scholarly journals A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

2016 ◽  
Vol 163 (1) ◽  
pp. 156-174 ◽  
Author(s):  
Yu Qiao ◽  
Xuejiao Liu ◽  
Minxin Chen ◽  
Benzhuo Lu
Keyword(s):  
Hard Sphere ◽  
Measure Theory ◽  
Three Dimensional ◽  
Local Approximation ◽  
Fundamental Measure Theory

scholarly journals A fundamental measure theory for the sticky hard sphere fluid

2011 ◽  
Vol 134 (1) ◽  
pp. 014506 ◽  
Author(s):  
Hendrik Hansen-Goos ◽  
J. S. Wettlaufer
Keyword(s):  
Hard Sphere ◽  
Measure Theory ◽  
Hard Sphere Fluid ◽  
Fundamental Measure Theory

scholarly journals Close to the edge of fundamental measure theory: a density functional for hard-sphere mixtures

2002 ◽  
Vol 14 (46) ◽  
pp. 11965-11980 ◽  
Author(s):  
Jos  A Cuesta ◽  
Yuri Mart nez-Rat n ◽  
Pedro Tarazona
Keyword(s):  
Hard Sphere ◽  
Density Functional ◽  
Measure Theory ◽  
Fundamental Measure Theory

Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
Hendrik Hansen-Goos ◽  
Mostafa Mortazavifar ◽  
Martin Oettel ◽  
Roland Roth
Keyword(s):  
Free Energy ◽  
Hard Sphere ◽  
Measure Theory ◽  
Fundamental Measure Theory

SEGREGATION OF FLUIDIZED BINARY HARD-SPHERE SYSTEMS UNDER GRAVITY

2005 ◽  
Vol 19 (04) ◽  
pp. 763-774
Author(s):  
SOON-CHUL KIM
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Local Density ◽  
Measure Theory ◽  
Density Approximation ◽  
Brazil Nut ◽  
Density Oscillation ◽  
Analytic Expression ◽  
Dynamics Simulations ◽  
Fundamental Measure Theory

We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.

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