The pair distribution function of a system of bose hard spheres, calculated up to the first order inα/λ

1959 ◽  
Vol 14 (1) ◽  
pp. 233-234 ◽  
Author(s):  
L. Colin ◽  
J. Peretti
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Hard Spheres ◽  
First Order

Pair distribution function for fluid hard spheres

1969 ◽  
Vol 16 (3) ◽  
pp. 217-223 ◽  
Author(s):  
R.O. Watts ◽  
D. Henderson
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Hard Spheres

scholarly journals Semiclassical Theory for Low Density Properties of Polar Hard D-Sphere Fluid Mixtures

2016 ◽  
Vol 5 ◽  
pp. 48-55
Author(s):  
Shyambhu Kumar ◽  
Ranjit Prasad Yadav
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Virial Coefficient ◽  
Hard Spheres ◽  
Semiclassical Limit ◽  
Second Virial Coefficient ◽  
Low Density ◽  
Fluid Mixtures ◽  
Increase With Increase ◽  
Independent Pair

In the present paper, expansions are obtained for density-independent pair distribution function and second virial coefficient for D-dimensional molecular fluid mixtures of dipolar hard D-spheres in the semiclassical limit. Numerical results for the second virial coefficient are also estimated for binary mixture of (i) hard spheres and dipolar hard spheres and (ii) hard discs and dipolar hard discs. It is found that the quantum effects increase with increase of dipole moment μ2 as well as the concentration x2. The purpose of the present work is to develop a theory for calculating the low density properties of the polar hard D-sphere fluid mixture in the semiclassical limit. We have also developed the theory for estimating the quantum corrections to the density independent pair distribution function (PDF) and second virial coefficient of the polar D-sphere fluid mixtures.Academic Voices Vol.5 2015: 48-55

Structure Properties in a Bidisperse Ferrofluid in the Absence of an External Magnetic Field

2015 ◽  
Vol 233-234 ◽  
pp. 323-326
Author(s):  
Yuliya E. Nekhoroshkova ◽  
Ekaterina A. Elfimova
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
External Magnetic Field ◽  
External Field ◽  
Pair Distribution Function ◽  
Interaction Strength ◽  
Dipole Interaction ◽  
First Order ◽  
Analytical Expressions ◽  
Structure Properties

The structure properties of a ferrofluid modeled by a bidisperse system of dipolar hardspheres are studied theoretically for the case of zero external field. Analytical expressions are providedfor the pair distribution function (PDF) and structure factor (SF) to within the first order in numberdensity and the second order in dipole-dipole interaction strength. The influence of the granulometriccomposition on the behavior of the PDF and the position of the first peak of the SF is analyzed.

Real-Space X-Ray Pair Distribution Function Analysis and Molecular-Dynamics Modelling of Diflunisal Channel Hydrates

2020 ◽  
Author(s):  
Anuradha Pallipurath ◽  
Francesco Civati ◽  
Jonathan Skelton ◽  
Dean Keeble ◽  
Clare Crowley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Structural Dynamics ◽  
First Principles ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Real Space ◽  
X Ray ◽  
Dynamics Modelling ◽  
Dynamics Simulations

X-ray pair distribution function analysis is used with first-principles molecular dynamics simulations to study the co-operative H<sub>2</sub>O binding, structural dynamics and host-guest interactions in the channel hydrate of diflunisal.

Engineering Porosity Through Defects in a Giant Pore Metal–Organic Framework

2020 ◽  
Author(s):  
Adam Sapnik ◽  
Duncan Johnstone ◽  
Sean M. Collins ◽  
Giorgio Divitini ◽  
Alice Bumstead ◽  
...  
Keyword(s):  
Distribution Function ◽  
Ball Milling ◽  
Local Structure ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Metal Organic Framework ◽  
Metal Organic Frameworks ◽  
Defect Engineering ◽  
Metal Organic ◽  
Unsaturated Metal Sites

<p>Defect engineering is a powerful tool that can be used to tailor the properties of metal–organic frameworks (MOFs). Here, we incorporate defects through ball milling to systematically vary the porosity of the giant pore MOF, MIL-100 (Fe). We show that milling leads to the breaking of metal–linker bonds, generating more coordinatively unsaturated metal sites, and ultimately causes amorphisation. Pair distribution function analysis shows the hierarchical local structure is partially</p><p>retained, even in the amorphised material. We find that the solvent toluene stabilises the MIL-100 (Fe) framework against collapse and leads to a substantial rentention of porosity over the non-stabilised material.</p>

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

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