Proof of a conjecture on the conductivity of checkerboards

DOI10.1063/1.1385564zbMath1063.82018OpenAlexW1972378083WikidataQ122957288 ScholiaQ122957288MaRDI QIDQ2774693

Graeme Walter Milton

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1385564

Mathematics Subject Classification ID

Equilibrium statistical mechanics (82B99)

Related Items (11)

Rapid computation of effective conductivity of 2D composites by equivalent circuit and spectral methods ⋮ Expansion formulae for the homogenized determinant of anisotropic checkerboards ⋮ Generalized chessboard structures whose effective conductivities are integer valued ⋮ The effective conductivity of random checkerboards ⋮ Two-component composites whose effective conductivities are power means of the local conductivities ⋮ Transformation media with variable optical axes ⋮ Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum ⋮ Bloch dispersion and high frequency homogenization for separable doubly-periodic structures ⋮ Homogenization of 3D finite photonic crystals with heterogeneous permittivity and permeability ⋮ Conductivity of a medium containing a dense array of perfectly conducting square cylinders ⋮ Homogenization of transport properties of composites based on stochastic dynamics

Cites Work

• G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates
• Bounds on the elastic and transport properties of two-component composites
• Asymptotics of the homogenized moduli for the elastic chess-board composite
• A high-order accurate algorithm for electrostatics of overlapping disks
• Duality relations, correspondences and numerical results for planar elastic composites
• Thin bridges in isotropic electrostatics
• Four-Phase Checkerboard Composites
• Exact solution of a boundary-value problem for a rectangular checkerboard field
• Effective conductivity of periodic composites composed of two very unequal conductors
• Conduction in a two-phase plane with diamond-shaped tiling
• Invariant properties of the stress in plane elasticity and equivalence classes of composites
• The Effective Conductivity of a Composite Material with a Periodic Rectangular Geometry
• Periodic Heterogeneous Structures: New Explicit Solutions and Effective Characteristics of Refraction of an Imposed Field
• A New Reiterated Structure with Optimal Macroscopic Behavior
• Third-order bounds on the conductivity of a random stacking of cubes
• A Theorem on the Conductivity of a Composite Medium

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