On the Stability of Objective Structures (Volume 38)
The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative o...
Shranjeno v:
| Glavni avtor: | |
|---|---|
| Format: | Online |
| Jezik: | angleščina |
| Izdano: |
Logos Verlag Berlin
2022
|
| Teme: | |
| Online dostop: | OCN: 1296693065 |
| Oznake: |
Brez oznak, prvi označite!
|
| _version_ | 1869527865652936704 |
|---|---|
| author | Steinbach, Martin |
| author_browse | Steinbach, Martin |
| author_facet | Steinbach, Martin |
| author_sort | Steinbach, Martin |
| collection | Directory of Open Access Books |
| description | The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second derivative of the configurational energy with respect to an appropriate semi-norm. Atomistic stability of a lattice is well understood, see, e.,g., [40]. The aim of this thesis is to generalize the theory to objective structures. In particular, we first investigate discrete subgroups of the Euclidean group, then define an appropriate seminorm and the atomistic stability for a given objective structure, and finally provide an efficient algorithm to check its atomistic stability. The algorithm particularly checks the validity of the Cauchy-Born rule for objective structures. To illustrate our results, we prove numerically the stability of a carbon nanotube by applying the algorithm. |
| format | Online |
| id | doab-20.500.12854ir-77421 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-774212025-07-30T09:58:24Z On the Stability of Objective Structures (Volume 38) Steinbach, Martin Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second derivative of the configurational energy with respect to an appropriate semi-norm. Atomistic stability of a lattice is well understood, see, e.,g., [40]. The aim of this thesis is to generalize the theory to objective structures. In particular, we first investigate discrete subgroups of the Euclidean group, then define an appropriate seminorm and the atomistic stability for a given objective structure, and finally provide an efficient algorithm to check its atomistic stability. The algorithm particularly checks the validity of the Cauchy-Born rule for objective structures. To illustrate our results, we prove numerically the stability of a carbon nanotube by applying the algorithm. 2022-01-21T04:01:34Z 2022-01-21T04:01:34Z 2022-01-20T05:31:19Z 2021 book OCN: 1296693065 https://library.oapen.org/handle/20.500.12657/52506 9783832553784 9783832553784 https://directory.doabooks.org/handle/20.500.12854/77421 eng open access image/jpeg image/jpeg image/jpeg image/jpeg image/jpeg n/a n/a n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/52506/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52506/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52506/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52506/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/52506/1/external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/5378 https://doi.org/10.30819/5378 04b263a1-7fba-4491-9eae-1c394ac42fc3 9783832553784 9783832553784 Knowledge Unlatched (KU) KU Open Services Logos Verlag Berlin open access |
| spellingShingle | Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics Steinbach, Martin On the Stability of Objective Structures (Volume 38) |
| title | On the Stability of Objective Structures (Volume 38) |
| title_full | On the Stability of Objective Structures (Volume 38) |
| title_fullStr | On the Stability of Objective Structures (Volume 38) |
| title_full_unstemmed | On the Stability of Objective Structures (Volume 38) |
| title_short | On the Stability of Objective Structures (Volume 38) |
| title_sort | on the stability of objective structures volume 38 |
| topic | Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics |
| topic_facet | Mathematics Science Physics thema EDItEUR::P Mathematics and Science::PB Mathematics thema EDItEUR::P Mathematics and Science::PH Physics |
| url | OCN: 1296693065 |
| work_keys_str_mv | AT steinbachmartin onthestabilityofobjectivestructuresvolume38 |