Reflection/refraction of a solid layer by Debye's series expansion

Ultrasonics ◽  
1991 ◽  
Vol 29 (4) ◽  
pp. 288-293 ◽  
Author(s):  
M. Deschamps ◽  
Cao Chengwei
Keyword(s):  
Series Expansion ◽  
Solid Layer

Some Notes on Taylors Series Expansion with ODE´S

2015 ◽  
Vol 18 (2) ◽  
pp. 149-156
Author(s):  
Shawki A.M. Abbas ◽  
Keyword(s):  
Series Expansion

scholarly journals Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials

2021 ◽  
pp. 1-26
Author(s):  
ELENA CHERKAEV ◽  
MINWOO KIM ◽  
MIKYOUNG LIM
Keyword(s):  
Composite Materials ◽  
Series Expansion ◽  
Function Theory ◽  
Effective Conductivity ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Geometric Function Theory ◽  
Boundary Integral Formulation ◽  
Geometric Function ◽  
Series Expression

The Neumann–Poincaré (NP) operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. Recently, a series expression of the NP operator was developed in two dimensions based on geometric function theory [34]. In this paper, we investigate geometric properties of composite materials using this series expansion. In particular, we obtain explicit formulas for the polarisation tensor and the effective conductivity for an inclusion or a periodic array of inclusions of arbitrary shape with extremal conductivity, in terms of the associated exterior conformal mapping. Also, we observe by numerical computations that the spectrum of the NP operator has a monotonic behaviour with respect to the shape deformation of the inclusion. Additionally, we derive inequality relations of the coefficients of the Riemann mapping of an arbitrary Lipschitz domain using the properties of the polarisation tensor corresponding to the domain.

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