On the Stability of Objective Structures / Volume 38 / Martin Steinbach.
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...
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Superior document: | Augsburger Schriften zur Mathematik, Physik und Informatik |
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Place / Publishing House: | [s.l.] : : Logos Verlag Berlin,, 2021. |
Year of Publication: | 2021 |
Language: | English |
Series: | Augsburger Schriften zur Mathematik, Physik und Informatik
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Physical Description: | 1 online resource (174 p.) |
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(CKB)5400000000045055 (ScCtBLL)a7e6ac82-a206-4fd4-a3e4-7c4cdacb3f5c (oapen)https://directory.doabooks.org/handle/20.500.12854/75074 (EXLCZ)995400000000045055 |
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Steinbach, Martin author. On the Stability of Objective Structures Martin Steinbach. Volume 38 Berlin Logos Verlag Berlin 2021 [s.l.] : Logos Verlag Berlin, 2021. 1 online resource (174 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier Augsburger Schriften zur Mathematik, Physik und Informatik Description based on print version record. CC BY-NC-ND 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. English Science / Physics bisacsh Mathematics bisacsh Mathematics Mathematical model Elasticity theory Stability theory Objective structure Discrete subgroup of the Euclidean group 3-8325-5378-9 |
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Steinbach, Martin |
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Steinbach, Martin On the Stability of Objective Structures Augsburger Schriften zur Mathematik, Physik und Informatik |
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Steinbach, Martin |
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Steinbach, Martin |
title |
On the Stability of Objective Structures |
title_full |
On the Stability of Objective Structures Martin Steinbach. Volume 38 |
title_fullStr |
On the Stability of Objective Structures Martin Steinbach. Volume 38 |
title_full_unstemmed |
On the Stability of Objective Structures Martin Steinbach. Volume 38 |
title_auth |
On the Stability of Objective Structures |
title_new |
On the Stability of Objective Structures |
title_sort |
on the stability of objective structures |
series |
Augsburger Schriften zur Mathematik, Physik und Informatik |
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Augsburger Schriften zur Mathematik, Physik und Informatik |
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Logos Verlag Berlin Logos Verlag Berlin, |
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2021 |
physical |
1 online resource (174 p.) |
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3-8325-5378-9 |
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Not Illustrated |
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AT steinbachmartin onthestabilityofobjectivestructuresvolume38 |
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(CKB)5400000000045055 (ScCtBLL)a7e6ac82-a206-4fd4-a3e4-7c4cdacb3f5c (oapen)https://directory.doabooks.org/handle/20.500.12854/75074 (EXLCZ)995400000000045055 |
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Augsburger Schriften zur Mathematik, Physik und Informatik |
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On the Stability of Objective Structures |
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Augsburger Schriften zur Mathematik, Physik und Informatik |
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