Eigenanalysis for a confocal prolate spheroidal resonator using the null-field BIEM in conjunction with degenerate kernels

2014 ◽  
Vol 226 (2) ◽  
pp. 475-490 ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Jia-Wei Lee ◽  
Yi-Chuan Kao ◽  
Shyue-Yuh Leu
Keyword(s):  
Prolate Spheroidal ◽  
Null Field

Green’s Function Problem of Laplace Equation with Spherical and Prolate Spheroidal Boundaries by Using the Null-Field Boundary Integral Equation

2016 ◽  
Vol 13 (05) ◽  
pp. 1650020 ◽  
Author(s):  
Yu-Lung Chang ◽  
Ying-Te Lee ◽  
Li-Jie Jiang ◽  
Jeng-Tzong Chen
Keyword(s):  
Integral Equation ◽  
Laplace Equation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Adaptive Observer ◽  
Degenerate Kernel ◽  
Prolate Spheroidal ◽  
Null Field ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates

A systematic approach of using the null-field integral equation in conjunction with the degenerate kernel and eigenfunction expansion is employed to solve three-dimensional (3D) Green’s functions of Laplace equation. The purpose of using degenerate kernels for interior and exterior expansions is to avoid calculating the principal values. The adaptive observer system is addressed to employ the property of degenerate kernels in the spherical coordinates and in the prolate spheroidal coordinates. After introducing the collocation points on each boundary and matching boundary conditions, a linear algebraic system is obtained without boundary discretization. Unknown coefficients can be easily determined. Finally, several examples are given to demonstrate the validity of the present approach.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

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