02540nam 22004573a 450 991055763590332120230124202330.0https://doi.org/10.30819/5378(CKB)5400000000045055(ScCtBLL)a7e6ac82-a206-4fd4-a3e4-7c4cdacb3f5c(oapen)https://directory.doabooks.org/handle/20.500.12854/75074(oapen)doab77421(EXLCZ)99540000000004505520220504i20212022 uu enguru||||||||||txtrdacontentcrdamediacrrdacarrierOn the Stability of Objective StructuresMartin SteinbachVolume 38BerlinLogos Verlag Berlin2021[s.l.] :Logos Verlag Berlin,2021.1 online resource (174 p.)Augsburger Schriften zur Mathematik, Physik und Informatik9783832553784 3832553789 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.Augsburger Schriften zur Mathematik, Physik und InformatikScience / PhysicsbisacshMathematicsbisacshMathematicsScience / PhysicsMathematicsMathematics.Steinbach Martin1229891ScCtBLLScCtBLLBOOK9910557635903321On the Stability of Objective Structures2854906UNINA