Approximate analytical expression for the direct correlation function of hard discs within the Percus-Yevick equation

1995 ◽  
Vol 85 (2) ◽  
pp. 423-428 ◽  
Author(s):  
M.S. Ripoll ◽  
C.F. Tejero
Keyword(s):  
Correlation Function ◽  
Direct Correlation Function ◽  
Approximate Analytical Expression ◽  
Analytical Expression

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

Ornstein–Zernike equation for the direct correlation function with a Yukawa tail

1975 ◽  
Vol 62 (11) ◽  
pp. 4247-4259 ◽  
Author(s):  
Douglas Henderson ◽  
George Stell ◽  
Eduardo Waisman
Keyword(s):  
Correlation Function ◽  
Direct Correlation Function

The Specific Heat of Liquid Metals

1991 ◽  
Vol 46 (5) ◽  
pp. 416-418
Author(s):  
K. N. Khanna ◽  
Abdul Quayoum
Keyword(s):  
Correlation Function ◽  
Specific Heat ◽  
Reference System ◽  
Hard Sphere ◽  
Random Phase Approximation ◽  
Liquid Metals ◽  
Random Phase ◽  
Direct Correlation Function ◽  
Phase Approximation ◽  
Semi Empirical

AbstractThe specific heat of liquid metals is calculated using a fluid of Percus-Yevick plus tail as a reference system together with the Cumming potential in a random-phase approximation. It is shown that the improved semi-empirical hard sphere direct correlation function proposed by Colot et al. leads to a drastic improvement of Cp values over the HS model

scholarly journals Degradation of multiphoton signal and resolution when focusing through a planar interface with index mismatch: Analytical approximation and numerical investigation

2018 ◽  
Vol 11 (04) ◽  
pp. 1850020
Author(s):  
Ping Qiu ◽  
Chen He
Keyword(s):  
Spherical Aberration ◽  
Numerical Aperture ◽  
Analytical Approximation ◽  
Planar Interface ◽  
Excitation Wavelength ◽  
Physical Parameters ◽  
Approximate Analytical Expression ◽  
Excitation Light ◽  
Analytical Expression ◽  
Imaging Depth

Multiphoton microscopy (MPM) is an invaluable tool for visualizing subcellular structures in biomedical and life sciences. High-numerical-aperture (NA) immersion objective lenses are used to deliver excitation light to focus inside the biological tissue. The refractive index of tissue is commonly different from that of the immersion medium, which introduces spherical aberration, leading to signal and resolution degradation as imaging depth increases. However, the explicit dependence of this index mismatch-induced aberration on the involved physical parameters is not clear, especially its dependence on index mismatch. Here, from the vectorial equations for focusing through a planar interface between materials of mismatched refractive indices, we derive an approximate analytical expression for the spherical aberration. The analytical expression explicitly reveals the dependence of spherical aberration on index mismatch, imaging depth and excitation wavelength, from which we can expect the following qualitative behaviors: (1) Multiphoton signal and resolution degradation is less for longer excitation wavelength, (2) a longer wavelength tolerates a higher index mismatch, (3) a longer wavelength tolerates a larger imaging depth and (4) both signal and resolution degradations show the same dependence on imaging depth, regardless of NA or immersion on the condition that the integration angle is the same. Detailed numerical simulation results agree quite well with the above expectations based on the analytical approximation. These theoretical results suggest the use of long excitation wavelength to better suppress index mismatch-induced signal and resolution degradation in deep-tissue MPM.

Solvation force in a hard-sphere fluid

1999 ◽  
Vol 77 (8) ◽  
pp. 585-590 ◽  
Author(s):  
M Moradi ◽  
M Kavosh Tehrani
Keyword(s):  
Correlation Function ◽  
Hard Sphere ◽  
Hard Core ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Direct Correlation Function ◽  
Functional Theory ◽  
Hard Sphere Fluid ◽  
Generalized Mean ◽  
Simulation Results

The solvation force in a hard-sphere fluid is obtained by the denisty functional theory proposed by Rickayzen and Augousti. The direct correlation function (DCF) with the tail introduced by Tang and Lu is used. This DCF (hereafter TL DCF ) is postulated to hold the Yukawa form outside the hard core; and the generalized mean spherical approximation (GMSA) approach has been applied. The results are compared with those obtained by using the Percus-Yevick (PY) DCF. These results are also compared with those of Monte Carlo simulations. At low densities and fairly high densities the results are in agreement. But at high densities there is more oscillation in the solvation force obtained by using TL DCF in comparison with the PY DCF. There are no simulation results at high densities to be compared with these results.PACS No. 61.20

Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection

2010 ◽  
Author(s):  
Sowmitra Singh ◽  
Jin-Keun Choi ◽  
Georges Chahine
Keyword(s):  
Bubble Dynamics ◽  
Bubbly Flow ◽  
Outlet Section ◽  
Inlet Section ◽  
Concept Design ◽  
Two Phase ◽  
Approximate Analytical Expression ◽  
Analytical Expression ◽  
Bubble Number ◽  
Analytical Approaches

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle. Two-phase models for bubbly flow in an expanding-contracting nozzle are developed, in parallel with laboratory experiments, and used to ascertain the geometry configuration for the nozzle that would lead to maximum thrust enhancement upon bubble injection. For preliminary optimization of experimental setup’s design, a quasi 1-D approach is used. Averaged flow quantities (such as velocities, pressures, and void fractions) in a cross-section are used for the analysis. The mixture continuity and momentum equations are numerically solved simultaneously, along with equations for bubble dynamics, bubble motion, and an equation for conservation of bubble number. Various geometric parameters such as the exit and inlet areas, the area of the bubble injection section, the presence of a throat and its location, the length of the diffuser section and the length of the contraction section are varied, and their effects on thrust enhancement are studied. Investigation on the effect of the injected void fraction is also carried out. The key objective function of the optimization is the normalized thrust parameter, which is the difference between the thrust with the bubble injection and the thrust before the bubble injection, normalized by the inlet momentum. An approximate analytical expression for the normalized thrust parameter was also derived starting from the mixture continuity and momentum equations. This analytical expression involved flow variables only at three locations; inlet section, injection section, and outlet section, and the expression is simple enough to produce a quick concept design of the diffuser-nozzle thruster. The numerical and analytical approaches are verified against each other and the limitations of the analytical approach are discussed.

Sign in / Sign up

Export Citation Format

Share Document