scholarly journals Basicsums: A Python package for computing structural sums and the effective conductivity of random composites

2019 ◽  
Vol 4 (39) ◽  
pp. 1327 ◽  
Author(s):  
Wojciech Nawalaniec
Keyword(s):  
Effective Conductivity ◽  
Random Composites ◽  
Python Package

scholarly journals Classifying and analysis of random composites using structural sums feature vector

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180698 ◽  
Author(s):  
Wojciech Nawalaniec
Keyword(s):  
Materials Science ◽  
Feature Vector ◽  
Effective Conductivity ◽  
Feature Space ◽  
Two Dimensional ◽  
Learning Tools ◽  
Classification Problems ◽  
Random Composites ◽  
Random Structures ◽  
Computational Materials

The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of two-dimensional random composites simulated by distributions of non-overlapping discs on the plane. Construction of the feature vector enables the immediate application of machine learning tools and data analysis techniques to random structures. In order to present the accuracy and the potential of structural sums as geometry descriptors, we apply them to classification problems comprising composites with circular inclusions as well as composites with shapes formed by discs. As an application, we perform the analysis of different models of composites in order to formulate the irregularity measure of random structures. We also visualize the relationship between the effective conductivity of two-dimensional composites and the geometry of inclusions.

The effective conductivity of strongly heterogeneous composites

1991 ◽  
Vol 433 (1888) ◽  
pp. 353-381 ◽  
Keyword(s):  
Real Axis ◽  
Complex Variable ◽  
Effective Conductivity ◽  
Numerical Calculations ◽  
Variable Method ◽  
High Contrast ◽  
Negative Real Axis ◽  
Two Phase ◽  
Periodic Arrays ◽  
Random Composites

We deal with the effective conductivity m = m(z) of two phase, ordered or disordered mixtures consisting of particles of material of conductivity z inserted in a matrix of conductivity 1. We focus on finding bounds on the set of values of z for which the function m is singular or vanishes, and we apply our results to the estimation of the effective conductivity of high contrast mixtures ( z = 0 or z = ∞). We find that the zeroes and singularities of the function m lie on an interval of the negative real axis, which depends on the shape of the particles and the interparticle distances. Our results agree with previous numerical calculations for periodic arrays of spheres. In some cases we show that our estimates are optimal. We apply our results about the zeroes and singularities together with the complex variable method, and find bounds on the effective conductivity of matrix-particle random composites. These bounds give good estimations even in cases of high contrast, and, in many cases, they improve substantially over the bounds obtained by other methods, for the same types of high contrast mixtures.

scholarly journals Effective Conductivity of Densely Packed Disks and Energy of Graphs

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2161
Author(s):  
Wojciech Nawalaniec ◽  
Katarzyna Necka ◽  
Vladimir Mityushev
Keyword(s):  
Effective Conductivity ◽  
Periodic Structures ◽  
Voronoi Tessellation ◽  
Two Dimensional ◽  
Random Composites ◽  
Geometrical Information

The theory of structural approximations is extended to two-dimensional double periodic structures and applied to determination of the effective conductivity of densely packed disks. Statistical simulations of non-overlapping disks with the different degrees of clusterization are considered. The obtained results shows that the distribution of inclusions in a composite, as an amount of geometrical information, remains in the discrete corresponding Voronoi tessellation, hence, precisely determines the effective conductivity for random composites.

Evaluation of Effective Conductivity of Copper-Clad Dielectric Laminate Substrates in Millimeter-Wave Bands Using Whispering Gallery Mode Resonators

2009 ◽  
Vol E92-C (12) ◽  
pp. 1504-1511 ◽  
Author(s):  
Thi Huong TRAN ◽  
Yuanfeng SHE ◽  
Jiro HIROKAWA ◽  
Kimio SAKURAI ◽  
Yoshinori KOGAMI ◽  
...  
Keyword(s):  
Millimeter Wave ◽  
Effective Conductivity ◽  
Whispering Gallery Mode ◽  
Whispering Gallery

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.

scholarly journals GriSPy: A Python package for fixed-radius nearest neighbors search

2020 ◽  
pp. 100443
Author(s):  
M. Chalela ◽  
E. Sillero ◽  
L. Pereyra ◽  
M.A. Garcia ◽  
J.B. Cabral ◽  
...  
Keyword(s):  
Nearest Neighbors ◽  
Fixed Radius ◽  
Python Package
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