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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 o...

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Autor principal: Martin Steinbach
Formato: Libro
Publicado: Logos Verlag Berlin 2021
Acceso en línea:Ver este registro en EBSCOhost
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        au: Martin Steinbach
      sertl: Augsburger Schriften Zur Mathematik, Physik Und Informatik
      isbn: 9783832553784
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        atl: On the Stability of Objective Structures
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        au: Martin Steinbach
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          MATHEMATICS / General
          SCIENCE / Physics / General
          Mathematics
      ab: 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.
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