The Practical Use of the Model of Penetrable Spheres

2017 ◽  
Vol 122 (13) ◽  
pp. 3217-3218 ◽  
Author(s):  
J. S. Rowlinson
Keyword(s):  
Penetrable Spheres

scholarly journals Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150060 ◽  
Author(s):  
A. Gillman ◽  
G. Amadio ◽  
K. Matouš ◽  
T. L. Jackson
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Three Dimensional ◽  
Adaptive Methods ◽  
Shape Effect ◽  
Third Order ◽  
Recent Letter ◽  
Penetrable Spheres ◽  
First Time

Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014 Phys. Lett. A 378, 3070–3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computing n -point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.

Numerical simulation of acoustic scattering from coaxial sound-penetrable spheres

2019 ◽  
Vol 14 (2) ◽  
pp. 115-124
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Radiation Source ◽  
Numerical Study ◽  
Numerical Technique ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Fixed Number ◽  
Helmholtz Equations ◽  
Spherical Waves ◽  
Penetrable Spheres

This paper presents a generalisation of the mathematical model and numerical study of the acoustic scattering problem from multiple spheres in the case of spheres through which the wave passes and whose centers are located on the same axis (the case of sound-penetrable and coaxial spheres) under the action of spherical waves from a monopoly radiation source arbitrarily located in space. When solving the Helmholtz equations, a numerical technique based on the fast multipole method has been adapted for this task, which allows one to achieve high accuracy of the results obtained with minimal computer time. Comparison of the different approaches to truncation infinite series in the expansion showed the following: the result with a good degree of accuracy by a single calculation gives approach based on the truncation of all the rows with a fixed number in each expansion, and the result with a certain degree of accuracy gives an approach based on comparing two consecutive values of the sum of the series. A numerical parametric analysis of the pressure distribution inside and outside the spheres is carried out for various values of their radii, physical characteristics of the external and internal media, the number of spheres, the distances between the centers of the spheres, the frequency of exposure and the location of the monopole radiation source. It is shown that at certain values of the parameters, the appearance of zones of decrease or increase in pressure behind sound-penetrable spheres is possible. The obtained results will further allow to carry out test calculations to verify the general numerical algorithm for the case of a multitude of spheres arbitrarily located in space.

Fourth-order bounds on the effective bulk and shear moduli of random dispersions of penetrable spheres

1995 ◽  
Vol 450 (1940) ◽  
pp. 651-665 ◽  
Keyword(s):  
Fourth Order ◽  
Correlation Functions ◽  
Structural Parameters ◽  
Numerical Calculations ◽  
Shear Moduli ◽  
Two Component ◽  
Point Correlation ◽  
Order Bounds ◽  
Penetrable Spheres

The structural parameters entering the fourth-order bounds of Milton & Phan-Thien ( Proc . R . Soc . Lond . A 380, 305 (1982)) on the effective bulk and shear moduli of two-component materials are expressed in terms of integrals over three- and four-point correlation functions to facilitate numerical calculations on systems for which the correlation functions are known. These integral expressions are then used to numerically calculate the structural parameters of random dispersions of penetrable spheres.

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