Density Functional Approach Based on Numerically Obtained Bridge Functional

The Ornstein-Zernike equation is solved with the Rogers-Young approximation for bull, 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 incorporates 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 flexible for various interaction potential fluid.

Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.

How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid

A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.

Enhancing PIV image and fractal descriptor for velocity and shear stresses propagation around a circular pier

In this study,the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented.In the study reported herein,the fractal dimension of velocity fluctuations（u′,v′,w′） and the Reynolds shear stresses（u′v′ and u′w′） of flow around a bridge pier were computed using a Fractal Interpolation Function（FIF） algorithm.The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter（ADV）and Particle Image Velocimetry（P1V）.The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots.In this study,PIV was used for detection of high resolution fractal scaling around a bridge pier.The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier.It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier.The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier.Furthermore,the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume.Finally,the results from ADV measurement were consistent with the result from PIV,therefore,the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.

The novel generating algorithm and properties of hybrid-P-ary generalized bridge functions

In this paper, we develop novel non-sine functions, named hybrid-P-ary generalized bridge functions, based on the copy and shift methods. The generating algorithm of hybrid-P-ary generalized bridge functions is introduced based on the hybrid-P-ary generalized Walsh function＇s copy algorithm. The main property, product property, is also discussed. This function may be viewed as the generalization of the theory of bridge functions. And a lot of non-sine orthogonal functions are the special subset of these novel functions, The hybrid-P-ary generalized bridge functions can be used to search many unknown non-sine functions by defining different parameters.