S.N. Khonina ◽  
S.G. Volotovskiy ◽  
M.S. Kirilenko
Keyword(s):  
Numerical Simulation ◽  
Correlation Function ◽  
Atmospheric Turbulence ◽  
Random Environment ◽  
Random Medium ◽  
Optical Field ◽  
Phase Singularity ◽  
Vortex Beams ◽  
Simulation Results ◽  
Random Field Generation

It is proposed to use the random field generation in the numerical simulation of the propagation of radiation through a random medium using method based on the Karhunen–Loeve expansion with various types of correlation operators to describe turbulence simulators. The properties of the calculated simulators of a random medium with a Gaussian correlation function were investigated in modeling the propagation of Laguerre-Gaussian vortex beams. The simulation results showed that an increase in the order of the optical vortex leads, as in the experiment, to lower stability of the phase singularity of the beams to random optical fluctuations. The similarity of the simulation results and the optical experiments indicates the promise of the proposed approach for the synthesis of random environment simulators.

Determination of strength of scattering potential by imaging visibility of intensity correlated field

Optik ◽  
2012 ◽  
Vol 123 (13) ◽  
pp. 1201-1206
Author(s):  
Jia Li ◽  
Yali Qin ◽  
Hongliang Ren ◽  
Shouli Zhou
Keyword(s):  
Scattering Potential

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.

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