Text

On the Stability of Objective Structures

---

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.

---

Availability

No copy data

Detail Information

Series Title

-

Call Number

540 STE s

Publisher

: Logos Verlag., 2021

Collation

163 halaman

Language

English

ISBN/ISSN

9783832553784

Classification

540

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

-

Subject(s)

Chemistry

Specific Detail Info

-

Statement of Responsibility

Martin Steinbach

Other Information

Cataloger

Kurnadi

Source

-

Validator

maya

Digital Object Identifier (DOI)

-

Journal Volume

-

Journal Issue

-

Subtitle

-

Parallel Title

-

Other version/related

File Attachment

Comments

---

You must be logged in to post a comment