Attainability by simply connected domains of optimal bounds for the polarization tensor
The notion of polarization tensor is employed for the derivation of the leading-order boundary perturbations in the steady-state voltage potentials that are due to the presence of conductivity inclusions of small diameter. Recently, Capdeboscq and Vogelius obtained optimal bounds of Hashin-Shtrikman...
| Main Authors: | , , , , , |
|---|---|
| Format: | Journal article |
| Izdano: |
Cambridge University Press
2006
|
| _version_ | 1826300353677623296 |
|---|---|
| author | Ammari, H Capdeboscq, Y Kang, H al., E Kim, E Lim, M |
| author_facet | Ammari, H Capdeboscq, Y Kang, H al., E Kim, E Lim, M |
| author_sort | Ammari, H |
| collection | OXFORD |
| description | The notion of polarization tensor is employed for the derivation of the leading-order boundary perturbations in the steady-state voltage potentials that are due to the presence of conductivity inclusions of small diameter. Recently, Capdeboscq and Vogelius obtained optimal bounds of Hashin-Shtrikman type for the trace of the polarization tensor, showing that every pair satisfying these optimal bounds arises as the eigenvalues of a polarization tensor associated with a coated ellipse. In this paper, we give numerical evidence of the fact that the set of possible polarization tensor eigenvalue pairs can also be obtained using simply connected domains. Our numerical computations are based on a boundary integral method. Copyright 2006 Cambridge University Press. |
| first_indexed | 2024-03-07T05:15:51Z |
| format | Journal article |
| id | oxford-uuid:dd260ad7-df6d-4e02-b689-bb8f94178dbf |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:15:51Z |
| publishDate | 2006 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:dd260ad7-df6d-4e02-b689-bb8f94178dbf2022-03-27T09:23:08ZAttainability by simply connected domains of optimal bounds for the polarization tensorJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dd260ad7-df6d-4e02-b689-bb8f94178dbfSymplectic Elements at OxfordCambridge University Press2006Ammari, HCapdeboscq, YKang, Hal., EKim, ELim, MThe notion of polarization tensor is employed for the derivation of the leading-order boundary perturbations in the steady-state voltage potentials that are due to the presence of conductivity inclusions of small diameter. Recently, Capdeboscq and Vogelius obtained optimal bounds of Hashin-Shtrikman type for the trace of the polarization tensor, showing that every pair satisfying these optimal bounds arises as the eigenvalues of a polarization tensor associated with a coated ellipse. In this paper, we give numerical evidence of the fact that the set of possible polarization tensor eigenvalue pairs can also be obtained using simply connected domains. Our numerical computations are based on a boundary integral method. Copyright 2006 Cambridge University Press. |
| spellingShingle | Ammari, H Capdeboscq, Y Kang, H al., E Kim, E Lim, M Attainability by simply connected domains of optimal bounds for the polarization tensor |
| title | Attainability by simply connected domains of optimal bounds for the polarization tensor |
| title_full | Attainability by simply connected domains of optimal bounds for the polarization tensor |
| title_fullStr | Attainability by simply connected domains of optimal bounds for the polarization tensor |
| title_full_unstemmed | Attainability by simply connected domains of optimal bounds for the polarization tensor |
| title_short | Attainability by simply connected domains of optimal bounds for the polarization tensor |
| title_sort | attainability by simply connected domains of optimal bounds for the polarization tensor |
| work_keys_str_mv | AT ammarih attainabilitybysimplyconnecteddomainsofoptimalboundsforthepolarizationtensor AT capdeboscqy attainabilitybysimplyconnecteddomainsofoptimalboundsforthepolarizationtensor AT kangh attainabilitybysimplyconnecteddomainsofoptimalboundsforthepolarizationtensor AT ale attainabilitybysimplyconnecteddomainsofoptimalboundsforthepolarizationtensor AT kime attainabilitybysimplyconnecteddomainsofoptimalboundsforthepolarizationtensor AT limm attainabilitybysimplyconnecteddomainsofoptimalboundsforthepolarizationtensor |