Effects of cross-correlated noises on the intensity fluctuation of the single-mode laser system

A single-mode laser model with cross-correlated additive and multiplicative noise terms is considered, and the effects of correlation between noises on the relaxation time and the intensity correlation function are studied. Using the projection operator method and taking into account the effects of the memory kernels of the intensity correlation function, the analytic expressions for the relaxation time and the correlation function are derived. Based on numerical computations, it is found that the self-correlation time and the cross-correlation time have the same effects on the single-mode laser system.     

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

Effects of cross-correlated noises on the intensity fluctuation of the single-mode laser system

A single-mode laser model with cross-correlated additive and multiplicative noise terms is considered, and the effects of correlation between noises on the relaxation time and the intensity correlation function are studied. Using the projection operator method and taking into account the effects of the memory kernels of the intensity correlation function, the analytic expressions for the relaxation time and the correlation function are derived. Based on numerical computations, it is found that the self-correlation time and the cross-correlation time have the same effects on the single-mode laser system.     

Experimental Characterization of Correlation—Functions of Random Surfaces by Speckle Measurement and Complementary Algorithm

A method for the extracting the correlation functions of random surfaces is proposed by using the image speckle intensity.Theoretically,we analyse the integral expression of average intensity of the image speckles,and compare it with the pair of Fourier-Bessel-transform-and-the-inversion of the exponential function of the height-height correlation function of the random surfaces.Then the algorithm is proposed numerically to complement the lacking Bessel function factor in the expression of the average speckle intensity,which changes the intensity data into the pair of the Fourier-Bessel-transforn.Experimentally,we measure the average image speckle intensities versus the radius of the filtering aperture in the 4f system and extract the height-height correlation function by using the proposed algorithm.The results of the practical measurements for three surface samples and the comparison with those by atomic force microscopy validate the feasibility of this method.     

SPATIAL AVERAGING OF STRUCTURE NOISE

The relation between the signal-to-noise ratio enhancement and the correlation function of the structurenoise for varying acoustic parameters has been deduced.Spatial averaging in a simple case has been discussedand expressions for the correlation function and the signal-to-noise ratio enhancement have been obtained.The calculated results are in good agreement with the experimental ones.     

Density Functional Approach Based on Numerically Obtained Bridge Functional

The ornstein-zenike equation is solved with the Rogers-Young approximation for bulk hard sphere fluid and Lennard-Jones fluid for several state points.Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function.It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve.Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J.Chem.Phys,112(2000)8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid.The good agreement of theoretical predictions with the computer simulation data is obtained.The present numerical procedure incroporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more filexible for various interaction potential fluid.     

Bell Operator Method to Classify Local Realistic Theories

We review the historical fact of multipartite Bell inequalities with an arbitrary number of settings. An explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment （two-setting model）, works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a continuous-infinite settings Bell experiment （infinite-setting model）, even though there exist two-setting models for all directions in space. Hence, the two-setting model does not have the property that the infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in an M-setting Bell experiment （M-setting model）, even though there exist two-setting models for the M measurement directions chosen in the given M-setting experiment. Hence, the two-setting model does not have the property that the M-setting model has.     

Source Function Determined from Hanbury—Brown／Twiss Correlations by the Maximum Entropy Principle

We study the reconstruction of the source function in space-time directly from the measured Hanbury-Brown/Twiss (HBT) correlation function using the maximum entropy principle.We find that the problem is ill-defined without at least one additional theoretical constraint as input.Using the requirement of a finite source lifetime for the problem we find a new Gaussian parametrization of the source function directly in terms of the measured HBT radius parameters and its lifetime,where the latter is a free parameter which is not directly measurable by HBT.We discuss the implication of our results for the remaining freed om in building source models consistent with a given set of measured HBT radius parameters.     

Thermodynamic Properties of Hard-Sphere Fluid under Confined Condition Based on Bridge Density Function

Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first-order direct correlation function to a non-uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non-uniform first-order direct correlation function.     

Theory and signal processing of acoustic correlation techniques for current velocity measurement

A theoretical model and signal processing of acoustic correlation measurements to estimate current velocity are discussed. The sonar space-time correlation function of volume reverberations within Fraunhofer zone is derived. The function, which is in exponential forms, is the theoretical model of acoustic correlation measurements. The characteristics of the correlation values around the maximum of the amplitude of the correlation function, where most information about current velocity is contained, are primarily analyzed. Localized Least Mean Squares （LLMS） criterion is put forward for velocity estimation. Sequential Quadratic Programming （SQP） method is adopted as the optimization method. So the systematic signal processing method of acoustic correlation techniques for current velocity measurement is established. A prototype acoustic correlation current profiler （ACCP） underwent several sea trials, the results show that theoretical model approximately coincides with experimental re- sults. Current profiles including the speed and direction from ACCP are compared with those from acoustic Doppler current profiler （ADCP）. The current profiles by both instruments agree reasonably well. Also, the standard deviation of velocity measurement by ACCP is statistically calculated and it is a little larger than predicted value.