English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

For certain shapes of inclusions embedded in a body, the field inside theinclusion is uniform for some boundary condition. We provide a constructionscheme for inclusions of general shapes having such a uniformity property intwo dimensions based on the conformal mapping technique for the potentialproblem. Using this complex analysis method, we also design non-ellipticalneutral coated inclusions with anisotropic conductivity. Neutral coatedinclusions do not perturb a background uniform field when they are insertedinto a homogeneous matrix. Although coated inclusions of various shapes areneutral to a single field, only concentric ellipses or confocal ellipsoids canbe neutral to all uniform fields. This paper presents our work relating to theconstruction of non-elliptical coated inclusions with anisotropic conductivityin two dimensions that are neutral to all uniform fields, where the assignmentof the flux condition on the boundary of the core depends on the appliedbackground field. Using these neutral inclusions, we obtain cylindrical neutralinclusions in three dimensions, with no flux applied to the boundary of thecore and with the anisotropic conductivity function of the shell given inaccordance with the background uniform field.

Inclusions of general shapes having constant field inside the core and non-elliptical neutral coated inclusions with anisotropic conductivity