Matches in SemOpenAlex for { <https://semopenalex.org/work/W2995463749> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2995463749 abstract "In this paper, we deal with an obstacle placement problem inside a disk, that can be formulated as an energy minimization problem with respect to the rotations of the obstacle about its center, with respect to the translations of the obstacle within a planar disk and also with respect to the expansion or contraction of the obstacle inside the disk. We also include its sensitivity with respect to the boundary data. We consider an inhomogeneous Dirichlet Boundary Value Problem on $ B setminus P$ as follows: $Delta u =0$ on $ B setminus P$, $u=0$ on $partial P$, $u=M$, a nonzero constant on $partial B$. Here, the planar obstacle $P$ is invariant under the action of a dihedral group $mathbb{D}_n$, $n in mathbb{N}$, $n geq 3$, and $B$ is a planar disk containing $P$. We make the following assumptions on $P$ and $B$: (0) the volume constraint on $P$ and $B$ both, (i) invariance of both $B$ and $P$ under the action of the same dihedral group, (ii) $B$ and $P$ need not be concentric, (iii) smoothness condition on both the boundaries, (iv) a monotonicity condition on the boundary $partial P$ of the obstacle $P$. Examples of such obstacles include regular polygons with smoothened corners, ellipses, among other star-shaped domains. In this setting, we investigate the extremal configurations of the obstacle $P$ with respect to the disk $B$, for the energy functional $E$ associated with the boundary value problem. The Dirichlet energy is the one-constant Oseen-Frank energy of a uniaxial planar nematic liquid crystal. The class of problems considered here sheds some light into optimal locations of holes with a certain symmetry inside a nematic-filled disc, so as to optimise the corresponding one-constant nematic Oseen-Frank energy." @default.
- W2995463749 created "2019-12-26" @default.
- W2995463749 creator A5085103846 @default.
- W2995463749 date "2019-07-23" @default.
- W2995463749 modified "2023-09-27" @default.
- W2995463749 title "Energy Minimization Problem related to certain Liquid Crystal Models with respect to the Position, Orientation and Size of an Obstacle having Dihedral Symmetry" @default.
- W2995463749 cites W1584280986 @default.
- W2995463749 cites W1993267802 @default.
- W2995463749 cites W2020805243 @default.
- W2995463749 cites W2075241401 @default.
- W2995463749 cites W2086845109 @default.
- W2995463749 cites W2196296724 @default.
- W2995463749 cites W2560516766 @default.
- W2995463749 cites W2575794986 @default.
- W2995463749 cites W2587939112 @default.
- W2995463749 cites W2797256054 @default.
- W2995463749 cites W2912932926 @default.
- W2995463749 cites W2963597222 @default.
- W2995463749 cites W2520542244 @default.
- W2995463749 hasPublicationYear "2019" @default.
- W2995463749 type Work @default.
- W2995463749 sameAs 2995463749 @default.
- W2995463749 citedByCount "0" @default.
- W2995463749 crossrefType "posted-content" @default.
- W2995463749 hasAuthorship W2995463749A5085103846 @default.
- W2995463749 hasConcept C112887158 @default.
- W2995463749 hasConcept C114614502 @default.
- W2995463749 hasConcept C121332964 @default.
- W2995463749 hasConcept C132369183 @default.
- W2995463749 hasConcept C134306372 @default.
- W2995463749 hasConcept C17744445 @default.
- W2995463749 hasConcept C190470478 @default.
- W2995463749 hasConcept C199539241 @default.
- W2995463749 hasConcept C2524010 @default.
- W2995463749 hasConcept C2776650193 @default.
- W2995463749 hasConcept C2781311116 @default.
- W2995463749 hasConcept C32909587 @default.
- W2995463749 hasConcept C33923547 @default.
- W2995463749 hasConcept C37914503 @default.
- W2995463749 hasConcept C62354387 @default.
- W2995463749 hasConcept C62520636 @default.
- W2995463749 hasConcept C72409365 @default.
- W2995463749 hasConcept C89025888 @default.
- W2995463749 hasConceptScore W2995463749C112887158 @default.
- W2995463749 hasConceptScore W2995463749C114614502 @default.
- W2995463749 hasConceptScore W2995463749C121332964 @default.
- W2995463749 hasConceptScore W2995463749C132369183 @default.
- W2995463749 hasConceptScore W2995463749C134306372 @default.
- W2995463749 hasConceptScore W2995463749C17744445 @default.
- W2995463749 hasConceptScore W2995463749C190470478 @default.
- W2995463749 hasConceptScore W2995463749C199539241 @default.
- W2995463749 hasConceptScore W2995463749C2524010 @default.
- W2995463749 hasConceptScore W2995463749C2776650193 @default.
- W2995463749 hasConceptScore W2995463749C2781311116 @default.
- W2995463749 hasConceptScore W2995463749C32909587 @default.
- W2995463749 hasConceptScore W2995463749C33923547 @default.
- W2995463749 hasConceptScore W2995463749C37914503 @default.
- W2995463749 hasConceptScore W2995463749C62354387 @default.
- W2995463749 hasConceptScore W2995463749C62520636 @default.
- W2995463749 hasConceptScore W2995463749C72409365 @default.
- W2995463749 hasConceptScore W2995463749C89025888 @default.
- W2995463749 hasLocation W29954637491 @default.
- W2995463749 hasOpenAccess W2995463749 @default.
- W2995463749 hasPrimaryLocation W29954637491 @default.
- W2995463749 hasRelatedWork W1530894991 @default.
- W2995463749 hasRelatedWork W1683983360 @default.
- W2995463749 hasRelatedWork W1841041024 @default.
- W2995463749 hasRelatedWork W1925985711 @default.
- W2995463749 hasRelatedWork W1993206373 @default.
- W2995463749 hasRelatedWork W2031897399 @default.
- W2995463749 hasRelatedWork W2035312650 @default.
- W2995463749 hasRelatedWork W2041215528 @default.
- W2995463749 hasRelatedWork W2056211552 @default.
- W2995463749 hasRelatedWork W2139565931 @default.
- W2995463749 hasRelatedWork W2168899702 @default.
- W2995463749 hasRelatedWork W2269737316 @default.
- W2995463749 hasRelatedWork W2284557637 @default.
- W2995463749 hasRelatedWork W251048310 @default.
- W2995463749 hasRelatedWork W2785773315 @default.
- W2995463749 hasRelatedWork W2912978056 @default.
- W2995463749 hasRelatedWork W2953120335 @default.
- W2995463749 hasRelatedWork W2962911796 @default.
- W2995463749 hasRelatedWork W3213645259 @default.
- W2995463749 hasRelatedWork W968612080 @default.
- W2995463749 isParatext "false" @default.
- W2995463749 isRetracted "false" @default.
- W2995463749 magId "2995463749" @default.
- W2995463749 workType "article" @default.